costFunctionReg.m

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

thetaReg = theta;
thetaReg(1) = 0;
J = (-1/m) * sum ( (y.*log (sigmoid(X * theta))) + ((1-y).*log (1-sigmoid(X * theta)))) + ((lambda/(2*m)) * sum((thetaReg).^2));
grad = (1/m) * (X'*((sigmoid(X * theta)) - y)) + ((lambda/m) * (thetaReg));
% =============================================================

end