Vectorized crosstabulation in Python for two arrays with two categories each

Question

I have two Python lists, label and presence. I want to do cross-tabulation and get the count for each block out of four, such as A, B, C, and D in the below code.

• Both the lists have values True and False.
• I have tried Pandas' crosstab function. However, it's slower than my code which is below.
• One problem with my code is it's not vectorized and is using a for loop which slows things down.

Could the below function in Python be made any faster?

def cross_tab(label,presence):
    A_token=0
    B_token=0
    C_token=0
    D_token=0
    for i,j in zip(list(label),list(presence)):
        if i==True and j==True:
            A_token+=1
        elif i==False and j==False:
            D_token+=1
        elif i==True and j==False:
            C_token+=1
        elif i==False and j==True:
            B_token+=1
    return A_token,B_token,C_token,D_token

Some sample data and example input and output.

##input
label=[True,True,False,False,False,False,True,False,False,True,True,True,True,False]
presence=[True,False,False,True,False,False,True,True,False,True,False,True,False,False]

##processing
A,B,C,D=cross_tab(label,presence)
print('A:',A,'B:',B,'C:',C,'D:',D)

##Output
A: 4 B: 2 C: 3 D: 5

Edit: Answer provided by Maarten Fabre below is working perfectly. To anyone who will stumble here in future, the logic flow is as follows.

Goal: find a way for vectorization: Below are the solution steps

1. Analyze and find unique value at each evaluation. This will help save logical output in single array.
2. By multiplying 2 with any given array and adding resultant array with other array we can get results in single array with unique coded value for each logic.
3. Get count of the unique element in array and fetch values.
4. Since calculation can be done in arrays without loop, convert list into np array to allow vectorized implementation.

Answer 1

Algorithm

If you look at your code, and follow the if-elif part, you see that there are 4 combinations of i and j

i      j     : result
True,  True  : A
False, True  : B
True,  False : C
False, False : D

If you use the tuple (i, j) as key, you can use a dict lookup

{
    (True, True): "A",
    (False, True): "B",
    (True, False): "C",
    (False, False): "D",
}

Or simpler:

{
    (True, True): 3,
    (False, True): 1,
    (True, False): 2,
    (False, False): 0,
}

The choice of numbers is deliberate, since when you use True as 1 and False as 0, you can do

def crosstab2(label, presence):
    for i, j in zip(label, presence):
        yield i * 2 + j

c = collections.Counter(crosstab2(label, presence))
print('A:',c[3],'B:',c[1],'C:',c[2],'D:',c[0])

This is not faster than your original solution, but this is something you can vectorize

label = np.array([True, True, False, False,False, False,True, False, False, True, True, True, True, False])
presence = np.array([True, False, False, True, False, False, True, True, False, True, False, True, False, False])
c = collections.Counter(label * 2 + presence)
print('A:',c[3],'B:',c[1],'C:',c[2],'D:',c[0])

Which is significantly faster, even if you account for the few seconds of overhead for the creation of the numpy arrays

Formatting

Try to follow pep8.

• spaces around operators (=, +, ...)
• spaces after a ,

naming

I try to give collections of elements a plural name. In this case, I would use labels., so if you ever need to iterate over them, you can do for label in labels, which is a lot more clear than for i in label:

list

The extra call to list in zip(list(label),list(presence)) is not necessary. zip takes any iterable, and doesn't modify it in place.