function J = computeCost(X, y, theta)
	
	m = length(y); % number of training examples
	J = 0;
	predictions = X * theta;
	J = 1/(2*m)*(predictions - y)'*(predictions - y);

end

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
% X is m*(n+1) matrix 
% y is m*1
% theta is (n+1)*1 matrix
% alpha is a number 
% num_iters is number of iterators

	
	m = length(y); % number of training examples
	J_history = zeros(num_iters, 1);  %cost function的值的变化过程
	%预先定义了迭代的次数

	for iter = 1:num_iters

		temp1 = theta(1) - (alpha / m) * sum((X * theta - y).* X(:,1));
		temp2 = theta(2) - (alpha / m) * sum((X * theta - y).* X(:,2));
		theta(1) = temp1;
		theta(2) = temp2;
		J_history(iter) = computeCost(X, y, theta);

	end

end