added type hints and doctests to arithmetic_analysis/newton_method.py

[spamegg1]

Continuing #2128
Also changed some variable names, made them more descriptive.

Describe your change:

• Fix a bug or typo in an existing algorithm?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.

[cclauss]

Is there a way to defined a type for Callable[[float], float] and then use that type to simplify the call parameters?

[spamegg1]

Hmm... I think there is. I could try defining a type hint alias as described here:
https://docs.python.org/3/library/typing.html#type-aliases
Let me try and see if it passes mypy.

[spamegg1]

What do you know? It does work!

[cclauss]

Suggested change

	if derivative(prev_guess) == 0:
	raise ZeroDivisionError("float division by zero, could not find root")
	next_guess: float = prev_guess - function(prev_guess) / derivative(prev_guess)
	try:
	next_guess: float = prev_guess - function(prev_guess) / derivative(prev_guess)
	except ZeroDivisionError:
	raise ZeroDivisionError("Could not find root")

Avoid calculating the derivative twice. The error type already says that we have a division by zero -- we do not need to repeat.

[spamegg1]

Makes sense, got it.

[dhruvmanila]

Hey @spamegg1, from OSSU here. I was just going through this issue and looking at the changes made and this will create a problem where if there is a ZeroDivisionError then two exceptions will be raised. This PR is merged so it's better for @cclauss to make this small change.

>>> try:
...     a = 1/0
... except ZeroDivisionError:
...     raise ZeroDivisionError("Not possible")
...
Traceback (most recent call last):
  File "<stdin>", line 2, in <module>
ZeroDivisionError: division by zero

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "<stdin>", line 4, in <module>
ZeroDivisionError: Not possible

Why? the except block is used to handle the exceptions, if you want to raise an exception inside it you need to use the from clause like so:

>>> try:
...     a = 1/0
... except ZeroDivisionError:
...     raise ZeroDivisionError("Not possible") from None
...
Traceback (most recent call last):
  File "<stdin>", line 4, in <module>
ZeroDivisionError: Not possible

You can also use from in other ways which I won't go into detail much here but just wanted to point this out. 😁

[cclauss]

Lines 36-38 can not raise a ZeroDivisionError so they should not be in the try block as discussed in PEP8.

[spamegg1]

OK, didn't know that. Understood.

[TravisBuddy]

Hey @spamegg1,
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[spamegg1]

Hi @cclauss I know this got merged, but something weird must have happened during the merging process. In your last commit d55491a, Line 30 changed from prev_guess: float = starting_int (which is what I had in my last commit 8e20e61) to prev_guess float(starting_int) which makes the file currently broken. I already deleted my forked repo and realized this only later. If you could change it back it would be greatly appreciated. I probably should not make another PR over this.

[cclauss]

It was my mistake... It is now fixed on master. Thanks!