kendall_tau_strict.py

def is_concordant_strict(pair, ls1, ls2):
    """
    Given a pair of indices, check if ls1 and ls2 agree
    on their ranking, if either is a tie, return False.
    """
    i1, i2 = pair
    return ( (ls1[i1] > ls1[i2]) and (ls2[i1] > ls2[i2])) or \
        ( (ls1[i1] < ls1[i2]) and (ls2[i1] < ls2[i2])) or \
        ( (ls1[i1] == ls1[i2]) and (ls2[i1] == ls2[i2]))


def ktau_strict(ls1, ls2):
    """
    A version of Kendall's tau where ties can be counted as disagreements.
    """
    assert (len(ls1) == len(ls2))
    num_of_items = len(ls1)
    all_pairs = [(i, j)
                 for i in range(num_of_items)
                 for j in range(i+1, num_of_items)]
    num_of_pairs = len(all_pairs)
    
    # count concordant pairs
    conc = sum([is_concordant_strict(pair, ls1, ls2) for pair in all_pairs])

    # anything that isn't concordant is discordant
    disc = num_of_pairs - conc

    # compute tau
    tau = (conc - disc) / num_of_pairs

    return tau


x1 = [1,2,3,4,5]
x2 = [37,40,40,40,40]

print(ktau_strict(x1,x2))