lu三角分解法解方程组python代码

以下是使用LU分解法求解线性方程组的Python代码：

import numpy as np

def LU_decomposition(A):
    n = A.shape[0]
    L = np.eye(n)
    U = A.copy()

    for k in range(n-1):
        for i in range(k+1, n):
            if U[i,k] != 0.0:
                lam = U[i,k]/U[k,k]
                U[i,k+1:n] = U[i,k+1:n] - lam*U[k,k+1:n]
                L[i,k] = lam
    return L, U

def solve(A, b):
    L, U = LU_decomposition(A)
    y = np.zeros_like(b)
    n = A.shape[0]

    # Solve Ly = b
    for i in range(n):
        y[i] = b[i]
        for j in range(i):
            y[i] -= L[i,j]*y[j]
        y[i] /= L[i,i]

    # Solve Ux = y
    x = np.zeros_like(b)
    for i in range(n-1, -1, -1):
        x[i] = y[i]
        for j in range(i+1, n):
            x[i] -= U[i,j]*x[j]
        x[i] /= U[i,i]

    return x

其中，`LU_decomposition`函数用于计算矩阵A的LU分解，返回L和U矩阵。`solve`函数用于求解线性方程组Ax=b，先利用L矩阵求解Ly=b，再利用U矩阵求解Ux=y。最终返回x向量作为方程组的解。