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);
predict = theta' .* X;



deviation = (sum(predict,2) - y);

size(deviation)

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.
    %


    for i = 1:length(theta)
        theta(i) = theta(i) - (alpha/m) * sum(deviation .* X(:,i));
    end








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

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

end

end