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added type hints and doctests to arithmetic_analysis/intersection.py (#2242)

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continuing #2128
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spamegg 2020-08-01 09:02:31 +03:00 committed by GitHub
parent b57b6abb48
commit 9cda130c07
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1 changed files with 28 additions and 5 deletions
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33
arithmetic_analysis/intersection.py
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@ -1,15 +1,38 @@
import math
from typing import Callable
def intersection(function, x0, x1):
def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
"""
function is the f we want to find its root
x0 and x1 are two random starting points
>>> intersection(lambda x: x ** 3 - 1, -5, 5)
0.9999999999954654
>>> intersection(lambda x: x ** 3 - 1, 5, 5)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
>>> intersection(lambda x: x ** 3 - 1, 100, 200)
1.0000000000003888
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
0.9999999998088019
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
2.9999999998088023
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
3.0000000001786042
>>> intersection(math.sin, -math.pi, math.pi)
0.0
>>> intersection(math.cos, -math.pi, math.pi)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
"""
x_n = x0
x_n1 = x1
x_n: float = x0
x_n1: float = x1
while True:
x_n2 = x_n1 - (
if x_n == x_n1 or function(x_n1) == function(x_n):
raise ZeroDivisionError("float division by zero, could not find root")
x_n2: float = x_n1 - (
function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
)
if abs(x_n2 - x_n1) < 10 ** -5:
@ -18,7 +41,7 @@ def intersection(function, x0, x1):
x_n1 = x_n2
def f(x):
def f(x: float) -> float:
return math.pow(x, 3) - (2 * x) - 5