%% Sample RBF script:  How does the width effect the function?
%First define the data

X=randn(1500,2);
Y=exp(-(X(:,1).^2+X(:,2).^2)/4)+0.15*randn(1500,1);  %Add some noise

%% Split the data into training and testing sets
% In this case, we'll use 300 points for training

temp=randperm(1500);
Xtrain=X(temp(1:300),:);
Xtest=X(temp(301:end),:);

Ytrain=Y(temp(1:300),:);
Ytest=Y(temp(301:end),:);

%% Create the Radial Basis Function.  
% For this example, we will use 10 points chosen at random from the data as
% our set of centers

temp=randperm(1500);
Centers=X(temp(1:10),:);

widths=10:-0.1:0.1;

%% Loop through possible widths

for j=1:length(widths);

    A=edm(Xtrain,Centers);
    Phi=rbf1(A,1,widths(j));
    alpha=pinv(Phi)*Ytrain;
    % Compute the error using the test set:
    A=edm(Xtest,Centers);
    Phi=rbf1(A,1,widths(j));
    Yout=Phi*alpha;
    Err(j)=norm(Ytest-Yout,'fro');
    
end

[minErr,val]=min(Err);
fprintf('The best width is %f\n',widths(val));