如何在Python中高效创建和处理4D稀疏矩阵

Question

I have a 4D sparse matrix of shape (21x21x21x21). Only one of the element will be set to 1. After which, I will vectorize this matrix and determine the non-zero row. The whole process takes about 6 mins to compute which is too long. Is there a way to do this efficiently in Python?

sparseMatrix = np.zeros((21,21,21,21), dtype = np.int8)
#w,x,y,z can be any random integer from 0 to 20.
w = 3
x = 5
y = 18
z = 16
sparseMatrix[w, x, y, z] = 1
sparseMatrix_vec = np.reshape(sparseMatrix, [-1,1])
sparseMatrix_vec_index = np.nonzero(sparseMatrix_vec)[0][0]

Answer 1

If you need (w,x,y,z) to form a unique integer, where each of (w,x,y,z) can vary between 0 and 20, then simply use base 21 representation. The integer you are looking for is:

N = w*(21 ** 0) + x*(21 ** 1) + y*(21 ** 2) + z*(21 ** 3).

Given an integer, you can go back to (w,x,y,z) by using integer division and modulus.