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
m = size(X, 1);

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

  X_ = X(1:i,:);
  y_ = y(1:i);

  % Train with regularization
  lambda = 1;
  theta = trainLinearReg(X_, y_, lambda);

  % Compute the error with lambda = 0
  lambda = 0;
  error_train(i) = linearRegCostFunction(X_, y_, theta, lambda);
  error_val(i) = linearRegCostFunction(Xval, yval, theta, lambda);

end
%

% ---------------------- Sample Solution ----------------------


%       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