How to pack the elements of product of matrix multiplication back

Question

A beginner to Python, I am trying to work my way into understanding how to do things in as Pythonic a way as possible.

I am attempting to write a function to which returns result of matrix multiplication of 2 matrices. here's what I came up with:

 def matmul(a,b):
     c = zip(*b)
     def element(i,j):
         return reduce(lambda x,y: x+y,map(lambda x:x[0]*x[1],zip(a[i],c[j])))
     print [element(i,j) for i in range(len(a)) for j in range(len(c))]

The list that I am printing contains the product of each element of the product, but it's a list not a matrix.

>>> a = [[1,2],[3,4]]
>>> b = [[1,1],[1,1]]
>>> matmul(a,b)
[3, 3, 7, 7] 
>>> a = [[1,1,1],[2,2,2],[3,3,3]]
>>> b = [[1,8,7],[8,7,11],[7,8,2]]
>>> matmul(a,b)
[16, 23, 20, 32, 46, 40, 48, 69, 60]

[3,3,7,7] should be actually be represented as [[3,3],[7,7]] and [16, 23, 20, 32, 46, 40, 48, 69, 60] as [[16, 23, 20],[32, 46, 40],[48, 69, 60]]

But, I am not able to think of a concise way to pack the list back into 2D.

How would I easily and concisely go about doing so ?

Answer 1

You were very close, you just need to use a nested list-comprehension with zip(*) :

zip(*[[element(i,j) for i in range(len(a))] for j in range(len(c))])

A re-factored version of your code:

from operator import mul
from itertools import starmap, izip, imap

def matmul(a, b):
     c = zip(*b)
     def element(row):
         # or   [sum(map(mul, row, col)) for col in c]  
         # or   [sum(imap(mul, row, col)) for col in c]  
         return [sum(starmap(mul, izip(row, col))) for col in c]
     print [element(row) for row in a]

---

Most concise way will be use numpy.matrix :

>>> import numpy as np
>>> a = np.matrix([[1,2],[3,4]])
>>> b = np.matrix([[1,1],[1,1]])
>>> a * b
matrix([[3, 3],
        [7, 7]])

---

In Python 3.5(not released yet) we will be able to use the @ operator on Python lists to do matrix multiplications .