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maths/numerical_analysis/bisection_2.py
63 строки
1 KB
Maxim Smolskiy
Enable ruff RUF002 rule (#11377)
22 апр 2024, 22:51
Не верифицирован
22 апр 2024, 22:51
4700297
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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) 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))