% 说明：grad_check 参数
% fun为函数
% num_checks 检查次数
% varagin为参数列 var1,var2,var3...这个varagin必须放在function最后一个项
function average_error = grad_check(fun, theta0, num_checks, varargin)

  delta=1e-3; 
  sum_error=0;

  fprintf(‘ Iter       i             err‘);
  fprintf(‘           g_est               g               f\n‘)

  for i=1:num_checks
    T = theta0;
    j = randsample(numel(T),1);
    T0=T; T0(j) = T0(j)-delta;
    T1=T; T1(j) = T1(j)+delta;

    [f,g] = fun(T, varargin{:}); %由于fun是linear_regression或logistic_regression
    f0 = fun(T0, varargin{:});   %所以这里的varagin{:}参数为train.X,train.y 
    f1 = fun(T1, varargin{:});

    g_est = (f1-f0) / (2*delta);
    error = abs(g(j) - g_est);

    fprintf(‘% 5d  % 6d % 15g % 15f % 15f % 15f\n‘, ...
            i,j,error,g(j),g_est,f);

    sum_error = sum_error + error;
  end

  average_error =sum_error/num_checks;

% Gradient Check
average_error = grad_check(@linear_regression_vec,theta,50,train.X,train.y);
fprintf(‘Average error :%f\n‘,average_error);