Week3.costFunction

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));
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives(偏导数) 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 = -1/m * sum( y.*log(h) + (1-y).*log( 1 - h ));
grad = 1/m * (X'*(h-y));
% =============================================================

end