%This is a demo for kernel estimates

data_n = 20;
point_n = 101;

data1 = randn(data_n, 1);
mu = mean(data1);
sigma = sqrt(sum((data1-mu).^2)/data_n);
tmp = max(abs(data1))+sigma;
x = linspace(tmp, -tmp, point_n);
desired = gaussmf(x, [1, 0])/sqrt(2*pi);
estimated = gaussmf(x, [sigma, mu])/(sigma*sqrt(2*pi));
subplot(2,1,1);
plot(x, desired, x, estimated, data1, zeros(size(data1)), 'g*');

data2 = 2*(rand(data_n, 1)-0.5);
mu = mean(data2);
sigma = sqrt(sum((data2-mu).^2)/data_n);
tmp = max(abs(data2))+sigma;
x = linspace(tmp, -tmp, point_n);
desired = zeros(size(x));
index = find((-1<x) & (x<1));
desired(index) = ones(size(index))/2;
estimated = gaussmf(x, [sigma, mu])/(sigma*sqrt(2*pi));
subplot(2,1,2);
plot(x, desired, x, estimated, data2, zeros(size(data2)), 'g*');

h = findobj(gcf, 'type', 'line');
set(h, 'linewidth', 2);