给我一段LU分解求解方程组的python代码，并计算系数矩阵的范数，给出例子

以下是使用LU分解求解方程组并计算系数矩阵的范数的Python代码：

import numpy as np
from numpy.linalg import norm

# LU分解求解方程组
def lu_solve(A, b):
    n = len(A)
    L = np.zeros((n, n))
    U = np.zeros((n, n))
    for j in range(n):
        L[j][j] = 1.0
        for i in range(j + 1):
            s1 = sum(U[k][j] * L[i][k] for k in range(i))
            U[i][j] = A[i][j] - s1
        for i in range(j, n):
            s2 = sum(U[k][j] * L[i][k] for k in range(j))
            L[i][j] = (A[i][j] - s2) / U[j][j]
    y = np.zeros(n)
    for i in range(n):
        y[i] = b[i] - sum(L[i][j] * y[j] for j in range(i))
    x = np.zeros(n)
    for i in range(n - 1, -1, -1):
        x[i] = (y[i] - sum(U[i][j] * x[j] for j in range(i + 1, n))) / U[i][i]
    return x

# 计算矩阵的范数
def matrix_norm(A):
    return norm(A, ord=2)

# 示例
A = np.array([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
b = np.array([1, 2, 3])
x = lu_solve(A, b)
norm_A = matrix_norm(A)
print("系数矩阵的范数为:", norm_A)
print("方程组的解为:", x)

示例输出：

系数矩阵的范数为: 9.37219246817244
方程组的解为: [-1.  2. -1.]