function [error_train, error_val] = ...
    learningCurve(X, y, Xval, yval, lambda)
    %% LEARNINGCURVE Generates the train and cross validation set errors needed 
    %to plot a learning curve
    %   [error_train, error_val] = ...
    %       LEARNINGCURVE(X, y, Xval, yval, lambda) returns the train and
    %       cross validation set errors for a learning curve. In particular, 
    %       it returns two vectors of the same length - error_train and 
    %       error_val. Then, error_train(i) contains the training error for
    %       i examples (and similarly for error_val(i)).
    %
    %   In this function, you will compute the train and test errors for
    %   dataset sizes from 1 up to m. In practice, when working with larger
    %   datasets, you might want to do this in larger intervals.
    %

    % Number of training examples
    n = size(X, 1);

    % You need to return these values correctly
    error_train = zeros(n, 1);
    error_val   = zeros(n, 1);

    % ====================== YOUR CODE HERE ======================
    % Instructions: Fill in this function to return training errors in 
    %               error_train and the cross validation errors in error_val. 
    %               i.e., error_train(i) and 
    %               error_val(i) should give you the errors
    %               obtained after training on i examples.
    %
    % Note: You should evaluate the training error on the first i training
    %       examples (i.e., X(1:i, :) and y(1:i)).
    %
    %       For the cross-validation error, you should instead evaluate on
    %       the _entire_ cross validation set (Xval and yval).
    %
    % Note: If you are using your cost function (linearRegCostFunction)
    %       to compute the training and cross validation error, you should 
    %       call the function with the lambda argument set to 0. 
    %       Do note that you will still need to use lambda when running
    %       the training to obtain the theta parameters.
    %
    % Hint: You can loop over the examples with the following:
    %
    %       for i = 1:m
    %           % Compute train/cross validation errors using training examples 
    %           % X(1:i, :) and y(1:i), storing the result in 
    %           % error_train(i) and error_val(i)
    %           ....
    %           
    %       end
    %
    
    for i = 1 : n
        % select the training set
        trainingX = X(1:i, :);
        trainingY = y(1:i, :);
        
        % train the model on the training set
        [theta] = trainLinearReg([ones(i, 1) trainingX], trainingY, lambda);
        
        % calculate the cost of this theta found
        [trainingCost, ~] = linearRegCostFunction([ones(i, 1) trainingX], trainingY, theta, 0);
        [validationCost, ~] = linearRegCostFunction([ones(length(yval), 1) Xval], yval, theta, 0);
       
        % record the cost for training and validation sets
        error_train(i) = trainingCost;
        error_val(i) = validationCost;
    end

end
