'''simple docstring'''




import math as m






def     snake_case__							(      _A: List[Any]				,       _A: int				,       _A: int=0.001			)   ->     List[Any]:
		return (f(a + h			) - f(a - h			)) / (2 * h)






def     snake_case__							(      _A: Dict				,       _A: List[str]=0				,       _A: Optional[int]=100				,       _A: List[str]=0.0_001				,       _A: Union[str, Any]=1e-6				,       _A: List[Any]=False			)   ->     Optional[int]:
		lowerCAmelCase        =  xa  # set the initial guess
		lowerCAmelCase        =  [a]
		lowerCAmelCase        =  abs(f(_A			)			)
		lowerCAmelCase        =  lambda _A			: calc_derivative(_A				,       _A				,       h=_A			)  # noqa: E731  Derivative of f(x)
		for _ in range(_A			):
				if fa(_A			) == 0:
						raise ValueError("""No converging solution found"""			)
				lowerCAmelCase        =  a - f(_A			) / fa(_A			)  # Calculate the next estimate
				if logsteps:
						steps.append(_A			)
				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

						__lowercase				   =  lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
						__lowercase   ,					__lowercase   ,					__lowercase				   =  newton_raphson(
						    f, xa=1_0, maxiter=1_0_0_0, 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 ..utils import DummyObject, requires_backends






class     a__( metaclass=lowerCAmelCase__     ):


			'''simple docstring'''






			UpperCAmelCase_      :					Optional[int]								=	['''torch''', '''transformers''', '''k_diffusion''']



			def __init__(       self	,   *__lowerCAmelCase	,   **__lowerCAmelCase):




					"""simple docstring"""


					requires_backends(self	,   ["""torch""", """transformers""", """k_diffusion"""])



			@classmethod
			def 							a_	(       cls	,   *__lowerCAmelCase	,   **__lowerCAmelCase):




					"""simple docstring"""


					requires_backends(cls	,   ["""torch""", """transformers""", """k_diffusion"""])







			@classmethod
			def 							a_	(       cls	,   *__lowerCAmelCase	,   **__lowerCAmelCase):




					"""simple docstring"""


					requires_backends(cls	,   ["""torch""", """transformers""", """k_diffusion"""])




