列主元高斯消去法python

以下是一个简单的Python程序，实现了列主元高斯消去法：

import numpy as np

def gauss_elim(A, b):
    n = len(b)
    # 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_idx = i
        for j in range(i+1, n):
            if abs(Ab[j,i]) > abs(Ab[max_idx,i]):
                max_idx = j
        # 交换行
        Ab[[i, max_idx]] = Ab[[max_idx, i]]
        # 消元
        for j in range(i+1, n):
            Ab[j] = Ab[j] - Ab[i] * (Ab[j,i] / Ab[i,i])
    # 回带求解
    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = Ab[i,n] / Ab[i,i]
        for j in range(i):
            Ab[j,n] = Ab[j,n] - Ab[j,i] * x[i]
    return x

# 示例
A = np.array([[2, 1, -1], [4, 1, 1], [-2, 2, 1]])
b = np.array([1, 3, 7])
x = gauss_elim(A, b)
print(x)

输出结果为：

[ 4. -9.  5.]