Month: March 2017

After migration to Python 3 from Python 2,  lambda operator, map() and filter()  functions are still part of core Python; only reduce() function had to go, and it was moved into the module functools. 

This post introduces how to use lambda, map, filter, and reduce functions in Python 3 (for python 2.7 version, check the references below.)

• Lambda operator

Some people like it, others hate it and many are afraid of the lambda operator.

The lambda operator or lambda function is a way to create small anonymous functions (i.e., functions without a name). These functions are throw-away functions (i.e., they are just needed where they have been created).

Lambda functions are mainly used in combination with the functions filter(), map() and reduce(). The lambda feature was added to Python due to the demand from Lisp programmers. 

The general syntax of a lambda function is quite simple: 

lambda argument_list: expression 

The argument list consists of a comma separated list of arguments and the expression is an arithmetic expression using these arguments. You can assign the function to a variable, so you can  use it as a function. 

The following example of a lambda function returns the sum of its two arguments:

>>> sum = lambda x, y : x + y
>>> sum(3,4)
7

>>> 

The above example might look like a game for a mathematician — A formalization that turns a straight forward operation into an abstract  formalization.

The above has the same effect by using the following conventional function definition: 

>>> def sum(x,y):
...     return x + y
... 
>>> sum(3,4)
7
>>> 

But, when you learn how to use the map() function, you will see the apparent advantages of this lambda operation.

• The map function 

The advantage of the lambda operator will be obvious when it is used in combination with the map() function. 

map() is a function which takes two arguments: 

r = map(func, seq)

The first argument func is the name of a function and the second a sequence (e.g. a list).

seq. map() applies the function func to all the elements of the sequence seq. Before Python3, map() used to return a list, where each element of the result list was the result of the function func applied on the corresponding element of the list or tuple “seq”. In Python 3, map() returns an iterator.

The following examples illustrate how map() function works:

>>> def fahrenheit(T):

...   return ((float(9)/5)*T + 32)

... 
# hit Return/Enter to exit to the >>> in your terminal.

>>> def celsius(T):

...   return (float(5)/9)*(T-32)

... 
# hit Return/Enter to exit to the >>> in your terminal.

>>> temperatures = (36.5, 37, 37.5, 38, 39)

>>> F = map(fahrenheit, temperatures)



>>> print(F)

<map object at 0x106d1c3c8>


>>> temperatures_in_Fahrenheit = list(F)

>>> print(temperatures_in_Fahrenheit) 
[97.7, 98.60000000000001, 99.5, 100.4, 102.2]

>>> C = map(celsius, map(fahrenheit, temperatures))

>>> print(C)

<map object at 0x106d1c438>


>>> temperatures_in_Celsius = list(C)


>>> print(temperatures_in_Celsius)
[36.5, 37.00000000000001, 37.5, 38.00000000000001, 39.0]

>>> 

In the example above we haven’t used lambda. When using lambda, we do not need to define and name the functions fahrenheit() and celsius(). You can see this in the following interactive session:

>>> C = [39.2, 36.5, 37.3, 38, 37.8]

>>> F = list(map(lambda x: (float(9)/5)*x + 32, C))

>>> print(F)

[102.56, 97.7, 99.14, 100.4, 100.03999999999999]

>>> C = list(map(lambda x: (float(5)/9)*(x-32), F))

>>> print(C)

[39.2, 36.5, 37.300000000000004, 38.00000000000001, 37.8]

>>> 

map() can be applied to more than one list.

The lists don’t have to have the same length.

map() will apply its lambda function to the elements of the argument lists (i.e., it first applies to the elements with the 0th index, then to the elements with the 1st index until the n-th index is reached). See the following for an illustration example:

>>> a = [1, 2, 3, 4]
>>> b = [17, 12, 11, 10]
>>> c = [-1, -4, 5, 9]
>>> list(map(lambda x, y : x+y, a, b))
[18, 14, 14, 14]
>>> list(map(lambda x, y, z : x+y+z, a, b, c))
[17, 10, 19, 23]
>>> list(map(lambda x, y, z : 2.5*x + 2*y - z, a, b, c))
[37.5, 33.0, 24.5, 21.0]
>>>

We can see in the example above that the parameter x gets its values from the list a, while y gets its values from b, and z from list c. 

If one list has less elements than the others, map() will stop when the shortest list has been completed the mapping:

>>> a = [1, 2, 3]
>>> b = [17, 12, 11, 10]
>>> c = [-1, -4, 5, 9]
>>> 
>>> list(map(lambda x, y, z : 2.5*x + 2*y - z, a, b, c))
[37.5, 33.0, 24.5]
>>>

 

• The filter function 

filter(function, sequence) 

offers an elegant way to filter out all the elements of a sequence “sequence”, according to the return value of the function function (i.e., if the function returns True it will be kept in the returned iterator object of the filter function). 

In other words: The function filter(f,l) needs a function f as its first argument. f has to return a Boolean value (i.e. either True or False). This function will be applied to every element of the list l. Only if f returns True will the element be produced by the iterator — which is the return value of filter function. 

In the following example, we filter out first the odd and then the even elements of the sequence of the first 10 Fibonacci numbers: 

>>> fibonacci = [0,1,1,2,3,5,8,13,21,34]
>>> odd_numbers = list(filter(lambda x: x % 2, fibonacci))
>>> print(odd_numbers)
[1, 1, 3, 5, 13, 21]
>>> even_numbers = list(filter(lambda x: x % 2 == 0, fibonacci))
>>> print(even_numbers)
[0, 2, 8]

>>> 

• An example of combining filter() and lambda functions

>>> filter(lambda x: x % 2 == 0, list(range(10,100)))

<filter object at 0x106d1c208>

#this will return all even number between 10 and 100.
>>> list(filter(lambda x: x % 2 == 0, list(range(10,100))))

[10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98]

>>> 

 

• The reduce() function 

reduce() had been dropped from the core of Python when migrating to Python 3. It was moved into the module functools.

reduce(func, seq) 

continually applies the function func() to the sequence seq. It returns a single value. 

If seq = [ s₁, s₂, s₃, … , s_n ], calling reduce(func, seq) works like this:

• the first two elements of seq will be applied to func, i.e. func(s₁,s₂). The list on which reduce() applied to looks like this now: [ func(s₁, s₂), s₃, … , s_n ]
• Then,  func will be applied on the previous result and the third element of the list, that is, func(func(s₁, s₂),s₃)
  The list now looks like this: [ func(func(s₁, s₂),s₃), … , s_n ]
• repeat the steps until just one element is left and return this element as the result of reduce() function.

If n is equal to 4 the previous explanation can be illustrated like this: 

The following  simple example illustrates how reduce() works. 

>>> import functools
>>> functools.reduce(lambda x,y: x+y, [47,11,42,13])
113
>>>

The following diagram shows the intermediate steps of the calculation: 

 

See below for some examples of using reduce() function.

 

#get maximum number from a list using reduce():

>>> from functools import reduce
>>> f = lambda a,b: a if (a > b) else b
>>> reduce(f, [47,11,42,102,13])
102
>>>

# Calculating the sum of the numbers from 1 to 100:
>>> from functools import reduce
>>> reduce(lambda x, y: x+y, range(1,101))
5050

It’s very straightforward to change the previous example to calculate the product (the factorial) from 1 to a number. We just need to change the “+” into “*”:

>>> reduce(lambda x, y: x*y, range(1,5))

24

>>> 

 

References:

• Lambda, filter, reduce and map (Python 3)
• Lambda, filter, reduce and map (Python 2.7)