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
one = ones(length(y),1);
J = -sum(log(sigmoid(X*theta)).*y+log(one-sigmoid(X*theta)).*(one-y))/m + (theta'*theta-theta(1)^2)*lambda/(2*m);
grad = ((sigmoid(X*theta)-y)'*X/m)' + lambda*theta/m;
grad0= (sigmoid(X*theta)-y)'*X/m;
grad(1)=grad0(1);





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

end