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Newton-Raphson Equation Root Finder
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| from abc import abstractmethod, ABC | |
| from typing import Tuple, List, Generator | |
| class Function(ABC): | |
| """Function for Newton-Raphson algorithm | |
| """ | |
| @abstractmethod | |
| def calculate(self, x: float) -> float: | |
| """Executes function on x which is iteratively corrected guess value, | |
| until is step is smaller than precision """ | |
| pass | |
| class FDx(Function): | |
| """Derived F(x) == F'(x), e.g. if F(x) = x^2 => F'(x) = 2x """ | |
| @abstractmethod | |
| def calculate(self, x: float) -> float: | |
| """see Function.calculate""" | |
| pass | |
| class Fx(Function): | |
| """Function from which we are calculating F(x) = 0""" | |
| @abstractmethod | |
| def calculate(self, x: float) -> float: | |
| """see Function.calculate""" | |
| pass | |
| @property | |
| @abstractmethod | |
| def derived(self) -> FDx: | |
| """Create a derivation of this function""" | |
| pass | |
| class NewtonRaphsonCalculator(object): | |
| """General implementation of Newton-Raphson method | |
| Accepts more functions, but every Fx should have its derived version FDx | |
| """ | |
| DEFAULT_GUESS = 0.01 | |
| DEFAULT_PRECISION = 7 | |
| MAXIMUM_ITERATIONS = 10000 | |
| def __init__(self, *fs: Fx, precision: int = DEFAULT_PRECISION): | |
| assert all(isinstance(f, Fx) for f in fs), \ | |
| "NewtonRaphsonCalculator accepts only `Fx` objects" | |
| self.fxs: List[Fx] = list(fs) | |
| self.precision = self._precision = precision | |
| def execute_functions(self, guess: float) -> Generator[Tuple[float, float], None, None]: | |
| """Executes functions on guessed value""" | |
| return ((fx.calculate(guess), fx.derived.calculate(guess)) for fx in self.fxs) | |
| @property | |
| def precision(self): | |
| return pow(10, -self._precision) | |
| @precision.setter | |
| def precision(self, value: int): | |
| assert isinstance(value, int) | |
| self._precision = value | |
| def calculate(self, guess: float = DEFAULT_GUESS) -> float: | |
| """Executes the iterative calculation | |
| See more about this method in https://en.wikipedia.org/wiki/Newton%27s_method | |
| basically you want to calculate x when F(x) = 0, so you will need F'(x) with this method | |
| If there are partial functions, they will summed together: | |
| F(x) = F1(x) + F2(x) + ... + Fn(x) | |
| F'(x) = F1'(x) + F2'(x) + ... + Fn'(x) | |
| """ | |
| diff = 1.0 | |
| value = guess | |
| iterations = 0 | |
| while diff > self.precision: | |
| assert iterations < self.MAXIMUM_ITERATIONS, \ | |
| "Maximum iteration loop `count:{}` exceeded".format(self.MAXIMUM_ITERATIONS) | |
| iterations += 1 | |
| # sum up all results of all functions | |
| ys, yds = zip(*self.execute_functions(value)) | |
| y, yd = sum(ys), sum(yds) | |
| # remember the last value | |
| old_value = value | |
| assert yd != 0, "for `value:{}` f'(x) returned bad value: 0".format(value) | |
| # value[n] = value[n-1] - Fn(x)/Fn'(x) | |
| value = old_value - y / yd | |
| diff = abs(old_value - value) | |
| return value |
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