import numpy as np def Gausselimination(A, b): n = len(b) for k in range(n-1):…

import numpy as np

def Gauss_elimination(A, b): n = len(b) for k in range(n-1):

选取绝对值最大的元素作为主元素

max_index = np.argmax(np.abs(A[k:n, k])) + k if max_index != k:

交换第k行和第max_index行

A[[k, max_index], :] = A[[max_index, k], :] b[[k, max_index]] = b[[max_index, k]]

消元

for i in range(k+1, n): factor = A[i, k] / A[k, k] A[i, k:n] -= factor * A[k, k:n] b[i] -= factor * b[k]

回代

x = np.zeros(n) x[-1] = b[-1] / A[-1, -1] for i in range(n-2, -1, -1): x[i] = (b[i] - np.dot(A[i, i+1:], x[i+1:])) / A[i, i] return x

输入系数矩阵A和常数向量b

A = np.array([ [1.1348, 3.8326, 1.1651, 3.4017], [0.5301, 1.7875, 2.5330, 1.5435], [3.4129, 4.9317, 8.7643, 1.3142], [0.2371, 4.998, 10.6721, 0.0147]])

b = np.array([9.5342, 6.3941, 18.4231, 16.9237])

调用Gauss_elimination函数求解

x = Gauss_elimination(A, b)

输出结果

print(“解为：”, x)

在以上代码每一行后面注释