source:trunk/src/tps_coeff.m@418

Last change on this file since 418 was 362, checked in by sommeria, 12 years ago

various bugs corrected

File size: 1.7 KB
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1%'tps_coeff': calculate the thin plate spline (tps) coefficients
2% (ref fasshauer@iit.edu MATH 590 ? Chapter 19 32)
3% this interpolation/smoothing minimises a linear combination of the squared curvature
4%  and squared difference form the initial data.
5% This function calculates the weight coefficients U_tps of the N sites where
6% data are known. Interpolated data are then obtained as the matrix product
7% EM*U_tps where the matrix EM is obtained by the function tps_eval.
8% The spatial derivatives are obtained as EMDX*U_tps and EMDY*U_tps, where
9% EMDX and EMDY are obtained from the function tps_eval_dxy.
10%------------------------------------------------------------------------
11% [U_smooth,U_tps]=tps_coeff(ctrs,U,rho)
12%------------------------------------------------------------------------
13% OUPUT:
14% U_smooth: values of the quantity U at the N centres after smoothing
15% U_tps: tps weights of the centres
16
17%INPUT:
18% ctrs: Nxs matrix  representing the postions of the M centers, sources of the tps (s=space dimension)
19% U: Nx1 column vector representing the initial values of the considered scalar at the centres ctrs
20% rho: smoothing parameter: the result is smoother for larger rho.
21
22
23function [U_smooth,U_tps]=tps_coeff(ctrs,U,rho)
24%------------------------------------------------------------------------
25%rho smoothing parameter
26% X=reshape(X,[],1);
27% Y=reshape(Y,[],1);
28N=size(ctrs,1);
29% rhs = reshape(U,[],1);
30U = [U; zeros(3,1)];
31% ctrs = [X Y];% coordinates of measurement sites, radial base functions are located at the measurement sites
32EM = tps_eval(ctrs,ctrs);
33RhoMat=rho*eye(N,N);%  rho=1/(2*omega) , omega given by fasshauer;
34RhoMat=[RhoMat zeros(N,3)];
35PM=[ones(N,1) ctrs];
36IM=[EM+RhoMat; [PM' zeros(3,3)]];
37U_tps=(IM\U);
38U_smooth=EM *U_tps;
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