function toyexample
% show how sigma converges for the simple 1 d case

N=100;
rho=0.4;
alpha=1;

epsilon=0.001;

mu=8 - 16*rand(1); % init mu
sig=100; % initial std dev.

xx=linspace(-8,8,500);

zz=exp(-((xx-2).^2)) + 0.8.*exp(-(xx+2).^2);

while sig>epsilon,


x=mu + sig.*randn(N,1);

S=exp(-((x-2).^2)) + 0.8.*exp(-(x+2).^2);

[S,I]=sort(S);

mu = alpha*mean(x(I((1-rho)*N:N))) + (1-alpha)*mu;
sig= alpha*std(x(I((1-rho)*N:N))) + (1-alpha)*sig;

  plot(xx,zz,'b-')
hold on
%  yy=exp(-((xx-mu).^2)./(2*sig.^2))./(sqrt(2*pi)*sig);
%length(mu)
  h=plot(x(I),S,'rx');
  set(h,'MarkerSize',12)
  hold off;
axis([-8 8 0 1])

  drawnow;


statuspress=waitforbuttonpress;
%pause(1.5)
end
