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.
    %


	%%%%%%%%%%%%%%%%%%%%%%%%%%%% this works %%%%%%%%%%%%%%%%%%%
	%h_theta = X * theta;
	
	%diff1 = (h_theta - y) .* X(:,1);
	%diff2 = (h_theta - y) .* X(:,2);
	
	%theta_temp1 = theta(1) - (alpha/m * sum(diff1));
	%theta_temp2 = theta(2) - (alpha/m * sum(diff2));
	
	%theta(1) = theta_temp1;
	%theta(2) = theta_temp2;

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

	%%%%%%%%% more universal version of above...
	
	%sneaky column matrix/vector!
	theta_temp = [1:length(theta)]';
	
	for i = 1:length(theta)
		diff = ((X * theta) - y) .* X(:,i);
		theta_temp(i) = theta(i) - (alpha/m * sum(diff));
	end
	
	theta = theta_temp;
	
	
	computeCost(X, y, theta)
		

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

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

end

end
