function check_grad(f, x0, varargin)
% a simple function that checks the correctness of gradient. 
% INPUT
%  f  - a function handle of f(x) that returns function values and gradients given parameter x 
%  x0 - the location near which the gradient will be evaluted. 

% For a correct gradiet, the displayed ratio should be near 1.0  
%
% to check why the code works there is a useful link:
%    http://ufldl.stanford.edu/tutorial/supervised/DebuggingGradientChecking/
%
% Jiayu, Dec 2, 2015

delta = rand(size(x0));
delta = delta ./ norm(delta);
epsilon = 10.^[-7:-1];

[f0, df0] = feval(f, x0, varargin{:});

for i = 1:length(epsilon)
    [f_left] = feval(f, x0-epsilon(i)*delta, varargin{:});
    [f_right] = feval(f, x0+epsilon(i)*delta, varargin{:});
    ys(i) = (f_right - f_left) / 2;
    ys_hat(i) = df0' * epsilon(i)*delta;    
    fprintf('epsilon: %d , gradient: %d \n', epsilon(i), ys(i) / ys_hat(i));
end