How to implement a nested for loop in functional programming in python?

Question

I was thinking of applying the map function twice in order to allow it to act as a double for loop but I don't know if that makes sense. Is that the way to go about it?

For example, this is what I am working on:

In imperative:

def degree(A):
    n = len(A)
    t = []
    for i in range(n):
        d = 0
        for j in range(n):
            d+=A[i][j]
        t.append(d)

    return t

In functional:

def degree(A):
    n = len(A)
    t = []
    map(lambda x,y:x+y,A)

If it was a single for loop then I would approach it as I did above. So I was trying to implement a double map, but I do not know what how to structure that. Any help would be appreciated!

You do much more than just have a double loop, you also create a sum in the inner loop. — Martijn Pieters
– Martijn Pieters, Commented Dec 16, 2017 at 21:32
You could get the same effect with map(sum, A), by the way, no need to nest anything. — Martijn Pieters
– Martijn Pieters, Commented Dec 16, 2017 at 21:33
Your attempt at map() doesn't make any sense in your context; where you thinking of reduce() perhaps? map() takes any number of iterables, and applies those together as inputs, but map(..., A) only has one input, so one argument for the lambda. You then build a sequence of results, not a total sum. reduce() produces a single result from repeated calls to a function and the input sequence. — Martijn Pieters
– Martijn Pieters, Commented Dec 16, 2017 at 21:47

Martijn Pieters · Accepted Answer · 2017-12-16 21:54:52Z

3

You are summing the inner lists A, so just apply sum to each nested list in A:

def degree(A):
    return map(sum, A)

You could also consider using a list comprehension or generator expression (depending on whether or not you need to produce the result lazily (map() in Python 2 produces a list, in Python 3 it works lazily):

def degree(A):
    # returns a list
    return [sum(row) for row in A]

def degree(A):
    # returns a generator
    return (sum(row) for row in A)

You can otherwise produce i and j as a cartesian product, using itertools.product(); however, you'd be passing in a tuple of integers to the map callable:

from itertools import product

map(lambda ij: A[ij[0]][ij[1]] ** 2, product(range(len(A)), 2))

This can be remedied by using itertools.starmap() instead:

from itertools import product, starmap

starmap(lambda i, j: A[i][i] ** 2, product(range(len(A)), 2))

Neither produces a sum; I demoed a lambda that produces the square of the innermost values instead, so you get one long sequence of all values, squared, without distinction between rows. That's how mapping works, it produces a value per item processed in the input.

You could also just nest the map() calls; put the inner map() in the callable for the outer map():

map(lambda r: map(lambda v: v ** 2, r), A)

but note that this then produces a lazy sequence of lazy objects in Python 3. Again, summing doesn't make sense in this scenario, as there is no accumulation of results.

For a generic cumulation of results across a sequence, you want to use the functools.reduce() function; that callable applies a callable on a running result and the next value in a sequence. You can produce a sum with your lambda x, y: x + y function and map():

map(lambda r: reduce(lambda x, y: x + y, r, 0), A)

But for just summing, the reduce(lambda x, y: x + y, <iterable>, 0) syntax is just a verbose and slower way of spelling sum(<iterable>).

edited Dec 16, 2017 at 21:54

answered Dec 16, 2017 at 21:34

Martijn Pieters

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5 Comments

aa1 Over a year ago

so I am wondering how would that take care of the A[i][j] part, the matrix that is formed with the double loop?

aa1 Over a year ago

are both those methods equivalent?

Martijn Pieters Over a year ago

@ce1: both what methods? No, the product() method doesn't produce the same results; you can't produce the same results with product() as you reset d each iteration of the outer loop.

aa1 Over a year ago

If the line were to be d+=A[i][j] * X[j] where X is a list passed to the function, how would the map(sum, A) change in functional programming?

Martijn Pieters Over a year ago

@ce1: use zip() to pair up rows from A with X: (sum(a * x for a, x in zip(r, X) for r in A) in a generator expression, or from operator import mul then map(lambda r: sum(map(prod, r, X)), A) if you must use map() over comprehensions.

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