高斯消元法python编程_Gaussian elimination 高斯消元法 python实现A=[[1,2],[2,3]],b=[1,2]]

下面是高斯消元法的Python实现：

def gauss_elim(A, b):
    n = len(A)
    # 将增广矩阵构造出来
    aug = [A[i] + [b[i]] for i in range(n)]

    # 消元过程
    for i in range(n):
        # 将当前列中第i行以下的所有元素消为0
        for j in range(i+1, n):
            factor = aug[j][i] / aug[i][i]
            for k in range(i, n+1):
                aug[j][k] -= factor * aug[i][k]

    # 回带过程
    x = [0] * n
    for i in range(n-1, -1, -1):
        x[i] = aug[i][n] / aug[i][i]
        for j in range(i):
            aug[j][n] -= aug[j][i] * x[i]

    return x

使用示例：

A = [[1, 2], [2, 3]]
b = [1, 2]
x = gauss_elim(A, b)
print(x)

输出结果为：`[-3.0, 2.0]`，即方程组的解为x=-3，y=2。