function [W phi]=train_rbf(X,Y,Xc,k_i,basisfunction)
%trains a radial basis function
%X is a N_p by N_dim matrix of training data
%Y is a N_p by N_dim matrix of training data
%Xc is a N_r by N_dim matrix of rbf centres
%basisfunction may be 'gaussian' or 'polyharmonicspline'
%k_i is a prescaler for 'gaussian' rbf and function order for
%'polyharmonicspline'. See k_i(i)=0 for constant bias
%
%Copyright (c) 2009, Travis Wiens
%All rights reserved.
%
%Redistribution and use in source and binary forms, with or without
%modification, are permitted provided that the following conditions are
%met:
%
% * Redistributions of source code must retain the above copyright
% notice, this list of conditions and the following disclaimer.
% * Redistributions in binary form must reproduce the above copyright
% notice, this list of conditions and the following disclaimer in
% the documentation and/or other materials provided with the distribution
%
%THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
%AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
%IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
%ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
%LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
%CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
%SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
%INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
%CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
%ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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% If you would like to request that this software be licensed under a less
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% contact Travis at travis.mlfx@nutaksas.com
if nargin<4
k_i=1;
end
if nargin<5
basisfunction='gaussian';
end
N_r=size(Xc,1);%number of centres
W=zeros(N_r,1);%weight matrix
[z phi]=sim_rbf(Xc,X,W,k_i,basisfunction);%simulate rbf
%A=pinv(phi'*phi)*phi';%do inverse
%W=A*Y;
W=phi\Y;%find weights