Understanding reduce with enumerate for a list of lists

I am trying to multiply the first number, 1, of the first list, the second number of the second list, 5, and so on for a list of lists. For example, for [[1, 2, 3], [4, 5, 6], [7, 8, 9]], I'd like to get 1*5*9.

While there are many possible ways to do this, I wondered how reduce does with enumerate:

def test(m):
    return reduce(lambda a, b: a[1][a[0]]*b[1][b[0]], enumerate(m))

print test([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

I would think that a in the beginning is (0, [1,2,3]) so that a[1] is [1,2,3], and a[0] is 0, and so a[1][a[0]] is 1.

However, I get the following exception:

return reduce(lambda a, b: a[1][a[0]]*b[1][b[0]], enumerate(mat))
TypeError: 'int' object has no attribute '__getitem__'

Why is a integer?

Solution

Your final and intermediate values are simple integers. So you should start with 1, and then lambda will always get an integer as a, namely the product so far. And b will be the next enumerated item. So here's how to do it:

>>> reduce(lambda a, b: a * b[1][b[0]],
           enumerate([[1, 2, 3], [4, 5, 6], [7,8,9]]), 1)
45

Python 2 still allows this, btw:

>>> reduce(lambda a, (i, b): a * b[i],
           enumerate([[1, 2, 3], [4, 5, 6], [7,8,9]]), 1)
45