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

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %
    
    tmat = repmat( theta, 1, size(X, 1) );
    h_theta = tmat' .* X;
    to_sum = (sum(h_theta,2) - y);
    
    to_sum_1 = to_sum .* X(:, 1);
    to_sum_2 = to_sum .* X(:, 2);
    
    theta(1) = theta(1) - (alpha * (1/m) * sum(to_sum_1));
    theta(2) = theta(2) - (alpha * (1/m) * sum(to_sum_2));

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

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

end

end
