diff --git a/maths/bisection.py b/maths/bisection.py new file mode 100644 index 000000000000..a9df15b775b3 --- /dev/null +++ b/maths/bisection.py @@ -0,0 +1,61 @@ +""" +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))