intersection.py

importmath
fromcollections.abcimportCallable


defintersection(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: float=x0
x_n1: float=x1
whileTrue:
ifx_n==x_n1orfunction(x_n1) ==function(x_n):
raiseZeroDivisionError("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))
 )
ifabs(x_n2-x_n1) <10**-5:
returnx_n2
x_n=x_n1
x_n1=x_n2


deff(x: float) ->float:
"""
 function is f(x) = x^3 - 2x - 5
 >>> f(2)
 -1.0
 """
returnmath.pow(x, 3) - (2*x) -5


if__name__=="__main__":
print(intersection(f, 3, 3.5))