cost_logistic.m

function [J, grad] = cost_logistic(a, x, y)
% cost_logistic Compute cost and gradient for logistic regression
%   J = cost_logistic(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
N = length(x); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(a));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of a.
%               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
%

e = exp(1);
sigma = @(t) 1./(1 + e.^(-t));
a0 = a(1);
a1 = a(2);
t = a0+a1*x;

J = 1/N*sum(-y.*log(sigma(t))-(1-y).*log(1-sigma(t)));
grad(1) = 1/N*sum((sigma(t)-y).*x.^0);
grad(2) = 1/N*sum((sigma(t)-y).*x.^1);

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

end