请写出蒙特卡洛方法求二重积分的matlab程序

function [I, err] = monte_carlo_double(f, a, b, c, d, n) % MONTE_CARLO_DOUBLE - Monte Carlo method for double integration % % I = monte_carlo_double(f, a, b, c, d, n) approximates the double % integral of f(x,y) over the rectangle [a,b]x[c,d] using n random % samples. The output I is the estimated value of the integral. % % [I, err] = monte_carlo_double(f, a, b, c, d, n) also returns the % estimated error in the approximation.

% Generate n random points in [a,b]x[c,d] x = a + (b-a)*rand(n,1); y = c + (d-c)*rand(n,1);

% Evaluate function at the random points z = f(x,y);

% Approximate integral using Monte Carlo method I = (b-a)*(d-c)*mean(z);

% Compute estimated error in the approximation err = (b-a)*(d-c)*std(z)/sqrt(n); en