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added type hints and doctests to arithmetic_analysis/newton_method.py #2259

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Merged
merged 4 commits into from
Aug 1, 2020
Merged

added type hints and doctests to arithmetic_analysis/newton_method.py #2259

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f26b8b2
added type hints and doctests to arithmetic_analysis/newton_method.py
spamegg1 Aug 1, 2020
4ad625d
Added type hints and doctests to arithmetic_analysis/newton_method.py
spamegg1 Aug 1, 2020
8e20e61
added type hints and doctests to arithmetic_analysis/newton_method.py
spamegg1 Aug 1, 2020
d55491a
Update newton_method.py
cclauss Aug 1, 2020
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49 changes: 38 additions & 11 deletions arithmetic_analysis/newton_method.py
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Original file line number Diff line number Diff line change
@@ -1,23 +1,50 @@
"""Newton's Method."""

# Newton's Method - https://en.wikipedia.org/wiki/Newton%27s_method


# function is the f(x) and function1 is the f'(x)
def newton(function, function1, startingInt):
x_n = startingInt
from typing import Callable


# function is the f(x) and derivative is the f'(x)
def newton(
function: Callable[[float], float],
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Is there a way to defined a type for Callable[[float], float] and then use that type to simplify the call parameters?

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@spamegg1 spamegg1 Aug 1, 2020 •
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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.

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What do you know? It does work!

derivative: Callable[[float], float],
starting_int: int,
) -> float:
"""
>>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
2.0945514815423474
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -2)
1.0
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -4)
1.0000000000000102
>>> import math
>>> newton(math.sin, math.cos, 1)
0.0
>>> newton(math.sin, math.cos, 2)
3.141592653589793
>>> newton(math.cos, lambda x: -math.sin(x), 2)
1.5707963267948966
>>> newton(math.cos, lambda x: -math.sin(x), 0)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
"""
prev_guess: float = starting_int
while True:
x_n1 = x_n - function(x_n) / function1(x_n)
if abs(x_n - x_n1) < 10 ** -5:
return x_n1
x_n = x_n1
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)
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@cclauss cclauss Aug 1, 2020 •
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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.

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Makes sense, got it.

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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. 😁

if abs(prev_guess - next_guess) < 10 ** -5:
return next_guess
prev_guess = next_guess


def f(x):
def f(x: float) -> float:
return (x ** 3) - (2 * x) - 5


def f1(x):
def f1(x: float) -> float:
return 3 * (x ** 2) - 2


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