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55 lines
1.5 KiB
Python
55 lines
1.5 KiB
Python
"""Newton's Method."""
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# Newton's Method - https://en.wikipedia.org/wiki/Newton%27s_method
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from typing import Callable
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RealFunc = Callable[[float], float] # type alias for a real -> real function
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# function is the f(x) and derivative is the f'(x)
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def newton(
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function: RealFunc,
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derivative: RealFunc,
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starting_int: int,
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) -> float:
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"""
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>>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
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2.0945514815423474
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>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -2)
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1.0
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>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -4)
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1.0000000000000102
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>>> import math
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>>> newton(math.sin, math.cos, 1)
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0.0
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>>> newton(math.sin, math.cos, 2)
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3.141592653589793
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>>> newton(math.cos, lambda x: -math.sin(x), 2)
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1.5707963267948966
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>>> newton(math.cos, lambda x: -math.sin(x), 0)
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Traceback (most recent call last):
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...
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ZeroDivisionError: Could not find root
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"""
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prev_guess = float(starting_int)
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while True:
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try:
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next_guess = prev_guess - function(prev_guess) / derivative(prev_guess)
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except ZeroDivisionError:
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raise ZeroDivisionError("Could not find root") from None
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if abs(prev_guess - next_guess) < 10 ** -5:
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return next_guess
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prev_guess = next_guess
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def f(x: float) -> float:
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return (x ** 3) - (2 * x) - 5
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def f1(x: float) -> float:
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return 3 * (x ** 2) - 2
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if __name__ == "__main__":
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print(newton(f, f1, 3))
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