写出一个函数高斯消除Gauss_elimination
时间: 2023-05-28 14:06:54 浏览: 67
def Gauss_elimination(A, b):
n = len(A)
for i in range(n):
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]
for j in range(i + 1, n):
factor = A[j][i] / A[i][i]
for k in range(i + 1, n):
A[j][k] -= factor * A[i][k]
b[j] -= factor * b[i]
x = [0] * n
for i in range(n - 1, -1, -1):
x[i] = b[i] / A[i][i]
for j in range(i):
b[j] -= A[j][i] * x[i]
return x
相关问题
jupyter写出高斯消除算法Gauss_elimination(A)
很高兴为您提供高斯消除算法的Jupyter代码:
```python
import numpy as np
def Gauss_elimination(A):
'''
高斯消元法解线性方程组
A: 系数矩阵
return: 解向量x
'''
n = len(A)
# 高斯消元
for i in range(n-1):
for j in range(i+1, n):
factor = A[j][i] / A[i][i]
for k in range(i+1, n):
A[j][k] -= factor * A[i][k]
A[j][i] = 0
A[j][n] -= factor * A[i][n]
# 回代求解
x = np.zeros(n)
x[n-1] = A[n-1][n] / A[n-1][n-1]
for i in range(n-2, -1, -1):
sum = A[i][n]
for j in range(i+1, n):
sum -= A[i][j] * x[j]
x[i] = sum / A[i][i]
return x
```
该函数接收一个系数矩阵A作为参数,返回线性方程组的解向量x。在函数中,首先进行高斯消元,将系数矩阵A化为上三角矩阵。然后进行回代,求解出线性方程组的解向量x。
import numpy as np def gauss_elimination(A): n = A.shape[0] U = A.copy() L = np.eye(n) for i in range(n): for j in range(i+1, n): k = U[j][i] / U[i][i] L[j][i] = k U[j][i:] -= k * U[i][i:] return L, U
看起来这段代码是一个正确的高斯消元实现,没有明显的语法错误。如果你遇到了报错,可能是由于调用这个函数的代码存在问题。以下是一个示例代码,演示如何调用这个函数:
```python
import numpy as np
def gauss_elimination(A):
n = A.shape[0]
U = A.copy()
L = np.eye(n)
for i in range(n):
for j in range(i+1, n):
k = U[j][i] / U[i][i]
L[j][i] = k
U[j][i:] -= k * U[i][i:]
return L, U
# 生成一个随机的4x4的方阵
A = np.random.rand(4, 4)
# 调用高斯消元函数
L, U = gauss_elimination(A)
# 输出结果
print("原矩阵A:\n", A)
print("下三角矩阵L:\n", L)
print("上三角矩阵U:\n", U)
print("L * U:\n", np.dot(L, U))
```
你可以尝试运行这段代码,看看是否能够正常输出结果。如果还有其他问题,请告诉我。