function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);

for iter = 1:num_iters
    % d = sum(X' * (X * theta - y)) / m;
    s = zeros(size(theta));
    for i = 1:m
        s += (theta' * X(i,:)' - y(i)) * X(i,:)';
    end
    theta = theta - alpha * (s / m);





    % ============================================================

    % Save the cost J in every iteration
    J_history(iter) = computeCost(X, y, theta);
    disp(J_history(iter))
end

end