难以理解Python中的矩阵运算

Question

Starting with an initial guess of a randomly created 4×4 binary matrix, write a code snippet that does the following over 100 iterations:

1. choose a random element of the matrix, and create a new matrix which is equal to the old matrix with one randomly chosen digit flipped (from 0 to 1, or vice versa);
2. If the new matrix has smaller objective value than the old matrix, replace with the new matrix, otherwise, remain at the present matrix.

Print the final 4×4 matrix and the value of the determinant found at the end of 100 iterations.

import numpy as np
MOld = np.random.randint(2, size=[4,4])
for j in range(100): #for loop over 100 iterations
    MNew = np.array(MOld) #new matrix equal to old matrix
    i,j = np.random.randint(4), np.random.randint(4) #choosing random elements of the matrix.
    MNew[i,j] = 1 - MNew[i,j] #do not understand this
    if f(MNew) < f(MOld): #if new matrix < old matrix
        MOld = MNew #replacing value

print(MOld) #printing original 4x4 matrix
print(f(MOld)) #printing determinant value

I am trying to improve my understanding of this code, if anyone could please check my comments after the hashtag #, I would be grateful.

In particular I do not understand this this step:

MNew[i,j] = 1 - MNew[i,j]

Thank you for any help in advance.

Answer 1

The step:

If MNew[i,j] was 1 then MNew[i,j] is now 1 - 1 = 0.
If MNew[i,j] was 0 then Mnew[i,j] is now 1 - 0 = 1

So you see it is a way to flip the value from the previous iteration.