Especially with mathematical-like programs, you want to write docstrings with your functions and classes.

In case you don't know what a docstring is, a docstring is a short piece of documentation that describes the parameters and return value of a function. And, it can include any sort of information/summary that is needed to fully explain a function.

Here is an example:

def add(a, b):
    """
    Adds two numbers together and returns the sum
    a + b
    @param(number) -- one number to add
    @param(number) -- another number to add
    @return(number) -- the sum of both parameters

    return a + b

In the case of your code where you have a few mathematical functions, providing a docstring is greatly important because there you can write out the formula that the function is using, what each part of the formula means, and what the return of the formula does for the rest of your code.

And, in places that aren't functions but need a docstring, you can just a # comments on the side (you don't have enough of these).

All of your main code (aside from functions) should be put into:

if __name__ == "__main__":
    [code or main()]

See here for why.

Your code seems very procedural. You have a few functions here and there but other than that, everything is just one after the other.

I'm having difficulty following your code so I can't give too many specific recommendations, but you should move more code to separate functions. For example, however, you could try to make a function call create_graph that will create a graph for you in just a single call.

That way, when you put your code into if __name__ == "__main__", every single line of code that you wrote won't be in there.

Especially with mathematical-like programs, you want to write docstrings with your functions and classes.

In case you don't know what a docstring is, a docstring is a short piece of documentation that describes the parameters and return value of a function. And, it can include any sort of information/summary that is needed to fully explain a function.

Here is an example:

def add(a, b):
    """
    Adds two numbers together and returns the sum
    a + b
    @param(number) -- one number to add
    @param(number) -- another number to add
    @return(number) -- the sum of both parameters

    return a + b

In the case of your code where you have a few mathematical functions, providing a docstring is greatly important because there you can write out the formula that the function is using, what each part of the formula means, and what the return of the formula does for the rest of your code.

And, in places that aren't functions but need a docstring, you can just a # comments on the side (you don't have enough of these).

All of your main code (aside from functions) should be put into:

if __name__ == "__main__":
    [code or main()]

See here for why.

Your code seems very procedural. You have a few functions here and there but other than that, everything is just one after the other.

I'm having difficulty following your code so I can't give too many specific recommendations, but you should move more code to separate functions. For example, however, you could try to make a function call create_graph that will create a graph for you in just a single call.

That way, when you put your code into if __name__ == "__main__", every single line of code that you wrote won't be in there.