






import math as m



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__=0.001	):


		'''simple docstring'''

		return (f(a + h	) - f(a - h	)) / (2 * h)



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__=0					,     lowerCAmelCase__=100					,     lowerCAmelCase__=0.0_001					,     lowerCAmelCase__=1E-6					,     lowerCAmelCase__=False	):


		'''simple docstring'''

		__A    =							xa  # set the initial guess
		__A    =							[a]
		__A    =							abs(f(lowerCAmelCase__	)	)
		__A    =							lambda lowerCAmelCase__	: calc_derivative(lowerCAmelCase__					,     lowerCAmelCase__					,     h=lowerCAmelCase__	)  # noqa: E731  Derivative of f(x)
		for _ in range(lowerCAmelCase__	):
				if fa(lowerCAmelCase__	) == 0:
						raise ValueError("No converging solution found"	)
				__A    =							a - f(lowerCAmelCase__	) / fa(lowerCAmelCase__	)  # Calculate the next estimate
				if logsteps:
						steps.append(lowerCAmelCase__	)
				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_   :	Tuple							      =lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
					snake_case_      ,	snake_case_      ,	snake_case_   :	str							      =newton_raphson(
					    f, xa=10, maxiter=1000, 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}}}""")








'''simple docstring'''


from typing import Callable




def       A							(      _UpperCAmelCase   :				Callable					)  ->				Dict:


  '''simple docstring'''




  def wrapper(_UpperCAmelCase   :				Optional[Any]					):
    __lowerCAmelCase		:    List[Any]			     =  function_with_docstring.__doc__
    return target_function

  return wrapper





