function [J, grad] = lrCostFunction(theta, X, y, lambda)
%LRCOSTFUNCTION Compute cost and gradient for logistic regression with %regularization
%   J = LRCOSTFUNCTION(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
%
% Hint: The computation of the cost function and gradients can be
%       efficiently vectorized. For example, consider the computation
%
%           sigmoid(X * theta)
%
%       Each row of the resulting matrix will contain the value of the
%       prediction for that example. You can make use of this to vectorize
%       the cost function and gradient computations.
%
% Hint: When computing the gradient of the regularized cost function,
%       there're many possible vectorized solutions, but one solution
%       looks like:
%           grad = (unregularized gradient for logistic regression)
%           temp = theta;
%           temp(1) = 0;   % because we don't add anything for j = 0
%           grad = grad + YOUR_CODE_HERE (using the temp variable)
%

% Cost function
h = sigmoid(X * theta);
theta1 = [0; theta(2:size(theta)) ];

cost = (1 / m) * sum( (-y .* log(h)) - ((1 - y) .* log(1 - h)) );
reg_cost = (lambda / (2 * m)) .* (theta1' * theta);

J = cost + reg_cost;

grad = (1 / m) * X' * (h - y);
reg_grad = (lambda / m) .* theta1;

grad = grad + reg_grad;



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

grad = grad(:);

end
