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added type hints and doctests to arithmetic_analysis/bisection.py (#2241)

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* added type hints and doctests to arithmetic_analysis/bisection.py

continuing in line with #2128

* modified arithmetic_analysis/bisection.py

Put back print statement at the end, replaced algorithm's print statement with an exception.

* modified arithmetic_analysis/bisection.py

Removed unnecessary type import "Optional"

* modified arithmetic_analysis/bisection.py

Replaced generic Exception with ValueError.

* modified arithmetic_analysis/bisection.py

fixed doctests
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spamegg 2020-07-27 16:23:55 +03:00 committed by GitHub
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1 changed files with 31 additions and 14 deletions
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arithmetic_analysis/bisection.py
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@ -1,12 +1,26 @@
import math
from typing import Callable
def bisection(
function, a, b
): # finds where the function becomes 0 in [a,b] using bolzano
start = a
end = b
def bisection(function: Callable[[float], float], a: float, b: float) -> float:
"""
finds where function becomes 0 in [a,b] using bolzano
>>> bisection(lambda x: x ** 3 - 1, -5, 5)
1.0000000149011612
>>> bisection(lambda x: x ** 3 - 1, 2, 1000)
Traceback (most recent call last):
...
ValueError: could not find root in given interval.
>>> bisection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
1.0
>>> bisection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
3.0
>>> bisection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
Traceback (most recent call last):
...
ValueError: could not find root in given interval.
"""
start: float = a
end: float = b
if function(a) == 0: # one of the a or b is a root for the function
return a
elif function(b) == 0:
@ -14,12 +28,11 @@ def bisection(
elif (
function(a) * function(b) > 0
): # if none of these are root and they are both positive or negative,
# then his algorithm can't find the root
print("couldn't find root in [a,b]")
return
# then this algorithm can't find the root
raise ValueError("could not find root in given interval.")
else:
mid = start + (end - start) / 2.0
while abs(start - mid) > 10 ** -7: # until we achieve precise equals to 10^-7
mid: float = start + (end - start) / 2.0
while abs(start - mid) > 10 ** -7: # until precisely equals to 10^-7
if function(mid) == 0:
return mid
elif function(mid) * function(start) < 0:
@ -30,9 +43,13 @@ def bisection(
return mid
def f(x):
return math.pow(x, 3) - 2 * x - 5
def f(x: float) -> float:
return x ** 3 - 2 * x - 5
if __name__ == "__main__":
print(bisection(f, 1, 1000))
import doctest
doctest.testmod()