请帮我用python代码解决以下问题。【问题描述】已知矩阵A,LU分解法求解Q矩阵(Q=L+U-I) 【输入形式】任意阶矩阵A按行输入 【输出形式】Q矩阵一行一行输出,结果保留小数点后3位 【样例输入】 2.0 1 5 4 1 12 -2 -4 5 【样例输出】 2.000 1.000 5.000 2.000 -1.000 2.000 -1.000 3.000 4.000 【样例说明】3阶矩阵A元素2.0 4 -2 1 1 -4 5 12 5
时间: 2024-02-26 14:57:37 浏览: 14
以下是用Python实现LU分解法求解Q矩阵的代码:
```python
import numpy as np
# 读入矩阵A
A = []
while True:
try:
row = input().strip().split()
row = [float(x) for x in row]
A.append(row)
except:
break
A = np.array(A)
# LU分解
n = A.shape[0]
L = np.zeros((n, n))
U = np.zeros((n, n))
for j in range(n):
L[j, j] = 1
for i in range(j, n):
U[j, i] = A[j, i] - L[j, :j] @ U[:j, i]
for i in range(j+1, n):
L[i, j] = (A[i, j] - L[i, :j] @ U[:j, j]) / U[j, j]
# 计算Q矩阵
Q = L + U - np.eye(n)
Q = np.around(Q, decimals=3)
# 输出Q矩阵
for i in range(n):
print(" ".join([str(x) for x in Q[i, :]]))
```
输入样例:
```
2.0 1 5
4 1 12
-2 -4 5
```
输出样例:
```
2.0 1.0 5.0
2.0 -1.0 2.0
-1.0 3.0 4.0
```