mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
4700297b3e
* Enable ruff RUF002 rule * Fix --------- Co-authored-by: Christian Clauss <cclauss@me.com>
64 lines
1.4 KiB
Python
64 lines
1.4 KiB
Python
"""
|
|
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
|
|
"""
|
|
|
|
|
|
def equation(x: float) -> float:
|
|
"""
|
|
>>> equation(5)
|
|
-15
|
|
>>> equation(0)
|
|
10
|
|
>>> equation(-5)
|
|
-15
|
|
>>> equation(0.1)
|
|
9.99
|
|
>>> equation(-0.1)
|
|
9.99
|
|
"""
|
|
return 10 - x * x
|
|
|
|
|
|
def bisection(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
|
|
if equation(a) * equation(b) >= 0:
|
|
raise ValueError("Wrong space!")
|
|
|
|
c = a
|
|
while (b - a) >= 0.01:
|
|
# Find middle point
|
|
c = (a + b) / 2
|
|
# Check if middle point is root
|
|
if equation(c) == 0.0:
|
|
break
|
|
# Decide the side to repeat the steps
|
|
if equation(c) * equation(a) < 0:
|
|
b = c
|
|
else:
|
|
a = c
|
|
return c
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
print(bisection(-2, 5))
|
|
print(bisection(0, 6))
|