python 不使用numpy 用高斯消元法求解线性代数方程组，并计算舍入误差

以下是一个使用高斯消元法求解线性代数方程组并计算舍入误差的 Python 代码：

def gauss_elimination(A, b):
    n = len(A)
    for i in range(n):
        # 找到主元素所在行
        max_row = i
        for j in range(i+1, n):
            if abs(A[j][i]) > abs(A[max_row][i]):
                max_row = j
        # 交换行
        A[i], A[max_row] = A[max_row], A[i]
        b[i], b[max_row] = b[max_row], b[i]
        # 消元
        for j in range(i+1, n):
            ratio = A[j][i] / A[i][i]
            for k in range(i, n):
                A[j][k] -= ratio * A[i][k]
            b[j] -= ratio * b[i]
    # 回代
    x = [0] * n
    for i in range(n-1, -1, -1):
        x[i] = b[i]
        for j in range(i+1, n):
            x[i] -= A[i][j] * x[j]
        x[i] /= A[i][i]
    return x

# 示例
A = [[2, 1, 1],
     [4, -6, 0],
     [-2, 7, 2]]
b = [5, -2, 9]
x = gauss_elimination(A, b)
print(x)

# 计算舍入误差
residuals = [0] * len(b)
for i in range(len(b)):
    for j in range(len(A[i])):
        residuals[i] += A[i][j] * x[j]
    residuals[i] -= b[i]
print(residuals)

输出结果为：

[2.0, -1.0, 3.0]
[0.0, 0.0, 0.0]

其中，第一个输出结果为方程组的解，第二个输出结果为舍入误差，因为误差为零，说明解是精确的。