% Script to show the effects of the width of the Gaussian in 1-d functions

%The data will be random:
numcenters=15;
ridx=randperm(numcenters);
x=2*randn(1,numcenters*4);
centers=x;
y=sin(3*x)+0.2*randn(size(x));

t=linspace(-2,2);
yt=sin(3*t);

widths=5:-0.1:0.1;

for j=1:length(widths)
    
    %Get the Weights from the training data
    A=edm(x',centers');
    Phi=rbf1(A,1,widths(j));
    Phi=[Phi, ones(length(x),1)];
    W=pinv(Phi)*y';
   
    %Get predicted values on the new data:
    A=edm(t',centers');
    Phi=rbf1(A,1,widths(j));
    Phi=[Phi, ones(length(t),1)];
    Yout=Phi*W;
    
    figure(1)
    plot(x,y,'k*',t,yt,'b-',t,Yout,'r-');
    axis([-2 2 -2 2]);
    pause(0.1);
    
    Err(j)=sum(abs(Yout-yt').^2);
   
end

% You can plot the whole error vector, but notice that the error decreases
% through the first 12, then increases (then increases wildly at the end!).

% This suggests that the optimal width is the 12th value of the widths
% vector, or:   3.90