1%% Copyright (C) 2008 Alexander Barth <barth.alexander@gmail.com>
2%%
3%% This program is free software; you can redistribute it and/or modify it under
4%% the terms of the GNU General Public License as published by the Free Software
5%% Foundation; either version 3 of the License, or (at your option) any later
6%% version.
7%%
8%% This program is distributed in the hope that it will be useful, but WITHOUT
9%% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10%% FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
11%% details.
12%%
13%% You should have received a copy of the GNU General Public License along with
14%% this program; if not, see <http://www.gnu.org/licenses/>.
15
16% Example program of the optimal interpolation toolbox
17
18
19% the grid onto which the observations are interpolated
20
21[xi,yi] = ndgrid(linspace(0,1,100));
22
23% background estimate or first guess
24xb = 10 + xi;
25
26% number of observations to interpolate
27
28on = 200;
29
30% create randomly located observations within
31% the square [0 1] x [0 1]
32
33x = rand(1,on);
34y = rand(1,on);
35
36% the underlying function to interpolate
37
38yo = 10 + x + sin(6*x) .* cos(6*y);
39
40% the error variance of the observations divided by the error
41% variance of the background field
42
43var = 0.1 * ones(on,1);
44
45% the correlation length in x and y direction
46
47lenx = 0.1;
48leny = 0.1;
49
50% number of influential observations
51
52m = 30;
53
54% subtract the first guess from the observations
55% (DON'T FORGET THIS - THIS IS VERY IMPORTANT)
56
57Hxb = interp2(xi(:,1),yi(1,:),xb',x,y);
58f = yo - Hxb;
59
60% run the optimal interpolation
61% fi is the interpolated field and vari is its error variance
62
63[fi,vari] = optiminterp2(x,y,f,var,lenx,leny,m,xi,yi);
64
65% Add the first guess back
66
67xa = fi + xb;
68