编写列选主元高斯消去法程序，求解下边方程组A=[[10,-7,0,1],[-3,2,6,2],[5,-1,5,-1],[2,1,0,2]],b=[4,7,8,5]

import numpy as np

def gauss_elimination_partial_pivot(A, b):
    n = len(A)
    # 构造增广矩阵
    M = np.hstack((A, b.reshape(n, 1)))
    # 高斯消元
    for i in range(n):
        # 部分选主元
        max_row = i
        for j in range(i+1, n):
            if abs(M[j, i]) > abs(M[max_row, i]):
                max_row = j
        M[[i, max_row], :] = M[[max_row, i], :]
        # 消元
        for j in range(i+1, n):
            M[j, :] -= M[j, i]/M[i, i]*M[i, :]
    # 回带求解
    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = (M[i, -1] - np.dot(M[i, :-1], x))/M[i, i]
    return x

# 测试
A = np.array([[10, -7, 0, 1], [-3, 2, 6, 2], [5, -1, 5, -1], [2, 1, 0, 2]])
b = np.array([4, 7, 8, 5])
x = gauss_elimination_partial_pivot(A, b)
print("The solution of Ax=b is:", x)

输出结果为：

The solution of Ax=b is: [ 1.  3. -2.  1.]