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 ======================
% ?????

for i = 1:m
  X_train = X(1:i,:);
  y_train = y(1:i,:);
  theta = trainLinearReg(X_train, y_train, lambda);  
  [error_train(i,:), grad] = linearRegCostFunction(X_train, y_train, theta, 0);
  [error_val(i,:), grad] = linearRegCostFunction(Xval, yval, theta, 0);  
endfor






% -------------------------------------------------------------

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

end