mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
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))
|