costFunction.m

function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for 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));
n = size(theta,1);

% ====================== 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
%
% Note: grad should have the same dimensions as theta
%

h = sigmoid(X*theta);
J = ( (-y)' *log(h)-(1-y)' * log(1-h))/m;



% Implementation 1
for i=1:m,
  hx = sigmoid(theta'*X(i,:)');
  temp = hx - y(i);   
  for j=1:n,  	
    grad(j) = grad(j) + temp * X(i,j); 
  end;
end;
grad = grad/m;






%grad = (X'*(h - y))/m;



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

end