# 8.18. Functional Pattern MapReduce¶

• split-apply-combine strategy

The map-reduce algorithm is a programming model used for processing large amounts of data in a distributed and parallel manner. It consists of two phases: the map phase and the reduce phase.

In Python, the map-reduce algorithm can be implemented using the built-in map() and reduce() functions.

Here's an example of using the map-reduce algorithm to calculate the sum of squares of a list of numbers:

>>> from functools import reduce
>>>
>>> numbers = [1, 2, 3, 4, 5]
>>>
>>> squared_numbers = list(map(lambda x: x ** 2, numbers))
>>> sum_of_squares = reduce(lambda x, y: x + y, squared_numbers)
>>>
>>> print(sum_of_squares)
55


In this example, the map() function is used to square each number in the numbers list. The resulting list of squared numbers is stored in the squared_numbers variable.

The reduce() function is then used to calculate the sum of the squared numbers. The lambda function passed to reduce() takes two arguments (x and y) and returns their sum. The reduce() function applies this function to the elements of the squared_numbers list, starting with the first two elements, and then applying the function to the result and the next element, and so on, until all elements have been processed.

The final result (55) is the sum of the squares of the original list of numbers.

The map-reduce algorithm can be used for a wide range of data processing tasks, such as filtering, sorting, and aggregating data. By dividing the work into smaller tasks that can be performed in parallel, the algorithm can process large amounts of data efficiently.

Apply function of two arguments cumulatively to the items of iterable, from left to right, so as to reduce the iterable to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). The left argument, x, is the accumulated value and the right argument, y, is the update value from the iterable. If the optional initializer is present, it is placed before the items of the iterable in the calculation, and serves as a default when the iterable is empty. If initializer is not given and iterable contains only one item, the first item is returned.

## 8.18.1. SetUp¶

>>> from functools import reduce


## 8.18.2. Pattern¶

>>> class MapReduce:
...     def __init__(self, values):
...         self.values = values
...
...     def filter(self, fn):
...          self.values = filter(fn, self.values)
...          return self
...
...     def map(self, fn):
...         self.values = map(fn, self.values)
...         return self
...
...     def reduce(self, fn):
...         return reduce(fn, self.values)


## 8.18.3. Usage¶

>>> DATA = [1, 2, 3, 4, 5, 6, 7, 8, 9]
>>>
>>> result = (
...     MapReduce(DATA)
...     .map(lambda x: x ** 2)
...     .map(lambda x: x / 2)
...     .map(lambda x: x + 2)
...     .map(lambda x: round(x, 2))
...     .map(lambda x: int(x))
...     .filter(lambda x: x > 10)
...     .reduce(lambda x,y: x + y)
... )
>>>
>>> result
136


## 8.18.4. Use Case - 0x01¶

>>> def even(x):
...     return x % 2 == 0
>>>
>>> def positive(x):
...     return x > 0
>>>
>>> def non_negative(x):
...     return x >= 0
>>>
>>> def square(x):
...     return x ** 2
>>>
>>> def increment(x):
...     return x + 1
>>>
>>> def decrement(x):
...     return x - 1

>>> from functools import reduce
>>> from operator import add
>>>
>>> data = range(0, 1024)
>>> data = filter(even, data)
>>> data = filter(positive, data)
>>> data = filter(non_negative, data)
>>> data = map(square, data)
>>> data = map(increment, data)
>>> data = map(decrement, data)
>>> result = reduce(add, data)
>>>
>>> result
178433024


## 8.18.5. Use Case - 0x02¶

>>> def even(x):
...     return x % 2 == 0
>>>
>>> def positive(x):
...     return x > 0
>>>
>>> def non_negative(x):
...     return x >= 0
>>>
>>> def square(x):
...     return x ** 2
>>>
>>> def increment(x):
...     return x + 1
>>>
>>> def decrement(x):
...     return x - 1

>>> filters = [
...     even,
...     positive,
...     non_negative,
... ]
>>>
>>> maps = [
...     square,
...     increment,
...     decrement,
... ]
>>>
>>> def apply(data, fn):
...     return map(fn, data)

>>> from functools import reduce
>>> from operator import add
>>>
>>> data = range(0, 1024)
>>> data = reduce(apply, filters, data)
>>> data = reduce(apply, maps, data)
>>> result = reduce(add, data)
>>>
>>> result
1024


## 8.18.6. Use Case - 0x03¶

This is our function library.

Transformation functions (non-reducing) - takes one argument and returns one value:

>>> def increment(x):
...     return x + 1
>>>
>>> def decrement(x):
...     return x - 1
>>>
>>> def square(x):
...     return x ** 2
>>>
>>> def cube(x):
...     return x ** 3


Reducing functions - takes two arguments returns one value:

>>> def add(x, y):
...     return x + y
>>>
>>> def sub(x, y):
...     return x - y
>>>
>>> def mul(x, y):
...     return x * x


We have data to compute:

>>> data = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]


On this data, we want to apply the following transformations:

>>> transformations = [increment, square, decrement, cube]


We need to create apply function, which takes data and apply the transformation:

>>> def apply(data, fn):
...     return map(fn, data)


Let's do it parallel. We will create three independent workers. Each worker will get part of the data (one-third) and will apply all the transformation (map) to their data subset.

>>> workerA = reduce(apply, transformations, data[0])  # [27, 512, 3375]
>>> workerB = reduce(apply, transformations, data[1])  # [13824, 42875, 110592]
>>> workerC = reduce(apply, transformations, data[2])  # [250047, 512000, 970299]


Note, that all workers will produce generators (maps). We need to merge the results using reduce function, but before that we need to evaluate maps to lists.

>>> def merge(x, y):
...     return list(x) + list(y)

>>> merged = reduce(merge, [workerA, workerB, workerC])  # [27, 512, 3375, 13824, 42875, 110592, 250047, 512000, 970299]
>>> result = reduce(add, merged)
>>>
>>> print(result)
1903551


## 8.18.7. Use Case - 0x04¶

>>> from itertools import chain
>>> from functools import reduce, partial
>>> from operator import add, sub, mul, pow
>>> from math import sqrt, cbrt

>>> transformations = [
...     partial(sub, 1),
...     partial(pow, 2),
...     partial(pow, 3),
... ]

>>> data = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]

>>> def apply(data, fn):
...     return map(fn, data)

>>> workerA = reduce(apply, transformations, data[0])  # [27, 512, 3375]
>>> workerB = reduce(apply, transformations, data[1])  # [13824, 42875, 110592]
>>> workerC = reduce(apply, transformations, data[2])  # [250047, 512000, 970299]

>>> reduce(add, chain(workerA, workerB, workerC))
10.333713311264441