bisection_2.py

"""
Given a function on floating number f(x) and two floating numbers `a` and `b` such that
f(a) * f(b) < 0 and f(x) is continuous in [a, b].
Here f(x) represents algebraic or transcendental equation.
Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)

https://en.wikipedia.org/wiki/Bisection_method
"""


defequation(x: float) ->float:
"""
 >>> equation(5)
 -15
 >>> equation(0)
 10
 >>> equation(-5)
 -15
 >>> equation(0.1)
 9.99
 >>> equation(-0.1)
 9.99
 """
return10-x*x


defbisection(a: float, b: float) ->float:
"""
 >>> bisection(-2, 5)
 3.1611328125
 >>> bisection(0, 6)
 3.158203125
 >>> bisection(2, 3)
 Traceback (most recent call last):
 ...
 ValueError: Wrong space!
 """
# Bolzano theory in order to find if there is a root between a and b
ifequation(a) *equation(b) >=0:
raiseValueError("Wrong space!")

c=a
while (b-a) >=0.01:
# Find middle point
c= (a+b) /2
# Check if middle point is root
ifequation(c) ==0.0:
break
# Decide the side to repeat the steps
ifequation(c) *equation(a) <0:
b=c
else:
a=c
returnc


if__name__=="__main__":
importdoctest

doctest.testmod()

print(bisection(-2, 5))
print(bisection(0, 6))