Lambda Lambda Lambda

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Is that some kind of fraternity? of anonymous functions? What is that!? There are many times where you need a callable, small function in python, and it is inconvenient to have to use def to create a named function. Lambda functions solve this problem. Let us look at some examples. First, we create a lambda function, and assign it to a variable. Then we show that variable is a function, and that we can call it with an argument.

f = lambda x: 2*x
print f
print f(2)
<function <lambda> at 0x0000000001E6AAC8>
4

We can have more than one argument:

f = lambda x,y: x + y
print f
print f(2, 3)
<function <lambda> at 0x0000000001E3AAC8>
5

And default arguments:

f = lambda x, y=3: x + y
print f
print f(2)
print f(4, 1)
<function <lambda> at 0x0000000001E9AAC8>
5
5

It is also possible to have arbitrary numbers of positional arguments. Here is an example that provides the sum of an arbitrary number of arguments.

import operator
f = lambda *x: reduce(operator.add, x)
print f

print f(1)
print f(1, 2)
print f(1, 2, 3)
<function <lambda> at 0x0000000001DFAAC8>
1
3
6

You can also make arbitrary keyword arguments. Here we make a function that simply returns the kwargs as a dictionary. This feature may be helpful in passing kwargs to other functions.

f = lambda **kwargs: kwargs

print f(a=1, b=3)
{'a': 1, 'b': 3}

Of course, you can combine these options. Here is a function with all the options.

f = lambda a, b=4, *args, **kwargs: (a, b, args, kwargs)

print f('required', 3, 'optional-positional', g=4)
('required', 3, ('optional-positional',), {'g': 4})

One of the primary limitations of lambda functions is they are limited to single expressions. They also do not have documentation strings, so it can be difficult to understand what they were written for later.

1 Applications of lambda functions

Lambda functions are used in places where you need a function, but may not want to define one using def. For example, say you want to solve the nonlinear equation \(\sqrt{x} = 2.5\).

from scipy.optimize import fsolve
import numpy as np

sol, = fsolve(lambda x: 2.5 - np.sqrt(x), 8)
print sol
6.25

Another time to use lambda functions is if you want to set a particular value of a parameter in a function. Say we have a function with an independent variable, \(x\) and a parameter \(a\), i.e. \(f(x; a)\). If we want to find a solution \(f(x; a) = 0\) for some value of \(a\), we can use a lambda function to make a function of the single variable \(x\). Here is a example.

from scipy.optimize import fsolve
import numpy as np

def func(x, a):
    return a * np.sqrt(x) - 4.0

sol, = fsolve(lambda x: func(x, 3.2), 3)
print sol
1.5625

Any function that takes a function as an argument can use lambda functions. Here we use a lambda function that adds two numbers in the reduce function to sum a list of numbers.

print reduce(lambda x, y: x + y, [0, 1, 2, 3, 4])
10

We can evaluate the integral \(\int_0^2 x^2 dx\) with a lambda function.

from scipy.integrate import quad

print quad(lambda x: x**2, 0, 2)
(2.666666666666667, 2.960594732333751e-14)

2 Summary

Lambda functions can be helpful. They are never necessary. You can always define a function using def, but for some small, single-use functions, a lambda function could make sense. Lambda functions have some limitations, including that they are limited to a single expression, and they lack documentation strings.

Copyright (C) 2013 by John Kitchin. See the License for information about copying.

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