Matrix question with python

[pythonstarter]

Is there an way to create matrix[a][c][d] in python? It seems that you can write this way in Perl but not Python? Thanks!

[Gribouillis]

A 2 dimensional matrix can easily be implemented as a list of lists

M = [
    [0, 1, 2],  # first row
    [3, 4, 5],  # second row
    [6, 7, 8], # third row
]

For heavy computations with matrices, there is a specialized module numpy .

[pythonstarter]

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!

[Gribouillis]

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)

[pythonstarter]

The code works great! But I am not quite understand how zero_matrix function, could you explain a little bit? Thanks a lot!

[Gribouillis]

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 :)

[pythonstarter]

Well done! I know it all about leap of faith with recursion happened. Your explanation is great, thanks again.

[TrustyTony]

You might find it usefull to use my pretty print function to print out your matrixes:
http://www.daniweb.com/code/snippet281208.html

[TrustyTony]

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'

[TrustyTony]

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

print("%i values" % len(mdict))