多维蒙特卡罗方法

Question

I am trying to evaluate the following multidimensional integral:

Integral

with the answer being 155/6. However the Python code I've used:

Attempted Code

doesn't work. How do I correct or what code should I do instead?

Answer 1

You have couple of bugs in your code.

Most important one is when you square point first and sum later, not as shown in formula. Then you divide by 'n' which is undefuned.

Here is correct code

import numpy as np

rng = np.random.default_rng()

D = 10
N = 1000000

I = 0.0

for k in range(0, N):
    pt = rng.random(D)
    I += np.sum(pt)**2

print(I/N*6.0/155.0)

On Python 3.8.5 x64, windows 10, it prints

0.9996726183447514