function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

J = ( ( 1 / m ) * sum( -y' * log( sigmoid( X*theta ) ) - ( 1 - y )' * log( 1 - sigmoid( X * theta) ) ) ) + ( lambda / ( 2 * m ) ) * sum( theta( 2:length(theta) ) .* theta( 2:length(theta) ) );
grad = ( 1 / m ) * sum( X .* repmat( ( sigmoid( X * theta ) - y ), 1, size( X, 2 ) ) );
grad( :, 2:length(grad) ) = grad( :, 2:length(grad) ) + ( lambda / m ) * theta( 2:length(theta) )';

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

end
