为什么传递一个数组的副本仍然会改变原始数组的值？

Question

在下面的main方法，

月1日：我试图通过a.copy()和b.copy()作为参数。虽然solve_linear_equations方法返回了有效的解决方案，但它仍然篡改原始参数a[][]和b[]。

第二：然后，我试图定义两个不同的变量，如tmp_a = a.copy()和tmp_b = b.copy()。使用这些新变量作为方法参数也没有帮助：不总是，但通常，该方法篡改原始数组值a[][]和b[]。

我认为，Python内部存在一些棘手的问题，我无法实现。有人可以举手吗？

import random 


def data_create(n): 
    a, x, b = [], [], [] 

    for i in range(n): 
    a.append([]) 
    s = random.randint(0, 2) 
    x.append(random.randint(0, 1000)/1000) 

    if s: 
     x[i] *= -1 

    for j in range(n): 
     s = random.randint(0, 2) 
     a[i].append(random.randint(0, 1000)/1000) 

     if s: 
     a[i][j] *= -1 

    for i in range(n): 
    b.append(0.0) 

    for j in range(n): 
     b[i] += a[i][j] * x[j] 

    return a, x, b 


def solve_linear_equations(n, a, x): 
    for i in range(n - 1): 
    max_row = i 
    max_val = abs(a[i][i]) 

    for j in range(i + 1, n): 
     if abs(a[j][i]) > max_val: 
     max_val = abs(a[j][i]) 
     max_row = j 

    if max_row != i: 
     x[i], x[max_row] = x[max_row], x[i] 
     a[i], a[max_row] = a[max_row].copy(), a[i].copy() 

    x[i] /= a[i][i] 

    for j in range(i + 1, n): 
     a[i][j] /= a[i][i] 

    a[i][i] = 1.0 

    for j in range(i + 1, n): 
     x[j] -= x[i] * a[j][i] 

     for k in range(i + 1, n): 
     a[j][k] -= a[i][k] * a[j][i] 

     a[j][i] = 0.0 

    x[n - 1] /= a[n - 1][n - 1] 
    a[n - 1][n - 1] = 1.0 

    for i in range(n - 1, 0, -1): 
    for j in range(i - 1, -1, -1): 
     x[j] -= x[i] * a[j][i] 

     for k in range(i, n): 
     a[j][k] -= a[i][k] * a[j][i] 

    return x 


def main(): 
    n = 3 
    a, x, b = data_create(n) 

    print("x\n", x) 
    print("a\n", a) 
    print("b\n", b, "\n") 

    tmp_a = a.copy() # creating a copy of a[][] 
    tmp_b = b.copy() # creating a copy of b[] 

    print("tmp_a\n", tmp_a) 
    print("tmp_b\n", tmp_b, "\n") 

    print("x\n", solve_linear_equations(n, tmp_a, tmp_b)) 
    print("a\n", a) 
    print("b\n", b, "\n") 


if __name__ == "__main__": 
    main() 

Answer 1

而不是

tmp_a = a.copy() # creating a copy of a[][] 
    tmp_b = b.copy() # creating a copy of b[] 

做

import copy 
... 
tmp_a = copy.deepcopy(a) # creating a deep copy of a[][] 
tmp_b = copy.deepcopy(b) # creating a deep copy of b[] 

这是因为list.copy()只到达下一层，并且看到不必要的更改两级下来。