learningCurve.m

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);

  error_train = zeros(m, 1);
  error_val   = zeros(m, 1);

  for i = 1:m
    [X_train, Y_train] = rangeSet(X, y, i);
    theta = trainLinearReg(X_train, Y_train, lambda);
    error_train(i) = linearRegCostFunction(X_train, Y_train, theta, 0);
    error_val(i) = linearRegCostFunction(Xval, yval, theta, 0);
  endfor
  
  function [X_set, Y_set] = rangeSet(X, y, index)
    X_set = X(1:index, :);
    Y_set = y(1:index);
  endfunction
end