Mercurial > hg > octave-lyh
annotate scripts/general/interp2.m @ 10780:6e7590d003dc
Fix bugs in interp2 (bug #29601)
| author | Thorsten Meyer <thorsten.meyier@gmx.de> |
|---|---|
| date | Fri, 09 Jul 2010 19:56:21 +0200 |
| parents | d1978e7364ad |
| children | 3140cb7a05a1 |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 2000, 2006, 2007, 2008 Kai Habel |
| 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} |
| 5837 | 31 ## format. |
| 32 ## | |
| 33 ## @table @code | |
| 34 ## @item interp2 (@var{x}, @var{y}, @var{Z}, @var{xi}, @var{yi}, @dots{}) | |
| 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}) |
| 5837 | 43 ## Assumes @code{@var{x} = 1:rows (@var{z})} and @code{@var{y} = |
| 44 ## 1:columns (@var{z})} | |
| 45 ## | |
| 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. |
| 5837 | 57 ## @item 'linear' |
| 6218 | 58 ## Linear interpolation from nearest neighbors. |
| 5837 | 59 ## @item 'pchip' |
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60 ## Piece-wise cubic hermite interpolating polynomial. |
| 5837 | 61 ## @item 'cubic' |
| 6218 | 62 ## Cubic interpolation from four nearest neighbors. |
| 5837 | 63 ## @item 'spline' |
| 64 ## Cubic spline interpolation--smooth first and second derivatives | |
| 6702 | 65 ## throughout the curve. |
| 5837 | 66 ## @end table |
| 67 ## | |
| 68 ## If a scalar value @var{extrapval} is defined as the final value, then | |
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69 ## values outside the mesh as set to this value. Note that in this case |
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70 ## @var{method} must be defined as well. If @var{extrapval} is not |
| 6742 | 71 ## defined then NA is assumed. |
| 5837 | 72 ## |
| 73 ## @seealso{interp1} | |
| 74 ## @end deftypefn | |
| 75 | |
| 10549 | 76 ## Author: Kai Habel <kai.habel@gmx.de> |
| 5837 | 77 ## 2005-03-02 Thomas Weber <weber@num.uni-sb.de> |
| 78 ## * Add test cases | |
| 79 ## 2005-03-02 Paul Kienzle <pkienzle@users.sf.net> | |
| 80 ## * Simplify | |
| 81 ## 2005-04-23 Dmitri A. Sergatskov <dasergatskov@gmail.com> | |
| 82 ## * Modified demo and test for new gnuplot interface | |
| 83 ## 2005-09-07 Hoxide <hoxide_dirac@yahoo.com.cn> | |
| 84 ## * Add bicubic interpolation method | |
| 5838 | 85 ## * Fix the eat line bug when the last element of XI or YI is |
| 86 ## negative or zero. | |
| 5837 | 87 ## 2005-11-26 Pierre Baldensperger <balden@libertysurf.fr> |
| 88 ## * Rather big modification (XI,YI no longer need to be | |
| 89 ## "meshgridded") to be consistent with the help message | |
| 90 ## above and for compatibility. | |
| 91 | |
| 92 function ZI = interp2 (varargin) | |
| 5838 | 93 Z = X = Y = XI = YI = n = []; |
| 5837 | 94 method = "linear"; |
| 6742 | 95 extrapval = NA; |
| 5837 | 96 |
| 5838 | 97 switch (nargin) |
| 98 case 1 | |
| 99 Z = varargin{1}; | |
| 100 case 2 | |
| 101 if (ischar (varargin{2})) | |
| 10549 | 102 [Z, method] = deal (varargin{:}); |
| 5838 | 103 else |
| 10549 | 104 [Z, n] = deal (varargin{:}); |
| 5838 | 105 endif |
| 106 case 3 | |
| 107 if (ischar (varargin{3})) | |
| 10549 | 108 [Z, n, method] = deal (varargin{:}); |
| 5838 | 109 else |
| 10549 | 110 [Z, XI, YI] = deal (varargin{:}); |
| 5838 | 111 endif |
| 112 case 4 | |
| 113 if (ischar (varargin{4})) | |
| 10549 | 114 [Z, XI, YI, method] = deal (varargin{:}); |
| 5838 | 115 else |
| 10549 | 116 [Z, n, method, extrapval] = deal (varargin{:}); |
| 5838 | 117 endif |
| 118 case 5 | |
| 119 if (ischar (varargin{4})) | |
| 10549 | 120 [Z, XI, YI, method, extrapval] = deal (varargin{:}); |
| 5838 | 121 else |
| 10549 | 122 [X, Y, Z, XI, YI] = deal (varargin{:}); |
| 5838 | 123 endif |
| 124 case 6 | |
| 10549 | 125 [X, Y, Z, XI, YI, method] = deal (varargin{:}); |
| 5838 | 126 case 7 |
| 10549 | 127 [X, Y, Z, XI, YI, method, extrapval] = deal (varargin{:}); |
| 5838 | 128 otherwise |
| 129 print_usage (); | |
| 5837 | 130 endswitch |
| 131 | |
| 132 ## Type checking. | |
| 5838 | 133 if (!ismatrix (Z)) |
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134 error ("interp2: expected matrix Z"); |
| 5837 | 135 endif |
| 5838 | 136 if (!isempty (n) && !isscalar (n)) |
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137 error ("interp2: expected scalar n"); |
| 5837 | 138 endif |
| 5838 | 139 if (!ischar (method)) |
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140 error ("interp2: expected string 'method'"); |
| 5837 | 141 endif |
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142 if (ischar (extrapval) || strcmp (extrapval, "extrap")) |
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143 extrapval = []; |
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144 elseif (!isscalar (extrapval)) |
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145 error ("interp2: expected n extrapval"); |
| 5837 | 146 endif |
| 147 | |
| 5838 | 148 ## Define X, Y, XI, YI if needed |
| 5837 | 149 [zr, zc] = size (Z); |
| 5838 | 150 if (isempty (X)) |
| 151 X = 1:zc; | |
| 152 Y = 1:zr; | |
| 5837 | 153 endif |
| 5838 | 154 if (! isnumeric (X) || ! isnumeric (Y)) |
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155 error ("interp2: expected numeric X, Y"); |
| 5837 | 156 endif |
| 5838 | 157 if (! isempty (n)) |
| 158 p = 2^n; | |
| 159 XI = (p:p*zc)/p; | |
| 160 YI = (p:p*zr)'/p; | |
| 5837 | 161 endif |
| 5838 | 162 if (! isnumeric (XI) || ! isnumeric (YI)) |
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163 error ("interp2: expected numeric XI, YI"); |
| 5837 | 164 endif |
| 165 | |
| 6702 | 166 |
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167 if (strcmp (method, "linear") || strcmp (method, "nearest") ... |
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168 || strcmp (method, "pchip")) |
| 6702 | 169 |
| 170 ## If X and Y vectors produce a grid from them | |
| 171 if (isvector (X) && isvector (Y)) | |
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172 X = X(:); Y = Y(:); |
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173 elseif (size_equal (X, Y)) |
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174 X = X(1,:)'; Y = Y(:,1); |
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175 else |
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176 error ("interp2: X and Y must be matrices of same size"); |
| 6702 | 177 endif |
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178 if (columns (Z) != length (X) || rows (Z) != length (Y)) |
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179 error ("interp2: X and Y size must match Z dimensions"); |
| 6702 | 180 endif |
| 181 | |
| 182 ## If Xi and Yi are vectors of different orientation build a grid | |
| 183 if ((rows (XI) == 1 && columns (YI) == 1) | |
| 10549 | 184 || (columns (XI) == 1 && rows (YI) == 1)) |
| 6702 | 185 [XI, YI] = meshgrid (XI, YI); |
| 186 elseif (! size_equal (XI, YI)) | |
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187 error ("interp2: XI and YI must be matrices of same size"); |
| 6702 | 188 endif |
| 5837 | 189 |
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190 ## if XI, YI are vectors, X and Y should share their orientation. |
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191 if (rows (XI) == 1) |
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192 if (rows (X) != 1) |
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193 X = X.'; |
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194 endif |
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195 if (rows (Y) != 1) |
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196 Y = Y.'; |
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197 endif |
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198 elseif (columns (XI) == 1) |
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199 if (columns (X) != 1) |
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200 X = X.'; |
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201 endif |
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202 if (columns (Y) != 1) |
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203 Y = Y.'; |
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204 endif |
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205 endif |
| 6702 | 206 |
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207 xidx = lookup (X, XI, "lr"); |
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208 yidx = lookup (Y, YI, "lr"); |
| 5837 | 209 |
| 6702 | 210 if (strcmp (method, "linear")) |
| 211 ## each quad satisfies the equation z(x,y)=a+b*x+c*y+d*xy | |
| 212 ## | |
| 213 ## a-b | |
| 214 ## | | | |
| 215 ## c-d | |
| 216 a = Z(1:(zr - 1), 1:(zc - 1)); | |
| 217 b = Z(1:(zr - 1), 2:zc) - a; | |
| 218 c = Z(2:zr, 1:(zc - 1)) - a; | |
| 219 d = Z(2:zr, 2:zc) - a - b - c; | |
| 5837 | 220 |
| 6702 | 221 ## scale XI, YI values to a 1-spaced grid |
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222 Xsc = (XI - X(xidx)) ./ (diff (X)(xidx)); |
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223 Ysc = (YI - Y(yidx)) ./ (diff (Y)(yidx)); |
| 6702 | 224 |
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225 ## Get 2D index. |
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226 idx = sub2ind (size (a), yidx, xidx); |
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227 ## We can dispose of the 1D indices at this point to save memory. |
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228 clear xidx yidx |
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229 |
| 6702 | 230 ## apply plane equation |
| 231 ZI = a(idx) + b(idx).*Xsc + c(idx).*Ysc + d(idx).*Xsc.*Ysc; | |
| 5837 | 232 |
| 6702 | 233 elseif (strcmp (method, "nearest")) |
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234 ii = (XI - X(xidx) >= X(xidx + 1) - XI); |
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235 jj = (YI - Y(yidx) >= Y(yidx + 1) - YI); |
| 6702 | 236 idx = sub2ind (size (Z), yidx+jj, xidx+ii); |
| 237 ZI = Z(idx); | |
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238 |
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239 elseif (strcmp (method, "pchip")) |
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240 |
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241 if (length (X) < 2 || length (Y) < 2) |
| 10549 | 242 error ("interp2: pchip2 requires at least 2 points in each dimension") |
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243 endif |
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244 |
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245 ## first order derivatives |
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246 DX = __pchip_deriv__ (X, Z, 2); |
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247 DY = __pchip_deriv__ (Y, Z, 1); |
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248 ## Compute mixed derivatives row-wise and column-wise, use the average. |
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249 DXY = (__pchip_deriv__ (X, DY, 2) + __pchip_deriv__ (Y, DX, 1))/2; |
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250 |
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251 ## do the bicubic interpolation |
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252 hx = diff (X); hx = hx(xidx); |
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253 hy = diff (Y); hy = hy(yidx); |
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254 |
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255 tx = (XI - X(xidx)) ./ hx; |
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256 ty = (YI - Y(yidx)) ./ hy; |
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257 |
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258 ## construct the cubic hermite base functions in x, y |
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259 |
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260 ## formulas: |
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261 ## b{1,1} = ( 2*t.^3 - 3*t.^2 + 1); |
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262 ## b{2,1} = h.*( t.^3 - 2*t.^2 + t ); |
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263 ## b{1,2} = (-2*t.^3 + 3*t.^2 ); |
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264 ## b{2,2} = h.*( t.^3 - t.^2 ); |
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265 |
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266 ## optimized equivalents of the above: |
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267 t1 = tx.^2; |
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268 t2 = tx.*t1 - t1; |
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269 xb{2,2} = hx.*t2; |
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270 t1 = t2 - t1; |
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271 xb{2,1} = hx.*(t1 + tx); |
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272 t2 += t1; |
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273 xb{1,2} = -t2; |
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274 xb{1,1} = t2 + 1; |
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275 |
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276 t1 = ty.^2; |
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277 t2 = ty.*t1 - t1; |
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278 yb{2,2} = hy.*t2; |
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279 t1 = t2 - t1; |
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280 yb{2,1} = hy.*(t1 + ty); |
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281 t2 += t1; |
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282 yb{1,2} = -t2; |
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283 yb{1,1} = t2 + 1; |
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284 |
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285 ZI = zeros (size (XI)); |
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286 for i = 1:2 |
| 10549 | 287 for j = 1:2 |
| 288 zidx = sub2ind (size (Z), yidx+(j-1), xidx+(i-1)); | |
| 289 ZI += xb{1,i} .* yb{1,j} .* Z(zidx); | |
| 290 ZI += xb{2,i} .* yb{1,j} .* DX(zidx); | |
| 291 ZI += xb{1,i} .* yb{2,j} .* DY(zidx); | |
| 292 ZI += xb{2,i} .* yb{2,j} .* DXY(zidx); | |
| 293 endfor | |
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294 endfor |
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295 |
| 6702 | 296 endif |
| 5837 | 297 |
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298 if (! isempty (extrapval)) |
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299 ## set points outside the table to 'extrapval' |
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300 if (X (1) < X (end)) |
| 10549 | 301 if (Y (1) < Y (end)) |
| 302 ZI (XI < X(1,1) | XI > X(end) | YI < Y(1,1) | YI > Y(end)) = ... | |
| 303 extrapval; | |
| 304 else | |
| 305 ZI (XI < X(1) | XI > X(end) | YI < Y(end) | YI > Y(1)) = ... | |
| 306 extrapval; | |
| 307 endif | |
| 6979 | 308 else |
| 10549 | 309 if (Y (1) < Y (end)) |
| 310 ZI (XI < X(end) | XI > X(1) | YI < Y(1) | YI > Y(end)) = ... | |
| 311 extrapval; | |
| 312 else | |
| 313 ZI (XI < X(1,end) | XI > X(1) | YI < Y(end) | YI > Y(1)) = ... | |
| 314 extrapval; | |
| 315 endif | |
| 6979 | 316 endif |
| 317 endif | |
| 318 | |
| 6702 | 319 else |
| 5837 | 320 |
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321 ## Check dimensions of X and Y |
| 6702 | 322 if (isvector (X) && isvector (Y)) |
| 323 X = X(:).'; | |
| 324 Y = Y(:); | |
| 325 if (!isequal ([length(X), length(Y)], size(Z))) | |
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326 error ("interp2: X and Y size must match Z dimensions"); |
| 6702 | 327 endif |
| 328 elseif (!size_equal (X, Y)) | |
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329 error ("interp2: X and Y must be matrices of same size"); |
| 6702 | 330 if (! size_equal (X, Z)) |
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331 error ("interp2: X and Y size must match Z dimensions"); |
| 6702 | 332 endif |
| 333 endif | |
| 5837 | 334 |
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335 ## Check dimensions of XI and YI |
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336 if (isvector (XI) && isvector (YI)) |
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337 XI = XI(:).'; |
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338 YI = YI(:); |
| 6702 | 339 elseif (! size_equal (XI, YI)) |
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340 error ("interp2: XI and YI must be matrices of same size"); |
| 6702 | 341 endif |
| 5837 | 342 |
| 6702 | 343 ## FIXME bicubic/__splinen__ don't handle arbitrary XI, YI |
| 344 if (strcmp (method, "cubic")) | |
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345 if (isgriddata (XI) && isgriddata (YI')) |
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346 ZI = bicubic (X, Y, Z, XI (1, :), YI (:, 1), extrapval); |
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347 elseif (isgriddata (X) && isgriddata (Y')) |
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348 ## Allocate output |
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349 ZI = zeros (size (X)); |
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350 |
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351 ## Find inliers |
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352 inside = !(XI < X (1) | XI > X (end) | YI < Y (1) | YI > Y (end)); |
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353 |
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354 ## Scale XI and YI to match indices of Z |
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355 XI = (columns (Z) - 1) * (XI - X (1)) / (X (end) - X (1)) + 1; |
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356 YI = (rows (Z) - 1) * (YI - Y (1)) / (Y (end) - Y (1)) + 1; |
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357 |
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358 ## Start the real work |
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359 K = floor (XI); |
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360 L = floor (YI); |
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361 |
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362 ## Coefficients |
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363 AY1 = bc ((YI - L + 1)); |
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364 AX1 = bc ((XI - K + 1)); |
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365 AY0 = bc ((YI - L + 0)); |
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366 AX0 = bc ((XI - K + 0)); |
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367 AY_1 = bc ((YI - L - 1)); |
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368 AX_1 = bc ((XI - K - 1)); |
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369 AY_2 = bc ((YI - L - 2)); |
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370 AX_2 = bc ((XI - K - 2)); |
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371 |
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372 ## Perform interpolation |
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373 sz = size(Z); |
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374 ZI = AY_2 .* AX_2 .* Z (sym_sub2ind (sz, L+2, K+2)) ... |
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375 + AY_2 .* AX_1 .* Z (sym_sub2ind (sz, L+2, K+1)) ... |
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376 + AY_2 .* AX0 .* Z (sym_sub2ind (sz, L+2, K)) ... |
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377 + AY_2 .* AX1 .* Z (sym_sub2ind (sz, L+2, K-1)) ... |
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378 + AY_1 .* AX_2 .* Z (sym_sub2ind (sz, L+1, K+2)) ... |
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379 + AY_1 .* AX_1 .* Z (sym_sub2ind (sz, L+1, K+1)) ... |
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380 + AY_1 .* AX0 .* Z (sym_sub2ind (sz, L+1, K)) ... |
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381 + AY_1 .* AX1 .* Z (sym_sub2ind (sz, L+1, K-1)) ... |
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382 + AY0 .* AX_2 .* Z (sym_sub2ind (sz, L, K+2)) ... |
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383 + AY0 .* AX_1 .* Z (sym_sub2ind (sz, L, K+1)) ... |
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384 + AY0 .* AX0 .* Z (sym_sub2ind (sz, L, K)) ... |
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385 + AY0 .* AX1 .* Z (sym_sub2ind (sz, L, K-1)) ... |
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386 + AY1 .* AX_2 .* Z (sym_sub2ind (sz, L-1, K+2)) ... |
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387 + AY1 .* AX_1 .* Z (sym_sub2ind (sz, L-1, K+1)) ... |
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388 + AY1 .* AX0 .* Z (sym_sub2ind (sz, L-1, K)) ... |
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389 + AY1 .* AX1 .* Z (sym_sub2ind (sz, L-1, K-1)); |
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390 ZI (!inside) = extrapval; |
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391 |
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392 else |
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393 error ("interp2: input data must have `meshgrid' format"); |
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394 endif |
| 5837 | 395 |
| 6702 | 396 elseif (strcmp (method, "spline")) |
|
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397 if (isgriddata (XI) && isgriddata (YI')) |
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398 ZI = __splinen__ ({Y(:,1).', X(1,:)}, Z, {YI(:,1), XI(1,:)}, extrapval, |
| 10549 | 399 "spline"); |
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400 else |
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401 error ("interp2: input data must have `meshgrid' format"); |
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402 endif |
| 6702 | 403 else |
|
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404 error ("interp2: interpolation method not recognized"); |
| 6702 | 405 endif |
| 5837 | 406 |
| 6702 | 407 endif |
| 5837 | 408 endfunction |
| 409 | |
|
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410 function b = isgriddata (X) |
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411 d1 = diff (X, 1, 1); |
|
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412 b = all (d1 (:) == 0); |
|
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413 endfunction |
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414 |
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415 ## Compute the bicubic interpolation coefficients |
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416 function o = bc(x) |
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417 x = abs(x); |
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418 o = zeros(size(x)); |
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419 idx1 = (x < 1); |
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420 idx2 = !idx1 & (x < 2); |
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421 o(idx1) = 1 - 2.*x(idx1).^2 + x(idx1).^3; |
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422 o(idx2) = 4 - 8.*x(idx2) + 5.*x(idx2).^2 - x(idx2).^3; |
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423 endfunction |
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424 |
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425 ## This version of sub2ind behaves as if the data was symmetrically padded |
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426 function ind = sym_sub2ind(sz, Y, X) |
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427 Y (Y < 1) = 1 - Y (Y < 1); |
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428 while (any (Y (:) > 2 * sz (1))) |
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429 Y (Y > 2 * sz (1)) = round (Y (Y > 2 * sz (1)) / 2); |
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430 endwhile |
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431 Y (Y > sz (1)) = 1 + 2 * sz (1) - Y (Y > sz (1)); |
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432 X (X < 1) = 1 - X (X < 1); |
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433 while (any (X (:) > 2 * sz (2))) |
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434 X (X > 2 * sz (2)) = round (X (X > 2 * sz (2)) / 2); |
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435 endwhile |
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436 X (X > sz (2)) = 1 + 2 * sz (2) - X (X > sz (2)); |
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437 ind = sub2ind(sz, Y, X); |
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438 endfunction |
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439 |
|
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|
440 |
| 5837 | 441 %!demo |
| 442 %! A=[13,-1,12;5,4,3;1,6,2]; | |
| 443 %! x=[0,1,4]; y=[10,11,12]; | |
| 444 %! xi=linspace(min(x),max(x),17); | |
| 445 %! yi=linspace(min(y),max(y),26)'; | |
| 446 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'linear')); | |
| 447 %! [x,y] = meshgrid(x,y); | |
| 448 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; | |
| 449 | |
| 450 %!demo | |
|
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451 %! [x,y,A] = peaks(10); |
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452 %! x = x(1,:)'; y = y(:,1); |
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453 %! xi=linspace(min(x),max(x),41); |
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454 %! yi=linspace(min(y),max(y),41)'; |
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455 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'linear')); |
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456 %! [x,y] = meshgrid(x,y); |
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457 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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|
458 |
|
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|
459 %!demo |
| 5837 | 460 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 461 %! x=[0,1,4]; y=[10,11,12]; | |
| 462 %! xi=linspace(min(x),max(x),17); | |
| 463 %! yi=linspace(min(y),max(y),26)'; | |
| 464 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'nearest')); | |
| 465 %! [x,y] = meshgrid(x,y); | |
| 466 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; | |
| 467 | |
| 6702 | 468 %!demo |
|
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469 %! [x,y,A] = peaks(10); |
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470 %! x = x(1,:)'; y = y(:,1); |
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471 %! xi=linspace(min(x),max(x),41); |
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472 %! yi=linspace(min(y),max(y),41)'; |
|
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473 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'nearest')); |
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474 %! [x,y] = meshgrid(x,y); |
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475 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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|
476 |
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477 %!demo |
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478 %! A=[13,-1,12;5,4,3;1,6,2]; |
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479 %! x=[0,1,2]; y=[10,11,12]; |
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480 %! xi=linspace(min(x),max(x),17); |
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481 %! yi=linspace(min(y),max(y),26)'; |
|
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482 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'pchip')); |
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483 %! [x,y] = meshgrid(x,y); |
|
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484 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
|
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|
485 |
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486 %!demo |
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487 %! [x,y,A] = peaks(10); |
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|
488 %! x = x(1,:)'; y = y(:,1); |
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489 %! xi=linspace(min(x),max(x),41); |
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490 %! yi=linspace(min(y),max(y),41)'; |
|
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|
491 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'pchip')); |
|
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|
492 %! [x,y] = meshgrid(x,y); |
|
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|
493 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
|
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
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494 |
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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495 %!demo |
| 5837 | 496 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 497 %! x=[0,1,2]; y=[10,11,12]; | |
| 498 %! xi=linspace(min(x),max(x),17); | |
| 6702 | 499 %! yi=linspace(min(y),max(y),26)'; |
| 5837 | 500 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic')); |
| 501 %! [x,y] = meshgrid(x,y); | |
| 502 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; | |
| 503 | |
| 6702 | 504 %!demo |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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505 %! [x,y,A] = peaks(10); |
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
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506 %! x = x(1,:)'; y = y(:,1); |
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
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507 %! xi=linspace(min(x),max(x),41); |
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
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508 %! yi=linspace(min(y),max(y),41)'; |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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509 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic')); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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510 %! [x,y] = meshgrid(x,y); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
diff
changeset
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511 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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512 |
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support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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513 %!demo |
| 6702 | 514 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 515 %! x=[0,1,2]; y=[10,11,12]; | |
| 516 %! xi=linspace(min(x),max(x),17); | |
| 517 %! yi=linspace(min(y),max(y),26)'; | |
| 518 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'spline')); | |
| 519 %! [x,y] = meshgrid(x,y); | |
| 520 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; | |
| 521 | |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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522 %!demo |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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523 %! [x,y,A] = peaks(10); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
diff
changeset
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524 %! x = x(1,:)'; y = y(:,1); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
diff
changeset
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525 %! xi=linspace(min(x),max(x),41); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
diff
changeset
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526 %! yi=linspace(min(y),max(y),41)'; |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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527 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'spline')); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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528 %! [x,y] = meshgrid(x,y); |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
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changeset
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529 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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010e15c7be9a
support pchip method in interp2
Jaroslav Hajek <highegg@gmail.com>
parents:
8479
diff
changeset
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530 |
| 5837 | 531 %!test % simple test |
| 532 %! x = [1,2,3]; | |
| 533 %! y = [4,5,6,7]; | |
| 534 %! [X, Y] = meshgrid(x,y); | |
| 535 %! Orig = X.^2 + Y.^3; | |
| 536 %! xi = [1.2,2, 1.5]; | |
| 537 %! yi = [6.2, 4.0, 5.0]'; | |
| 538 %! | |
| 539 %! Expected = ... | |
| 540 %! [243, 245.4, 243.9; | |
| 541 %! 65.6, 68, 66.5; | |
| 542 %! 126.6, 129, 127.5]; | |
| 543 %! Result = interp2(x,y,Orig, xi, yi); | |
| 544 %! | |
| 545 %! assert(Result, Expected, 1000*eps); | |
| 546 | |
| 547 %!test % 2^n form | |
| 548 %! x = [1,2,3]; | |
| 549 %! y = [4,5,6,7]; | |
| 550 %! [X, Y] = meshgrid(x,y); | |
| 551 %! Orig = X.^2 + Y.^3; | |
| 552 %! xi = [1:0.25:3]; yi = [4:0.25:7]'; | |
| 553 %! Expected = interp2(x,y,Orig, xi, yi); | |
| 554 %! Result = interp2(Orig,2); | |
| 555 %! | |
| 556 %! assert(Result, Expected, 10*eps); | |
| 557 | |
| 558 %!test % matrix slice | |
| 559 %! A = eye(4); | |
| 560 %! assert(interp2(A,[1:4],[1:4]),[1,1,1,1]); | |
| 561 | |
| 562 %!test % non-gridded XI,YI | |
| 563 %! A = eye(4); | |
| 564 %! assert(interp2(A,[1,2;3,4],[1,3;2,4]),[1,0;0,1]); | |
| 565 | |
| 566 %!test % for values outside of boundaries | |
| 567 %! x = [1,2,3]; | |
| 568 %! y = [4,5,6,7]; | |
| 569 %! [X, Y] = meshgrid(x,y); | |
| 570 %! Orig = X.^2 + Y.^3; | |
| 571 %! xi = [0,4]; | |
| 572 %! yi = [3,8]'; | |
| 6742 | 573 %! assert(interp2(x,y,Orig, xi, yi),[NA,NA;NA,NA]); |
| 5837 | 574 %! assert(interp2(x,y,Orig, xi, yi,'linear', 0),[0,0;0,0]); |
| 575 | |
| 576 %!test % for values at boundaries | |
| 577 %! A=[1,2;3,4]; | |
| 578 %! x=[0,1]; | |
| 579 %! y=[2,3]'; | |
| 580 %! assert(interp2(x,y,A,x,y,'linear'), A); | |
| 581 %! assert(interp2(x,y,A,x,y,'nearest'), A); | |
| 582 | |
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62bb59f927b1
scripts/general/interp2.m, scripts/general/interpn.m: For nearest neighbour interpolation ceil (instead of floor) at the center of the data intervals to be compatible with Matlab. Add test.
Soren Hauberg <hauberg@gmail.com>
parents:
10328
diff
changeset
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583 %!test % for Matlab-compatible rounding for 'nearest' |
|
62bb59f927b1
scripts/general/interp2.m, scripts/general/interpn.m: For nearest neighbour interpolation ceil (instead of floor) at the center of the data intervals to be compatible with Matlab. Add test.
Soren Hauberg <hauberg@gmail.com>
parents:
10328
diff
changeset
|
584 %! X = meshgrid (1:4); |
|
62bb59f927b1
scripts/general/interp2.m, scripts/general/interpn.m: For nearest neighbour interpolation ceil (instead of floor) at the center of the data intervals to be compatible with Matlab. Add test.
Soren Hauberg <hauberg@gmail.com>
parents:
10328
diff
changeset
|
585 %! assert (interp2 (X, 2.5, 2.5, 'nearest'), 3); |
|
62bb59f927b1
scripts/general/interp2.m, scripts/general/interpn.m: For nearest neighbour interpolation ceil (instead of floor) at the center of the data intervals to be compatible with Matlab. Add test.
Soren Hauberg <hauberg@gmail.com>
parents:
10328
diff
changeset
|
586 |