
'''simple docstring'''





from collections.abc import Callable

A							     = Callable[[float], float]  # type alias for a real -> real function
def 	snake_case_							(				_a  :				RealFunc			,       _a  :				RealFunc			,       _a  :				int			,       ):
      snake_case_    							=				float(_a      )
      while True:
            try:
                  snake_case_    							=				prev_guess - function(_a      ) / derivative(_a      )
            except ZeroDivisionError:
                  raise ZeroDivisionError("Could not find root"      ) from None
            if abs(prev_guess - next_guess      ) < 10**-5:
                  return next_guess
            snake_case_    							=				next_guess
def 	snake_case_							(				_a  :				float      ):
      return (x**3) - (2 * x) - 5
def 	snake_case_							(				_a  :				float      ):
      return 3 * (x**2) - 2


if __name__ == "__main__":
     print(newton(f, fa, 3))





"""simple docstring"""





import math as m


def   _snake_case    (    _snake_case					:      List[Any]			, _snake_case					:      Tuple			, _snake_case					:      Tuple=0.001      ):
      return (f(a + h      ) - f(a - h      )) / (2 * h)


def   _snake_case    (    _snake_case					:      int			, _snake_case					:      List[Any]=0			, _snake_case					:      Any=100			, _snake_case					:      Any=0.0001			, _snake_case					:      Optional[Any]=1E-6			, _snake_case					:      Any=False      ):
      lowerCAmelCase       :						Optional[Any]							= xa  # set the initial guess
      lowerCAmelCase       :						str							= [a]
      lowerCAmelCase       :						List[str]							= abs(f(_snake_case      )      )
      lowerCAmelCase       :						Dict							= lambda _snake_case      : calc_derivative(_snake_case			, _snake_case			, h=_snake_case      )  # noqa: E731  Derivative of f(x)
      for _ in range(_snake_case      ):
            if fa(_snake_case      ) == 0:
                  raise ValueError('''No converging solution found'''      )
            lowerCAmelCase       :						Tuple							= a - f(_snake_case      ) / fa(_snake_case      )  # Calculate the next estimate
            if logsteps:
                  steps.append(_snake_case      )
            if error < maxerror:
                  break
      else:
            raise ValueError('''Iteration limit reached, no converging solution found'''      )
      if logsteps:
            # If logstep is true, then log intermediate steps
            return a, error, steps
      return a, error


if __name__ == "__main__":
 from matplotlib import pyplot as plt

 snake_case__		:  Any     					=					lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
 snake_case__					,  snake_case__					,  snake_case__		:  List[str]     					=					newton_raphson(
     f, xa=10, maxiter=1_000, step=1e-6, logsteps=True
 )
 plt.plot([abs(f(x)) for x in steps])
 plt.xlabel('''step''')
 plt.ylabel('''error''')
 plt.show()
 print(f"""solution = {{{solution:f}}}, error = {{{error:f}}}""")


