用python写雅可比迭代法的代码

以下是使用Python实现雅可比迭代法的代码示例：

import numpy as np

def jacobi_iteration(A, b, max_iterations=100, tolerance=1e-7):
    """
    使用雅可比迭代法求解Ax = b的线性方程组

    Args:
        A (ndarray): n x n的系数矩阵
        b (ndarray): n个常数值的向量
        max_iterations (int, optional): 迭代的最大次数. Defaults to 100.
        tolerance (float, optional): 迭代停止的绝对误差. Defaults to 1e-7.

    Returns:
        x (ndarray): n维向量, 表示Ax = b的解
        iterations (int): 迭代次数
    """

    n = len(b)
    x = np.zeros(n)
    x_new = np.zeros(n)

    # 记录迭代次数
    iterations = 0

    # 迭代过程
    while iterations < max_iterations:
        for i in range(n):
            s = 0
            for j in range(n):
                if j != i:
                    s += A[i][j] * x[j]
            x_new[i] = (b[i] - s) / A[i][i]

        # 判断绝对误差是否小于预设值
        if np.abs(x - x_new).max() < tolerance:
            return x_new, iterations

        # 更新迭代解
        x = x_new.copy()

        # 迭代次数加1
        iterations += 1

    # 迭代次数已达到最大值, 返回当前的迭代解和迭代次数
    return x_new, iterations

使用方法：

A = np.array([[5, 1, 1],
              [1, 5, 1],
              [1, 1, 5]])
b = np.array([7, 7, 7])
x, iterations = jacobi_iteration(A, b)
print("解:", x)
print("迭代次数:", iterations)