Vectorized logistic regression with regularization using gradient descent for the Coursera course Machine Learning. Cost function (J) and partial derivatives of the cost w.r.t. each parameter in theta (grad).

lrCostFunction

len = size(theta);
J = 1/m*(-y'*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta))) + lambda/(2*m)*sum(theta(2:len).^2);

grad = 1./m*((sigmoid(X*theta)-y)'*X);
temp = theta;
temp(1) = 0;
grad = grad + (lambda/m.*temp)';