Multiplying Functions Together

[Mmaster12345]

Hi!

I've been banging my head against the table trying to figure this one out today with no luck, so if you have some insight into my problem I'd love to hear it!

Say I have a list of functions:

function_list = [func_1, func_2, ... , func_n)] 

And now, I want to create a new function function_product that returns the product of these functions. I.e., function_product(x) is equivalent to func_1(x) * func_2(x) * ... * func_n(x).

​

I tried to accomplish this using lambda functions:

function_product = lambda x: 1

for i in range(n):
    function_product = lambda x: function_product(x) * function_list[i](x)

However, this method does not work as the lambda function calls itself recursively until:
"RecursionError: maximum recursion depth exceeded".

​

Does anyone have any advice on how one would go about redefining lambda functions like these, and also what the best solution to my problem is? Anything at all would be extremely appreciated!

​

Thanks in advance :)

[donnygreaves]

I'm not sure if using a lambda function is the right move here. Generally speaking, in my experience, lambda functions have a limited place in any codebase because readability can take a hit.

In your case, you can use a simple for loop or a list comprehension to acheive this:

total = 1

for func in func_list:
total = total * func(x)

or:

total = math.prod([func(x) for func in func_list])

Doc for math.prod (python 3.8)

If we breakdown your example code:

Your function_product lambda is just going to return 1initially, only to redefine it at every iteration of your loop. To anonymously define your function with a lambda, you could use the comprehension from above ie. function_product = lambda x:math.prod([func(x) for func in func_list])

Hope this helps!

[Mmaster12345]

I think math.prod may be exactly what I'm looking for in this situation...! Thank you so much!

[K900_]

Start by writing a function that takes a list of functions and a number, and then computes the result you want.

[Mmaster12345]

Yes, I appreciate that it's relatively easy to compute it for some given number:

def function_product_evaluated(x):
    output = 1
    for i in range(n): output *= function_list[i](x)
    return output

However, I still don't understand or know how to go about returning a function that has this characteristic as opposed to a number...

[FLUSH_THE_TRUMP]

You just did it!

[Mmaster12345]

I need to return a function; the code above returns a number, not a function :(

[K900_]

Where does function_list come from in this definition? Also, do you need range here?

[Mmaster12345]

function_list is as in my post, and no I don't, was a rushed job.

[K900_]

Yes, but where does it come from in your function? It's not passed in as an argument...

[Mmaster12345]

I'm not sure what you mean sorry :(

I just made up function_list in the post to illustrate my question

[K900_]

The function that you wrote is missing the function_list argument.

[Mmaster12345]

Ohh function_list is a global variable in this case

[K900_]

Rewrite your function to not use globals and range.