collaborative filtering

cf.m

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
                                  num_features, lambda)

% 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);

% You need to return the following values correctly
J = 0;
X_grad = zeros(size(X));
Theta_grad = zeros(size(Theta));

% Compute the cost function and gradient for collaborative filtering. 
% Implemented the cost function and gradient

J = sum(sum(R.*((X*Theta' - Y).^2)))/2 + ...
       (sum(sum(Theta.^2)) + sum(sum(X.^2)))*lambda/2;

X_grad = (R.*(X*Theta' - Y))*Theta + lambda.*X;

Theta_grad = (R.*(X*Theta' - Y))'*X + lambda.*Theta;

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

end