efficient algorithm instead of looping

Question

I have a data set where each samples has a structure similar to this

X=[ [[],[],[],[]], [[],[]] , [[],[],[]] ,[[][]]]

for example:

Answer 1

You can also bypass the need for itertools.product by directly doing the dot product on inner matrices:

def calc_matrix(l1, l2):
    return np.array(l1).dot(np.array(l2).T).sum()

def kernel(x1, x2):
    return sum(
       calc_matrix(l1, l2)
       for l1, l2 in zip(x1, x2)
    )

Edit:

On short lists (less than a few thousand elements) this will be faster than Claudiu's (awesome) answer. His will scale better above these numbers:

Using Claudiu's benchmarks:

# len(l1) == 500

In [9]: %timeit calc_matrix(l1, l2)
10 loops, best of 3: 8.11 ms per loop

In [10]: %timeit calc_fast(l1, l2)
10 loops, best of 3: 14.2 ms per loop

# len(l2) == 5000

In [19]: %timeit calc_matrix(l1, l2)
10 loops, best of 3: 61.2 ms per loop

In [20]: %timeit calc_fast(l1, l2)
10 loops, best of 3: 56.7 ms per loop