Defining functions recursively in python

Question

I have a simple question about lambda functions. I want to do a loop, in which every iteration defines a new lambda function based on a lambda function from the previous iteration.

f = lambda x: x**2
j=0
J=2
while j<J:
    f2 = lambda x: 0.5*f(x)
    f = f2
    j+=1

I expect the result of f(3) to be 2.25 = 0.5*0.5*3**2. However, I get the following error:

RecursionError: maximum recursion depth exceeded

I thought lambda functions can be used flexibly like this. I suppose there is a known pythonic way of how to do this properly?

jasonharper · Accepted Answer · 2017-02-21 03:05:05Z

4

The name f inside your lambda is looked up at the time the lambda is called - at which point it refers to the lambda itself, thus the infinite recursion.

The usual idiom for capturing a value at a particular moment in time is to make it a default parameter of the lambda, which gets evaluated at definition time:

    f2 = lambda x, f=f: 0.5*f(x)

answered Feb 21, 2017 at 3:05

jasonharper

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2 Comments

splinter Over a year ago

Is there also a way to do this using def rather than lambda?

jasonharper Over a year ago

Sure, the same trick with default parameters works just as well for a regular function. Keep in mind that lambdas do not add any actual new functionality to Python, they're just a shortcut for defining really simple functions.

Andrew Guy · Accepted Answer · 2017-02-21 03:05:58Z

3

When a lambda function is created, it maintains a reference to the local environment so that it can look up variables within the lambda when it is called. You need to pass in your first lambda function as a parameter to the second one:

f = lambda x: x**2
j=0
J=2
while j<J:
    f2 = lambda x, f=f: 0.5*f(x)
    f = f2
    j+=1

Note that this is covered in the Python docs FAQ.

answered Feb 21, 2017 at 3:05

Andrew Guy

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2 Comments

splinter Over a year ago

Because the answers are exactly the same, I accepted the first one. Thank you

splinter Over a year ago

Is there also a way to do this using def rather than lambda?

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