Python recursion error when multiplying functions

Question

I'm using python 3 and trying to multiply functions within a for loop. I wrote a simple example code to demonstrate my problem. What I want this code to do was to start with the funciton x^2, then multiply it by x^2 in first loop, to get x^4. Then multiply x^4 again with x^2 to get x^6 e.t.c.

fun = lambda x: x**2

function = lambda x: x**2
for i in range(2):
    function = lambda x: function(x) * fun(x)

print(function(2))

But the code comes out with a Recursion error. I have no idea how this is causing a recursion though? Any help will be much appreciated.

fzbd · Accepted Answer · 2018-11-12 23:09:57Z

The assignment in your loop is equivalent to:

def function(x):
    return function(x) * fun(x)

Which is a recursive function without a stop condition. Your initial definition of function is shadowed, due to python's binding rules:

The following constructs bind names: formal parameters to functions, import statements, class and function definitions (these bind the class or function name in the defining block)

You can trace it and verify such behaviour using python3 -m trace --trace script.py :

--- modulename: script, funcname: <lambda>
script.py(6):     function = lambda x: function(x) * fun(x)
--- modulename: script, funcname: <lambda>
script.py(6):     function = lambda x: function(x) * fun(x)

# Repeated until a RecursionError is thrown

You can instead bind your function as an argument of the lambda:

fun = lambda x: x**2
function = lambda x: x**2
for i in range(2):
    function = lambda x, y=function: y(x) * fun(x)

print(function(2))

Which will produce the following trace:

--- modulename: script, funcname: <module>
script.py(3): fun = lambda x: x**2
script.py(4): function = lambda x: x**2
script.py(5): for i in range(2):
script.py(6):     function = lambda x, y=function: y(x) * fun(x)
script.py(5): for i in range(2):
script.py(6):     function = lambda x, y=function: y(x) * fun(x)
script.py(5): for i in range(2):
script.py(8): print(function(2))
--- modulename: script, funcname: <lambda>
script.py(6):     function = lambda x, y=function: y(x) * fun(x)
--- modulename: script, funcname: <lambda>
script.py(6):     function = lambda x, y=function: y(x) * fun(x)
--- modulename: script, funcname: <lambda>
script.py(4): function = lambda x: x**2
--- modulename: script, funcname: <lambda>
script.py(3): fun = lambda x: x**2
--- modulename: script, funcname: <lambda>
script.py(3): fun = lambda x: x**2
64

Oh haha I just wrote this workout myself, crazy timing. Thank you for the explanation though!

ZWang · Accepted Answer · 2018-11-12 23:12:39Z

0

I never found a solution to this, but did find a workaround. Rather than trying to multiply it straight away, I wrote a function to do the multiplication. This seems to works so I'll just use this instead.

def multiplyFun(fun1,fun2):
    fun = lambda x: fun1(x) * fun2(x)
    return fun


fun = lambda x: x**2

function = lambda x: x**2
for i in range(5):
    print(i)
    function = multiplyFun(function,fun)

print(function(2))

answered Nov 12, 2018 at 23:12

ZWang

8925 silver badges18 bronze badges

Comments

cdlane · Accepted Answer · 2018-11-13 00:43:19Z

0

An alternate syntax: rather than pass a second argument to the lambda, you can use a nested lambda where the outer one is evaulated to return the inner one:

squared = lambda x: x**2
function = lambda x: x**2

for i in range(2):
    function = (lambda f: lambda x: f(x) * squared(x))(function)

print(function(2))

Just seems more generic solution (language-wise) than a defaulted argument.

answered Nov 13, 2018 at 0:43

cdlane

42.2k5 gold badges37 silver badges87 bronze badges

Collectives™ on Stack Overflow

Python recursion error when multiplying functions

3 Answers 3

1 Comment

Comments

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

3 Answers 3

1 Comment

Comments

Comments

Your Answer

Sign up or log in

Post as a guest

Related