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


g=sigmoid(X*theta);

for i=1:m,

  J= J + (-y(i)*log(g(i))-(1-y(i))*log(1-g(i)));

endfor
  
J = J/m;

L=0;

for i=2:size(theta),
  L=L+ theta(i)*theta(i);  
endfor

L = L*lambda/(2*m);
J=J+L;
  
for i=1:size(theta,1),  
  for j=1:m,
    grad(i)= grad(i)+(g(j)-y(j))*X(j,i);
  endfor
endfor

grad =grad./m;

for(i=2:size(theta))
grad(i) = grad(i) + (lambda/m).*theta(i);

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

end