Python写雅可比迭代法

Python实现雅可比迭代法的代码如下：

import numpy as np

def jacobi(A, b, x0, tol=1e-6, max_iter=10000):
    """
    Jacobi iteration method for solving linear equation Ax=b,
    where A is a matrix, b is a vector, and x0 is the initial guess.

    Parameters
    ----------
    A : numpy.ndarray
        Coefficient matrix.
    b : numpy.ndarray
        Constant vector.
    x0 : numpy.ndarray
        Initial guess.
    tol : float, optional
        Tolerance for stopping criterion. The default is 1e-6.
    max_iter : int, optional
        Maximum number of iterations to perform. The default is 10000.

    Returns
    -------
    x : numpy.ndarray
        Solution vector.
    """
    D = np.diag(np.diag(A))
    L = -np.tril(A, k=-1)
    U = -np.triu(A, k=1)
    M = D
    N = L + U
    x = x0
    for i in range(max_iter):
        x_new = np.dot(np.linalg.inv(M), b - np.dot(N, x))
        if np.linalg.norm(x_new - x) < tol:
            return x_new
        x = x_new
    return x

其中，A是系数矩阵，b是常数向量，x0是初值，tol是容差，max_iter是最大迭代次数。函数返回解向量x。