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
%
a=1/m;
d=0;
for I=1:m;
d+=-(y(I)*log(sigmoid(X(I,:)*theta)))-(1-y(I))*log(1-sigmoid(X(I,:)*theta));
end

J=a*d;

kum=0;
for j=2:size(theta);
kum+=theta(j)^2;

end;
 
kum=kum*lambda/(2*m);
J=J+kum;
%=======================================================================
grad1=zeros(size(theta));
for I=1:size(theta);
grad(I)=(1/m)*(X(:,I)')*(sigmoid(X*theta)-y);
if I != 1;
grad(I)+=(lambda*theta(I)/m);
end
end;


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

end