Decoding the python function - Not able to understand what the function's inner workings are

Question

I'm trying to understand the below code and deduce some kind of a pattern to see what this function this, can you please help me with this?

from math import floor
from itertools import groupby

def function3(l, n):
    assert(len(l) > 0 and n > 0)
    minimum = min(l)
    maximum = max(l)
    d = (maximum - minimum) / n
    values = [(floor((l[i] - minimum) / d)) for i in range(len(l))]
    dictionary = dict([(key, len(list(group))) for key, group in groupby(sorted(values))])
    return [(minimum+(i+0.5)*d, dictionary.get(i, 0)) for i in range(0,n,1)]

Answer 1

I don't have a full explanation of the background of your snippet, but hopefully I can shed some light on the programming going on.

Let's go through it step by step:

# import statements
from math import floor # method to round down to the nearest integer, see [here][1] 
from itertools import groupby # method to group by keys, see [here][2]

def function3(l, n): 
# as thebadgateway said, this looks like the standard score, 
# with l being the interval and n the number of values
    assert(len(l) > 0 and n > 0) # tests to see that both length of l and n are > 0
    minimum = min(l) # self-explanatory
    maximum = max(l)
    d = (maximum - minimum) / n # this is a kind of mid-range of the input, see [here][3]
    values = [(floor((l[i] - minimum) / d)) for i in range(len(l))] 
    # this (above) takes each element in l, subtracts the minimum 
    # and divides the result by our "mid-range" d for all elements in l
    dictionary = dict([(key, len(list(group))) for key, group in groupby(sorted(values))])
    # this (above) groups the computed values by identity, 
    # and fills a dictionary with the keys and length of the groups
    return [(minimum+(i+0.5)*d, dictionary.get(i, 0)) for i in range(0,n,1)]
    # this computes the minimum + the counting variable + 0.5 * the "mid-range", 
    # puts it into a tuple with the same i-index in the dictionary (0 if element is not found)
    # it does this for n steps with a step size of 1 and returns the whole list

I hope this helps! [1]: https://en.wikipedia.org/wiki/Standard_score [2]: https://www.geeksforgeeks.org/itertools-groupby-in-python/ [3]: https://en.wikipedia.org/wiki/Mid-range

Answer 2

This function looks like it’s producing something akin to the z-score in statistics in the values list, then creating a dict of z-score, z-score count key value pairs in dictionary, and then possibly returning n-tiles. I would review z-score, and quantiles with, eg, Wikipedia to verify.