满足特定条件的随机矩阵 3 x 3 生成器的算法（最好在 Python 或伪代码中）

Question

How to generate a random 3x3 matrix that satisfies a condition that the sum of column n is equal to the sum of row n .

For instance, here is the illustration of matrix that satisfied the condition:

column 1	column 2	column 3
a	b	c
d	e	f
g	h	i

should satisfies:

1. a + b + c = a + d + g
2. d + e + f = b + e + h
3. g + h + i = c + f + i

I need a scratch of the pseudocode of those algorithm.

Answer 1

You have 9 variables with 3 constraints, meaning you can only choose 6 of them freely, so generate 6 random numbers and calculate the rest 3.

import numpy as np
mat = np.random.normal(size = (3,3))
for i in range(3):
    mat[-1, i] = mat[i, :].sum() - mat[:2, i].sum()
for i in range(3):
    print(mat[i, :].sum() - mat[:, i].sum())

0.0
0.0
0.0

Answer 2

One approach is to generate random numbers for a, b, c, d, e and f, then calculate the rest based on the equations.