此Jacobi方法程序是否有效？

我试图制作一个python函数来模拟Jacobi线性系统对Ax = b的求解，以实现近似误差的最大容限和最大迭代次数。 我的代码如下

import numpy as np
import numpy.linalg as nla


def jacobi_iterative(A, b, tolerance, max_it):  # a_ii!= 0 for all i
    n = A.shape[0]
    x = np.zeros(np.shape(b))
    err = 1.0
    it_num = 0
    while it_num < max_it:
        for i in range(n):
            x_k = x.copy()
            temp_i_row = A[i, :].copy()
            temp_i_row[i] = 0.0
            x_k[i] = (-1) * (1 / A[i][i]) * (np.dot(temp_i_row, x_k) + b[i])
        err = nla.norm(x_k - x, np.inf) / nla.norm(x_k, np.inf)
        if err < tolerance:
            x = x_k
            it_num += 1
            break
        else:
            x = x_k
            it_num += 1
    return x, err, it_num

但我不确定它是否能正常工作