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maths/numerical_analysis/square_root.py
63 строки
1 KB
Tianyi Zheng
Delete `arithmetic_analysis/` directory and relocate its contents (#10824)
23 окт 2023, 10:31
Не верифицирован
23 окт 2023, 10:31
a8b6bda
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import math def fx(x: float, a: float) -> float: return math.pow(x, 2) - a def fx_derivative(x: float) -> float: return 2 * x def get_initial_point(a: float) -> float: start = 2.0 while start <= a: start = math.pow(start, 2) return start def square_root_iterative( a: float, max_iter: int = 9999, tolerance: float = 1e-14 ) -> float: """ Square root approximated using Newton's method. https://en.wikipedia.org/wiki/Newton%27s_method >>> all(abs(square_root_iterative(i) - math.sqrt(i)) <= 1e-14 for i in range(500)) True >>> square_root_iterative(-1) Traceback (most recent call last): ... ValueError: math domain error >>> square_root_iterative(4) 2.0 >>> square_root_iterative(3.2) 1.788854381999832 >>> square_root_iterative(140) 11.832159566199232 """ if a < 0: raise ValueError("math domain error") value = get_initial_point(a) for _ in range(max_iter): prev_value = value value = value - fx(value, a) / fx_derivative(value) if abs(prev_value - value) < tolerance: return value return value if __name__ == "__main__": from doctest import testmod testmod()