Calling a function parallelly that does internal parallelization?

MAJOR EDIT

Suppose I have a function that does internal parallelization, and I want to parallelize this function. How do I do this in Python?

Let's consider a very simple concrete example.

The function fun1 takes two numbers as input and adds them up.

def fun1(a, b):
 return a+b

The function fun2 takes two integer inputs m and n. It generates a list of size mn containing tuples as the following code shows. Then it parallelizes fun1 on this list.

def fun2(m, n):

 # create list of mn tuples
 list_tuple = [(i, j) for i in range(m) for j in range(n)]

 # apply fun1 parallelly to list_tuple

 pool = multiprocessing.Pool()
 return pool.starmap(fun1, list_tuple)

Thus, fun2 returns a list of size mn. We want to apply fun2 parallelly to a list of (m,n) pairs.

if __name__ == '__main__':
 # create the list of (m, n) tuples
 list_tuple = [(m, n) for m in range(10) for n in range(10)]

 # parallellize fun2
 pool = multiprocessing.Pool()
 pool.starmap(fun2, list_tuple)

My questions:

1. Can I write everything above in the same script?
2. If answer to 1 is yes, what is the correct way to write it? For example should there be if __name__ == 'main' inside the definition of fun2 as well?
3. If answer to 1 is no, then how to write this correctly in two scripts?

I am a beginner at parallelization and don't yet understand how the threads are connected so help is highly appreciated.

Thanks!

source https://stackoverflow.com/questions/75820729/calling-a-function-parallelly-that-does-internal-parallelization