[python] Transpose/Unzip Function (inverse of zip)?

Naive approach

def transpose_finite_iterable(iterable):
    return zip(*iterable)  # `itertools.izip` for Python 2 users

works fine for finite iterable (e.g. sequences like list/tuple/str) of (potentially infinite) iterables which can be illustrated like

| |a_00| |a_10| ... |a_n0| |
| |a_01| |a_11| ... |a_n1| |
| |... | |... | ... |... | |
| |a_0i| |a_1i| ... |a_ni| |
| |... | |... | ... |... | |

where

  • n in N,
  • a_ij corresponds to j-th element of i-th iterable,

and after applying transpose_finite_iterable we get

| |a_00| |a_01| ... |a_0i| ... |
| |a_10| |a_11| ... |a_1i| ... |
| |... | |... | ... |... | ... |
| |a_n0| |a_n1| ... |a_ni| ... |

Python example of such case where a_ij == j, n == 2

>>> from itertools import count
>>> iterable = [count(), count()]
>>> result = transpose_finite_iterable(iterable)
>>> next(result)
(0, 0)
>>> next(result)
(1, 1)

But we can't use transpose_finite_iterable again to return to structure of original iterable because result is an infinite iterable of finite iterables (tuples in our case):

>>> transpose_finite_iterable(result)
... hangs ...
Traceback (most recent call last):
  File "...", line 1, in ...
  File "...", line 2, in transpose_finite_iterable
MemoryError

So how can we deal with this case?

... and here comes the deque

After we take a look at docs of itertools.tee function, there is Python recipe that with some modification can help in our case

def transpose_finite_iterables(iterable):
    iterator = iter(iterable)
    try:
        first_elements = next(iterator)
    except StopIteration:
        return ()
    queues = [deque([element])
              for element in first_elements]

    def coordinate(queue):
        while True:
            if not queue:
                try:
                    elements = next(iterator)
                except StopIteration:
                    return
                for sub_queue, element in zip(queues, elements):
                    sub_queue.append(element)
            yield queue.popleft()

    return tuple(map(coordinate, queues))

let's check

>>> from itertools import count
>>> iterable = [count(), count()]
>>> result = transpose_finite_iterables(transpose_finite_iterable(iterable))
>>> result
(<generator object transpose_finite_iterables.<locals>.coordinate at ...>, <generator object transpose_finite_iterables.<locals>.coordinate at ...>)
>>> next(result[0])
0
>>> next(result[0])
1

Synthesis

Now we can define general function for working with iterables of iterables ones of which are finite and another ones are potentially infinite using functools.singledispatch decorator like

from collections import (abc,
                         deque)
from functools import singledispatch


@singledispatch
def transpose(object_):
    """
    Transposes given object.
    """
    raise TypeError('Unsupported object type: {type}.'
                    .format(type=type))


@transpose.register(abc.Iterable)
def transpose_finite_iterables(object_):
    """
    Transposes given iterable of finite iterables.
    """
    iterator = iter(object_)
    try:
        first_elements = next(iterator)
    except StopIteration:
        return ()
    queues = [deque([element])
              for element in first_elements]

    def coordinate(queue):
        while True:
            if not queue:
                try:
                    elements = next(iterator)
                except StopIteration:
                    return
                for sub_queue, element in zip(queues, elements):
                    sub_queue.append(element)
            yield queue.popleft()

    return tuple(map(coordinate, queues))


def transpose_finite_iterable(object_):
    """
    Transposes given finite iterable of iterables.
    """
    yield from zip(*object_)

try:
    transpose.register(abc.Collection, transpose_finite_iterable)
except AttributeError:
    # Python3.5-
    transpose.register(abc.Mapping, transpose_finite_iterable)
    transpose.register(abc.Sequence, transpose_finite_iterable)
    transpose.register(abc.Set, transpose_finite_iterable)

which can be considered as its own inverse (mathematicians call this kind of functions "involutions") in class of binary operators over finite non-empty iterables.


As a bonus of singledispatching we can handle numpy arrays like

import numpy as np
...
transpose.register(np.ndarray, np.transpose)

and then use it like

>>> array = np.arange(4).reshape((2,2))
>>> array
array([[0, 1],
       [2, 3]])
>>> transpose(array)
array([[0, 2],
       [1, 3]])

Note

Since transpose returns iterators and if someone wants to have a tuple of lists like in OP -- this can be made additionally with map built-in function like

>>> original = [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
>>> tuple(map(list, transpose(original)))
(['a', 'b', 'c', 'd'], [1, 2, 3, 4])

Advertisement

I've added generalized solution to lz package from 0.5.0 version which can be used like

>>> from lz.transposition import transpose
>>> list(map(tuple, transpose(zip(range(10), range(10, 20)))))
[(0, 1, 2, 3, 4, 5, 6, 7, 8, 9), (10, 11, 12, 13, 14, 15, 16, 17, 18, 19)]

P.S.

There is no solution (at least obvious) for handling potentially infinite iterable of potentially infinite iterables, but this case is less common though.

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