给我一段高斯消元法的python代码

以下是高斯消元法的 Python 代码实现：

import numpy as np

def gaussian_elimination(A, b):
    n = len(A)
    for i in range(n):
        # Find pivot row and swap
        max_row = i
        for j in range(i+1, n):
            if abs(A[j][i]) > abs(A[max_row][i]):
                max_row = j
        A[i], A[max_row] = A[max_row], A[i]
        b[i], b[max_row] = b[max_row], b[i]
        
        # Eliminate
        for j in range(i+1, n):
            scale = A[j][i] / A[i][i]
            b[j] -= scale * b[i]
            for k in range(i, n):
                A[j][k] -= scale * A[i][k]
    
    # Back substitution
    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = (b[i] - np.dot(A[i][i+1:], x[i+1:])) / A[i][i]
    
    return x

其中，`A` 是系数矩阵，`b` 是常数向量。在函数中，首先进行了行交换以确保主元素是最大的。然后进行消元操作，最后使用回代法计算出解向量 `x`。