二元函数网格数据的插值法

nshukwrd

1. function zi = interp2(varargin)
   
2. %二元函数网格数据的插值
   
3. %ZI=interp2(X,Y,Z,XI,YI,'方法')  求二元函数z=f(x,y)的插值.
   
4. %   这里X,Y,Z是同维数矩阵表示网格数据,XI,YI,ZI是同维数矩阵表示插值点.
   
5. %或ZI=interp2(x,y,z,xi,yi)其中,x,xi为行向量,y,yi为列向量.
   
6. %  'bilinear',使用双线性插值(默认)
   
7. %  'spline' 使用二元三次样条插值.
   
8. %  'cubic' 使用二元三次插值.
   
9. %例如
   
10. %   clear;close;x=0:4;y=2:4;
    
11. %   Z=[82 81 80 82 84;79 63 61 65 81;84 84 82 85 86];
    
12. %   [X,Y]=meshgrid(x,y);
    
13. %   subplot(2,1,1);
    
14. %   mesh(X,Y,Z);title('RAW DATA');
    
15. %   xi=0:0.1:4;yi=2:0.2:4;
    
16. %   [XI,YI]=meshgrid(xi,yi);
    
17. %   zspline=interp2(x,y,z,XI,YI,'spline');
    
18. %   subplot(2,1,2);
    
19. %   mesh(XI,YI,zspline);
    
20. %   title('SPLINE');
    
21. %
    
22. %INTERP2 2-D interpolation (table lookup).
    
23. %   ZI = INTERP2(X,Y,Z,XI,YI) interpolates to find ZI, the values of the
    
24. %   underlying 2-D function Z at the points in matrices XI and YI.
    
25. %   Matrices X and Y specify the points at which the data Z is given.
    
26. %   Out of range values are returned as NaN.
    
27. %
    
28. %   XI can be a row vector, in which case it specifies a matrix with
    
29. %   constant columns. Similarly, YI can be a column vector and it
    
30. %   specifies a matrix with constant rows.
    
31. %
    
32. %   ZI = INTERP2(Z,XI,YI) assumes X=1:N and Y=1:M where [M,N]=SIZE(Z).
    
33. %   ZI = INTERP2(Z,NTIMES) expands Z by interleaving interpolates between
    
34. %   every element, working recursively for NTIMES.  INTERP2(Z) is the
    
35. %   same as INTERP2(Z,1).
    
36. %
    
37. %   ZI = INTERP2(...,'method') specifies alternate methods.  The default
    
38. %   is linear interpolation.  Available methods are:
    
39. %
    
40. %     'nearest' - nearest neighbor interpolation
    
41. %     'linear'  - bilinear interpolation
    
42. %     'cubic'   - bicubic interpolation
    
43. %     'spline'  - spline interpolation
    
44. %
    
45. %   All the interpolation methods require that X and Y be monotonic and
    
46. %   plaid (as if they were created using MESHGRID).  X and Y can be
    
47. %   non-uniformly spaced.  For faster interpolation when X and Y are
    
48. %   equally spaced and monotonic, use the methods '*linear', '*cubic', or
    
49. %   '*nearest'.
    
50. %
    
51. %   For example, to generate a coarse approximation of PEAKS and
    
52. %   interpolate over a finer mesh:
    
53. %       [x,y,z] = peaks(10); [xi,yi] = meshgrid(-3:.1:3,-3:.1:3);
    
54. %       zi = interp2(x,y,z,xi,yi); mesh(xi,yi,zi)
    
55. %      
    
56. %   See also INTERP1, INTERP3, INTERPN, MESHGRID, GRIDDATA.
    
57. 
    
58. %   Copyright (c) 1984-98 by The MathWorks, Inc.
    
59. %   $Revision: 5.26 $
    
60. 
    
61. error(nargchk(1,6,nargin));
    
62. 
    
63. bypass = 0;
    
64. uniform = 1;
    
65. if isstr(varargin{end}),
    
66.   narg = nargin-1;
    
67.   method = [varargin{end} '    ']; % Protect against short string.
    
68.   if method(1)=='*', % Direct call bypass.
    
69.     if method(2)=='l' | all(method(2:4)=='bil'), % bilinear interpolation.
    
70.       zi = linear(varargin{1:end-1});
    
71.       return
    
72. 
    
73.     elseif method(2)=='c' | all(method(2:4)=='bic'), % bicubic interpolation
    
74.       zi = cubic(varargin{1:end-1});
    
75.       return
    
76. 
    
77.     elseif method(2)=='n', % Nearest neighbor interpolation
    
78.       zi = nearest(varargin{1:end-1});
    
79.       return
    
80.    
    
81.     elseif method(2)=='s', % spline interpolation
    
82.       method = 'spline'; bypass = 1;
    
83. 
    
84.     else
    
85.       error([deblank(method),' is an invalid method.']);
    
86. 
    
87.     end
    
88.   elseif method(1)=='s', % Spline interpolation
    
89.     method = 'spline'; bypass = 1;
    
90.   end
    
91. 
    
92. else
    
93.   narg = nargin;
    
94.   method = 'linear';
    
95. end
    
96. 
    
97. if narg==1, % interp2(z), % Expand Z
    
98.   [nrows,ncols] = size(varargin{1});
    
99.   xi = 1:.5:ncols; yi = (1:.5:nrows)';
    
100.   x = 1:ncols; y = (1:nrows);
     
101.   [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi);
     
102. 
     
103. elseif narg==2. % interp2(z,n), Expand Z n times
     
104.   [nrows,ncols] = size(varargin{1});
     
105.   ntimes = floor(varargin{2}(1));
     
106.   xi = 1:1/(2^ntimes):ncols; yi = (1:1/(2^ntimes):nrows)';
     
107.   x = 1:ncols; y = (1:nrows);
     
108.   [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi);
     
109. 
     
110. elseif narg==3, % interp2(z,xi,yi)
     
111.   [nrows,ncols] = size(varargin{1});
     
112.   x = 1:ncols; y = (1:nrows);
     
113.   [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1:3});
     
114. 
     
115. elseif narg==4,
     
116.   error('Wrong number of input arguments.');
     
117. 
     
118. elseif narg==5, % linear(x,y,z,xi,yi)
     
119.   [msg,x,y,z,xi,yi] = xyzchk(varargin{1:5});
     
120. 
     
121. end
     
122. 
     
123. if ~isempty(msg), error(msg); end
     
124. 
     
125. %
     
126. % Check for plaid data.
     
127. %
     
128. xx = x(1,:); yy = y(:,1);
     
129. if (size(x,2)>1 & ~isequal(repmat(xx,size(x,1),1),x)) | ...
     
130.    (size(y,1)>1 & ~isequal(repmat(yy,1,size(y,2)),y)),
     
131.   error(sprintf(['X and Y must be matrices produced by MESHGRID. Use' ...
     
132.      ' GRIDDATA instead \nof INTERP2 for scattered data.']));
     
133. end
     
134. 
     
135. %
     
136. % Check for non-equally spaced data.  If so, map (x,y) and
     
137. % (xi,yi) to matrix (row,col) coordinate system.
     
138. %
     
139. if ~bypass,
     
140.   xx = xx.'; % Make sure it's a column.
     
141.   dx = diff(xx); dy = diff(yy);
     
142.   xdiff = max(abs(diff(dx))); if isempty(xdiff), xdiff = 0; end
     
143.   ydiff = max(abs(diff(dy))); if isempty(ydiff), ydiff = 0; end
     
144.   if (xdiff > eps*max(abs(xx))) | (ydiff > eps*max(abs(yy))),
     
145.     if any(dx < 0), % Flip orientation of data so x is increasing.
     
146.       x = fliplr(x); y = fliplr(y); z = fliplr(z);
     
147.       xx = flipud(xx); dx = -flipud(dx);
     
148.     end
     
149.     if any(dy < 0), % Flip orientation of data so y is increasing.
     
150.       x = flipud(x); y = flipud(y); z = flipud(z);
     
151.       yy = flipud(yy); dy = -flipud(dy);
     
152.     end
     
153.   
     
154.     if any(dx<=0) | any(dy<=0),
     
155.       error('X and Y must be monotonic vectors or matrices produced by MESHGRID.');
     
156.     end
     
157.   
     
158.     % Bypass mapping code for cubic
     
159.     if method(1)~='c',
     
160.       % Determine the nearest location of xi in x
     
161.       [xxi,j] = sort(xi(:));
     
162.       [dum,i] = sort([xx;xxi]);
     
163.       ui(i) = (1:length(i));
     
164.       ui = (ui(length(xx)+1:end)-(1:length(xxi)))';
     
165.       ui(j) = ui;
     
166.    
     
167.       % Map values in xi to index offset (ui) via linear interpolation
     
168.       ui(ui<1) = 1;
     
169.       ui(ui>length(xx)-1) = length(xx)-1;
     
170.       ui = ui + (xi(:)-xx(ui))./(xx(ui+1)-xx(ui));
     
171.      
     
172.       % Determine the nearest location of yi in y
     
173.       [yyi,j] = sort(yi(:));
     
174.       [dum,i] = sort([yy;yyi(:)]);
     
175.       vi(i) = (1:length(i));
     
176.       vi = (vi(length(yy)+1:end)-(1:length(yyi)))';
     
177.       vi(j) = vi;
     
178.    
     
179.       % Map values in yi to index offset (vi) via linear interpolation
     
180.       vi(vi<1) = 1;
     
181.       vi(vi>length(yy)-1) = length(yy)-1;
     
182.       vi = vi + (yi(:)-yy(vi))./(yy(vi+1)-yy(vi));
     
183.       
     
184.       [x,y] = meshgrid(1:size(x,2),1:size(y,1));
     
185.       xi(:) = ui; yi(:) = vi;
     
186.     else
     
187.       uniform = 0;
     
188.     end
     
189.   end
     
190. end
     
191. 
     
192. % Now do the interpolation based on method.
     
193. method = [lower(method),'   ']; % Protect against short string
     
194. 
     
195. if method(1)=='l' | all(method(1:3)=='bil'), % bilinear interpolation.
     
196.   zi = linear(x,y,z,xi,yi);
     
197. 
     
198. elseif method(1)=='c' | all(method(1:3)=='bic'), % bicubic interpolation
     
199.   if uniform
     
200.     zi = cubic(x,y,z,xi,yi);
     
201.   else
     
202.     d = find(xi < min(x(:)) | xi > max(x(:)) | ...
     
203.              yi < min(y(:)) | yi > max(y(:)));
     
204.     zi = spline2(x,y,z,xi,yi);
     
205.     zi(d) = NaN;
     
206.   end
     
207. 
     
208. elseif method(1)=='n', % Nearest neighbor interpolation
     
209.   zi = nearest(x,y,z,xi,yi);
     
210. 
     
211. elseif method(1)=='s', % Spline interpolation
     
212.   zi = spline2(x,y,z,xi,yi);
     
213. 
     
214. else
     
215.   error([deblank(method),' is an invalid method.']);
     
216. 
     
217. end
     
218. 
     
219. %------------------------------------------------------
     
220. function F = linear(arg1,arg2,arg3,arg4,arg5)
     
221. %LINEAR 2-D bilinear data interpolation.
     
222. %   ZI = LINEAR(X,Y,Z,XI,YI) uses bilinear interpolation to
     
223. %   find ZI, the values of the underlying 2-D function in Z at the points
     
224. %   in matrices XI and YI.  Matrices X and Y specify the points at which
     
225. %   the data Z is given.  X and Y can also be vectors specifying the
     
226. %   abscissae for the matrix Z as for MESHGRID. In both cases, X
     
227. %   and Y must be equally spaced and monotonic.
     
228. %
     
229. %   Values of NaN are returned in ZI for values of XI and YI that are
     
230. %   outside of the range of X and Y.
     
231. %
     
232. %   If XI and YI are vectors, LINEAR returns vector ZI containing
     
233. %   the interpolated values at the corresponding points (XI,YI).
     
234. %
     
235. %   ZI = LINEAR(Z,XI,YI) assumes X = 1:N and Y = 1:M, where
     
236. %   [M,N] = SIZE(Z).
     
237. %
     
238. %   ZI = LINEAR(Z,NTIMES) returns the matrix Z expanded by interleaving
     
239. %   bilinear interpolates between every element, working recursively
     
240. %   for NTIMES.  LINEAR(Z) is the same as LINEAR(Z,1).
     
241. %
     
242. %   This function needs about 4 times SIZE(XI) memory to be available.
     
243. %
     
244. %   See also INTERP2, CUBIC.
     
245. 
     
246. %   Clay M. Thompson 4-26-91, revised 7-3-91, 3-22-93 by CMT.
     
247. 
     
248. if nargin==1, % linear(z), Expand Z
     
249.   [nrows,ncols] = size(arg1);
     
250.   s = 1:.5:ncols; sizs = size(s);
     
251.   t = (1:.5:nrows)'; sizt = size(t);
     
252.   s = s(ones(sizt),:);
     
253.   t = t(:,ones(sizs));
     
254. 
     
255. elseif nargin==2, % linear(z,n), Expand Z n times
     
256.   [nrows,ncols] = size(arg1);
     
257.   ntimes = floor(arg2);
     
258.   s = 1:1/(2^ntimes):ncols; sizs = size(s);
     
259.   t = (1:1/(2^ntimes):nrows)'; sizt = size(t);
     
260.   s = s(ones(sizt),:);
     
261.   t = t(:,ones(sizs));
     
262. 
     
263. elseif nargin==3, % linear(z,s,t), No X or Y specified.
     
264.   [nrows,ncols] = size(arg1);
     
265.   s = arg2; t = arg3;
     
266. 
     
267. elseif nargin==4,
     
268.   error('Wrong number of input arguments.');
     
269. 
     
270. elseif nargin==5, % linear(x,y,z,s,t), X and Y specified.
     
271.   [nrows,ncols] = size(arg3);
     
272.   mx = prod(size(arg1)); my = prod(size(arg2));
     
273.   if any([mx my] ~= [ncols nrows]) & ...
     
274.      ~isequal(size(arg1),size(arg2),size(arg3))
     
275.     error('The lengths of the X and Y vectors must match Z.');
     
276.   end
     
277.   if any([nrows ncols]<[2 2]), error('Z must be at least 2-by-2.'); end
     
278.   s = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1);
     
279.   t = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1);
     
280.   
     
281. end
     
282. 
     
283. if any([nrows ncols]<[2 2]), error('Z must be at least 2-by-2.'); end
     
284. if ~isequal(size(s),size(t)),
     
285.   error('XI and YI must be the same size.');
     
286. end
     
287. 
     
288. % Check for out of range values of s and set to 1
     
289. sout = find((s<1)|(s>ncols));
     
290. if length(sout)>0, s(sout) = ones(size(sout)); end
     
291. 
     
292. % Check for out of range values of t and set to 1
     
293. tout = find((t<1)|(t>nrows));
     
294. if length(tout)>0, t(tout) = ones(size(tout)); end
     
295. 
     
296. % Matrix element indexing
     
297. ndx = floor(t)+floor(s-1)*nrows;
     
298. 
     
299. % Compute intepolation parameters, check for boundary value.
     
300. if isempty(s), d = s; else d = find(s==ncols); end
     
301. s(:) = (s - floor(s));
     
302. if length(d)>0, s(d) = s(d)+1; ndx(d) = ndx(d)-nrows; end
     
303. 
     
304. % Compute intepolation parameters, check for boundary value.
     
305. if isempty(t), d = t; else d = find(t==nrows); end
     
306. t(:) = (t - floor(t));
     
307. if length(d)>0, t(d) = t(d)+1; ndx(d) = ndx(d)-1; end
     
308. d = [];
     
309. 
     
310. % Now interpolate, reuse u and v to save memory.
     
311. if nargin==5,
     
312.   F =  ( arg3(ndx).*(1-t) + arg3(ndx+1).*t ).*(1-s) + ...
     
313.        ( arg3(ndx+nrows).*(1-t) + arg3(ndx+(nrows+1)).*t ).*s;
     
314. else
     
315.   F =  ( arg1(ndx).*(1-t) + arg1(ndx+1).*t ).*(1-s) + ...
     
316.        ( arg1(ndx+nrows).*(1-t) + arg1(ndx+(nrows+1)).*t ).*s;
     
317. end
     
318. 
     
319. % Now set out of range values to NaN.
     
320. if length(sout)>0, F(sout) = NaN; end
     
321. if length(tout)>0, F(tout) = NaN; end
     
322. 
     
323. 
     
324. 
     
325. %------------------------------------------------------
     
326. function F = cubic(arg1,arg2,arg3,arg4,arg5)
     
327. %CUBIC 2-D bicubic data interpolation.
     
328. %   CUBIC(...) is the same as LINEAR(....) except that it uses
     
329. %   bicubic interpolation.
     
330. %   
     
331. %   This function needs about 7-8 times SIZE(XI) memory to be available.
     
332. %
     
333. %   See also LINEAR.
     
334. 
     
335. %   Clay M. Thompson 4-26-91, revised 7-3-91, 3-22-93 by CMT.
     
336. 
     
337. %   Based on "Cubic Convolution Interpolation for Digital Image
     
338. %   Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and
     
339. %   Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160.
     
340. 
     
341. if nargin==1, % cubic(z), Expand Z
     
342.   [nrows,ncols] = size(arg1);
     
343.   s = 1:.5:ncols; sizs = size(s);
     
344.   t = (1:.5:nrows)'; sizt = size(t);
     
345.   s = s(ones(sizt),:);
     
346.   t = t(:,ones(sizs));
     
347. 
     
348. elseif nargin==2, % cubic(z,n), Expand Z n times
     
349.   [nrows,ncols] = size(arg1);
     
350.   ntimes = floor(arg2);
     
351.   s = 1:1/(2^ntimes):ncols; sizs = size(s);
     
352.   t = (1:1/(2^ntimes):nrows)'; sizt = size(t);
     
353.   s = s(ones(sizt),:);
     
354.   t = t(:,ones(sizs));
     
355. 
     
356. elseif nargin==3, % cubic(z,s,t), No X or Y specified.
     
357.   [nrows,ncols] = size(arg1);
     
358.   s = arg2; t = arg3;
     
359. 
     
360. elseif nargin==4,
     
361.   error('Wrong number of input arguments.');
     
362. 
     
363. elseif nargin==5, % cubic(x,y,z,s,t), X and Y specified.
     
364.   [nrows,ncols] = size(arg3);
     
365.   mx = prod(size(arg1)); my = prod(size(arg2));
     
366.   if any([mx my] ~= [ncols nrows]) & ...
     
367.      ~isequal(size(arg1),size(arg2),size(arg3))
     
368.     error('The lengths of the X and Y vectors must match Z.');
     
369.   end
     
370.   if any([nrows ncols]<[3 3]), error('Z must be at least 3-by-3.'); end
     
371.   s = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1);
     
372.   t = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1);
     
373.   
     
374. end
     
375. 
     
376. if any([nrows ncols]<[3 3]), error('Z must be at least 3-by-3.'); end
     
377. if ~isequal(size(s),size(t)),
     
378.   error('XI and YI must be the same size.');
     
379. end
     
380. 
     
381. % Check for out of range values of s and set to 1
     
382. sout = find((s<1)|(s>ncols));
     
383. if length(sout)>0, s(sout) = ones(size(sout)); end
     
384. 
     
385. % Check for out of range values of t and set to 1
     
386. tout = find((t<1)|(t>nrows));
     
387. if length(tout)>0, t(tout) = ones(size(tout)); end
     
388. 
     
389. % Matrix element indexing
     
390. ndx = floor(t)+floor(s-1)*(nrows+2);
     
391. 
     
392. % Compute intepolation parameters, check for boundary value.
     
393. if isempty(s), d = s; else d = find(s==ncols); end
     
394. s(:) = (s - floor(s));
     
395. if length(d)>0, s(d) = s(d)+1; ndx(d) = ndx(d)-nrows-2; end
     
396. 
     
397. % Compute intepolation parameters, check for boundary value.
     
398. if isempty(t), d = t; else d = find(t==nrows); end
     
399. t(:) = (t - floor(t));
     
400. if length(d)>0, t(d) = t(d)+1; ndx(d) = ndx(d)-1; end
     
401. d = [];
     
402. 
     
403. if nargin==5,
     
404.   % Expand z so interpolation is valid at the boundaries.
     
405.   zz = zeros(size(arg3)+2);
     
406.   zz(1,2:ncols+1) = 3*arg3(1,:)-3*arg3(2,:)+arg3(3,:);
     
407.   zz(2:nrows+1,2:ncols+1) = arg3;
     
408.   zz(nrows+2,2:ncols+1) = 3*arg3(nrows,:)-3*arg3(nrows-1,:)+arg3(nrows-2,:);
     
409.   zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4);
     
410.   zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1);
     
411.   nrows = nrows+2; ncols = ncols+2;
     
412. else
     
413.   % Expand z so interpolation is valid at the boundaries.
     
414.   zz = zeros(size(arg1)+2);
     
415.   zz(1,2:ncols+1) = 3*arg1(1,:)-3*arg1(2,:)+arg1(3,:);
     
416.   zz(2:nrows+1,2:ncols+1) = arg1;
     
417.   zz(nrows+2,2:ncols+1) = 3*arg1(nrows,:)-3*arg1(nrows-1,:)+arg1(nrows-2,:);
     
418.   zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4);
     
419.   zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1);
     
420.   nrows = nrows+2; ncols = ncols+2;
     
421. end
     
422. 
     
423. % Now interpolate using computationally efficient algorithm.
     
424. t0 = ((2-t).*t-1).*t;
     
425. t1 = (3*t-5).*t.*t+2;
     
426. t2 = ((4-3*t).*t+1).*t;
     
427. t(:) = (t-1).*t.*t;
     
428. F     = ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
     
429.         .* (((2-s).*s-1).*s);
     
430. ndx(:) = ndx + nrows;
     
431. F(:)  = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
     
432.         .* ((3*s-5).*s.*s+2);
     
433. ndx(:) = ndx + nrows;
     
434. F(:)  = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
     
435.         .* (((4-3*s).*s+1).*s);
     
436. ndx(:) = ndx + nrows;
     
437. F(:)  = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
     
438.        .* ((s-1).*s.*s);
     
439. F(:) = F/4;
     
440. 
     
441. % Now set out of range values to NaN.
     
442. if length(sout)>0, F(sout) = NaN; end
     
443. if length(tout)>0, F(tout) = NaN; end
     
444. 
     
445. 
     
446. %------------------------------------------------------
     
447. function F = nearest(arg1,arg2,arg3,arg4,arg5)
     
448. %NEAREST 2-D Nearest neighbor interpolation.
     
449. %   ZI = NEAREST(X,Y,Z,XI,YI) uses nearest neighbor interpolation to
     
450. %   find ZI, the values of the underlying 2-D function in Z at the points
     
451. %   in matrices XI and YI.  Matrices X and Y specify the points at which
     
452. %   the data Z is given.  X and Y can also be vectors specifying the
     
453. %   abscissae for the matrix Z as for MESHGRID. In both cases, X
     
454. %   and Y must be equally spaced and monotonic.
     
455. %
     
456. %   Values of NaN are returned in ZI for values of XI and YI that are
     
457. %   outside of the range of X and Y.
     
458. %
     
459. %   If XI and YI are vectors, NEAREST returns vector ZI containing
     
460. %   the interpolated values at the corresponding points (XI,YI).
     
461. %
     
462. %   ZI = NEAREST(Z,XI,YI) assumes X = 1:N and Y = 1:M, where
     
463. %   [M,N] = SIZE(Z).
     
464. %
     
465. %   F = NEAREST(Z,NTIMES) returns the matrix Z expanded by interleaving
     
466. %   interpolates between every element.  NEAREST(Z) is the same as
     
467. %   NEAREST(Z,1).
     
468. %
     
469. %   See also INTERP2, LINEAR, CUBIC.
     
470. 
     
471. %   Clay M. Thompson 4-26-91, revised 7-3-91 by CMT.
     
472. 
     
473. if nargin==1, % nearest(z), Expand Z
     
474.   [nrows,ncols] = size(arg1);
     
475.   u = ones(2*nrows-1,1)*(1:.5:ncols);
     
476.   v = (1:.5:nrows)'*ones(1,2*ncols-1);
     
477. 
     
478. elseif nargin==2, % nearest(z,n), Expand Z n times
     
479.   [nrows,ncols] = size(arg1);
     
480.   ntimes = floor(arg2);
     
481.   u = 1:1/(2^ntimes):ncols; sizu = size(u);
     
482.   v = (1:1/(2^ntimes):nrows)'; sizv = size(v);
     
483.   u = u(ones(sizv),:);
     
484.   v = v(:,ones(sizu));
     
485. 
     
486. elseif nargin==3, % nearest(z,u,v)
     
487.   [nrows,ncols] = size(arg1);
     
488.   u = arg2; v = arg3;
     
489. 
     
490. elseif nargin==4,
     
491.   error('Wrong number of input arguments.');
     
492. 
     
493. elseif nargin==5, % nearest(x,y,z,u,v), X and Y specified.
     
494.   [nrows,ncols] = size(arg3);
     
495.   mx = prod(size(arg1)); my = prod(size(arg2));
     
496.   if any([mx my] ~= [ncols nrows]) & (size(arg1)~=size(arg3) |   ...
     
497.     size(arg2)~=size(arg3)),
     
498.     error('The lengths of the X and Y vectors must match Z.');
     
499.   end
     
500.   if all([nrows ncols]>[1 1]),
     
501.     u = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1);
     
502.     v = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1);
     
503.   else
     
504.     u = 1 + (arg4-arg1(1));
     
505.     v = 1 + (arg5-arg2(1));
     
506.   end
     
507. end
     
508. 
     
509. if size(u)~=size(v), error('XI and YI must be the same size.'); end
     
510. 
     
511. % Check for out of range values of u and set to 1
     
512. uout = (u<.5)|(u>=ncols+.5);
     
513. nuout = sum(uout(:));
     
514. if any(uout(:)), u(uout) = ones(nuout,1); end
     
515. 
     
516. % Check for out of range values of v and set to 1
     
517. vout = (v<.5)|(v>=nrows+.5);
     
518. nvout = sum(vout(:));
     
519. if any(vout(:)), v(vout) = ones(nvout,1); end
     
520. 
     
521. % Interpolation parameters
     
522. s = (u - round(u));  t = (v - round(v));
     
523. u = round(u); v = round(v);
     
524. 
     
525. % Now interpolate
     
526. ndx = v+(u-1)*nrows;
     
527. if nargin==5,
     
528.   F = arg3(ndx);
     
529. else
     
530.   F = arg1(ndx);
     
531. end
     
532. 
     
533. % Now set out of range values to NaN.
     
534. if any(uout(:)), F(uout) = NaN; end
     
535. if any(vout(:)), F(vout) = NaN; end
     
536. 
     
537. %----------------------------------------------------------
     
538. function F = spline2(varargin)
     
539. %2-D spline interpolation
     
540. 
     
541. % Determine abscissa vectors
     
542. varargin{1} = varargin{1}(1,:);
     
543. varargin{2} = varargin{2}(:,1).';
     
544. 
     
545. %
     
546. % Check for plaid data.
     
547. %
     
548. xi = varargin{4}; yi = varargin{5};
     
549. xxi = xi(1,:); yyi = yi(:,1);
     
550. if (size(xi,2)>1 & ~isequal(repmat(xxi,size(xi,1),1),xi)) | ...
     
551.    (size(yi,1)>1 & ~isequal(repmat(yyi,1,size(yi,2)),yi)),
     
552.   F = splncore(varargin(2:-1:1),varargin{3},varargin(5:-1:4));
     
553. else
     
554.   F = splncore(varargin(2:-1:1),varargin{3},{yyi(:).' xxi},'gridded');
     
555. end
     

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