function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(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.
    %

    
    h_theta = X * theta;
    hy = (h_theta - y);
    
    % https://octave.org/doc/v4.0.3/Arithmetic-Ops.html
    % use .* to do element by element multiplicaton
    
    temp0 = theta(1,1) - alpha / m * sum(hy .* X(:,1));
    temp1 = theta(2,1) - alpha / m * sum(hy .* X(:,2));
    %fprintf ("temp0/1: %f // %f / %f\n", temp0, temp1, temp1 + temp0);
    theta = [temp0;temp1];
    


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

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

end

end