cofiCostFunc.m

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
                                  num_features, lambda)
  %COFICOSTFUNC Collaborative filtering cost function
  %   [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
  %   num_features, lambda) returns the cost and gradient for the
  %   collaborative filtering problem.
  %

  % Unfold the U and W matrices from params
  X = reshape(params(1:num_movies*num_features), num_movies, num_features);
  Theta = reshape(params(num_movies*num_features+1:end), ...
                  num_users, num_features);

  J = 1/2 * sum(sum((R.* ((X*Theta') - Y)).^2));
  X_grad = (R .* (X*Theta' - Y)) * Theta;
  Theta_grad = (R .* (X*Theta' - Y))' * X;

  % With regularization
  J = J + lambda/2 * (sum(sum(Theta.^2)) + sum(sum(X.^2)));
  X_grad = X_grad + lambda * X;
  Theta_grad = Theta_grad + lambda * Theta;

  grad = [X_grad(:); Theta_grad(:)];
end