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  1. import time
  2. import random
  3. import math
  4. from typing import *
  5.  
  6.  
  7. def newton(f, fder, x0, iteration_limit=1000, tolerance=1e-10) -> Tuple[float, int]:
  8.     i = 0
  9.     xn = x0
  10.     xn_1 = x0
  11.     while i < iteration_limit and not math.isclose(f(xn), 0, abs_tol=tolerance):
  12.         xn = xn_1 - f(xn_1) / fder(xn_1)
  13.         xn_1 = xn
  14.         i += 1
  15.     return (xn, i)
  16.  
  17.  
  18. def find_null_point(f, fder, x0) -> None:
  19.     calculation_start = time.perf_counter()
  20.     (null_point, iterations_needed) = newton(f, fder, x0)
  21.     calculation_end = time.perf_counter()
  22.     calculation_time = calculation_end - calculation_start
  23.  
  24.     print("Newtons method result: {} (f(x): {}, iterations needed: {}, starting point: {}, time spent: {})".format(
  25.         null_point, f(null_point), iterations_needed, x0, calculation_time))
  26.  
  27.  
  28. f = lambda x: x - 3
  29. fder = lambda x: 1
  30. g = lambda x: x**2 - 3
  31. gder = lambda x: 2 * x
  32. x0 = random.uniform(-100, 100) # start at random x0 point at x axis
  33. find_null_point(f, fder, x0)
  34. find_null_point(g, gder, x0)
Success #stdin #stdout 0.03s 12556KB
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Newtons method result: 3.0 (f(x): 0.0, iterations needed: 1, starting point: 94.16773059053784, time spent: 1.1803116649389267e-05)
Newtons method result: 1.7320508075688774 (f(x): 4.440892098500626e-16, iterations needed: 10, starting point: 94.16773059053784, time spent: 1.0865973308682442e-05)
https://ideone.com/Iwofkg
language:
Python 3 (python  3.9.5)
created:
3 years ago
visibility:
public

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