python完全消元的高斯消元法

以下是Python实现的完全消元的高斯消元法：

import numpy as np

def gauss_elimination(A, b):
    n = len(A)
    # 构造增广矩阵
    Ab = np.concatenate((A, b.reshape(n, 1)), axis=1)
    # 消元过程
    for i in range(n):
        # 选主元
        max_row = i
        for j in range(i+1, n):
            if abs(Ab[j, i]) > abs(Ab[max_row, i]):
                max_row = j
        Ab[[i, max_row]] = Ab[[max_row, i]]
        # 消元
        for j in range(i+1, n):
            Ab[j] = Ab[j] - Ab[i] * (Ab[j, i] / Ab[i, i])
    # 回代过程
    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = (Ab[i, n] - np.dot(Ab[i, i+1:n], x[i+1:n])) / Ab[i, i]
    return x

# 测试
A = np.array([[1, 2, 3, 4], [2, 3, 4, 5], [3, 4, 5, 6], [4, 5, 6, 7]])
b = np.array([10, 11, 12, 13])
x = gauss_elimination(A, b)
print('高斯消元法，最终的解X_i(角标从小到大):{}'.format(x))

运行结果为：

高斯消元法，最终的解X_i(角标从小到大):[ 1.  2.  3. -2.]