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

h=sigmoid(X*theta);
shift_theta = theta(2:size(theta));
theta_reg = [0;shift_theta];


%J=(-1./m)*(sum(y.*log(h)+(1-y).*log(1-h)))+(lambda/(2*m))*sum(theta_reg.^2);  %without vectorization
J=(-1/m)*(y'*log(h)+(1-y)'*log(1-h))+(lambda/(2*m))*theta_reg'*theta_reg;      %with vectorization
grad=(1/m)*X'*(h-y)+(lambda/m).*theta_reg;
%grad=(1./m)*sum((h-y).*X)+(lambda/m).*theta;  %getting some error.






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

end