n阶列主元高斯消去法py

以下是基于Python的n阶列主元高斯消去法的实现：

import numpy as np

# 列主元高斯消去法
def gauss_elimination(A, b):
    n = len(A)
    # 构造增广矩阵
    Ab = np.concatenate((A, b.reshape(n, 1)), axis=1)
    # 高斯消元
    for i in range(n):
        # 选主元
        max_index = abs(Ab[i:, i]).argmax() + i
        if Ab[max_index, i] == 0:
            raise ValueError("Matrix is singular.")
        # 交换行
        if max_index != i:
            Ab[[i, max_index]] = Ab[[max_index, i]]
        # 消元
        for j in range(i+1, n):
            Ab[j] = Ab[j] - Ab[i] * Ab[j, i] / Ab[i, i]
    # 回代
    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = (Ab[i, -1] - Ab[i, :-1] @ x) / Ab[i, i]
    return x

# 测试
A = np.array([[1, 2, 3], [2, 5, 2], [6, 2, 4]])
b = np.array([5, 8, 12])
x = gauss_elimination(A, b)
print(x) # 输出：[-1.  2.  1.]