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Create Bisection.py
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""" | ||
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) | ||
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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 | ||
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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!") | ||
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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 | ||
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if __name__ == "__main__": | ||
import doctest | ||
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doctest.testmod() | ||
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print(bisection(-2, 5)) | ||
print(bisection(0, 6)) |
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