Sorry I didn't make myself clear, I think it is like 4D matrix, so I can get an element like M[1][2][3][4], with list of list, it seems still 2D. Can I just nest list to reach 4D? Also how to iterate the matrix for initialization seems quite a task. Thanks!

It's not at all difficult, here is a code which creates a 4-dimensional tensor of size 2 x 4 x 3 x 2

# python 2 or 3
def zero_matrix(shape):
if len(shape) == 1:
return [0] * shape[0]
else:
return [zero_matrix(shape[1:]) for i in range(shape[0])]
if __name__ == "__main__":
M = zero_matrix((2, 4, 3, 2))
print(M)

It is a recursive function. The 'shape' argument is a non empty tuple like (2, 4, 3, 2).
Suppose by induction on the length of 'shape' that zero_matrix returns a tensor with the given shape.
Then in line 6, shape[1:] is (4, 3, 2), and shape[0] is 2, so zero_matrix((4, 3, 2)) is called 2 times in line 6, which creates a list of two 3-dimensional matrices. This list is returned and this is our matrix M.

Each call to zero_matrix((4, 3, 2)) returns a list of 4 matrices with shape (3, 2). Finally, each call
to zero_matrix((3,2)) returns a list of 3 matrices of shape (2,): here we are in the limit case where the
length of the shape tuple is 1, and a list of two 0's is returned in line 4 :)

Alternative in native Python for nested lists as matrix is the dictionary with tuple key:

# python 2 or 3
import itertools
try:
from pretty import ppr as pprint
except:
from pprint import pprint
def zero_matrix(shape):
return [zero_matrix(shape[1:])
for i in range(shape[0])] if len(shape) > 1 else [0] * shape[0]
def zero_dict(shape):
# with dict:
return dict([(tuple(values), 0)
for values in itertools.product(*(range(dimension) for dimension in shape))])
if __name__ == "__main__":
M = zero_matrix((2, 4, 3, 2))
pprint(M)
print('-'*40)
mdict = zero_dict((2,4,3,2))
pprint(mdict)
print len(mdict), 'values'

Line
print len(mdict), 'values'
does not work in Python 3, to make print which work in bot Python 2 and three without from __future__ import print_function, we can use

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