




'''simple docstring'''




import math as m




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




def     snake_case__     (			lowerCamelCase__					: Tuple      ,		lowerCamelCase__					: int=0      ,		lowerCamelCase__					: List[Any]=1_0_0      ,		lowerCamelCase__					: Optional[int]=0.0001      ,		lowerCamelCase__					: int=1e-6      ,		lowerCamelCase__					: Optional[Any]=False      ) -> Tuple:
					A_			:  int			=				xa  # set the initial guess
					A_			:  int			=				[a]
					A_			:  Union[str, Any]			=				abs(f(lowerCamelCase__      )      )
					A_			:  List[str]			=				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_			:  Dict			=				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__ 							=    lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
							snake_case__							,    snake_case__							,    snake_case__ 							=    newton_raphson(
							    f, xa=10, maxiter=10_00, 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'''




import abc
import copy
import dataclasses
from dataclasses import dataclass
from typing import ClassVar, Dict, Type, TypeVar

from ..features import Features


snake_case__ 							=    TypeVar("""T""", bound="""TaskTemplate""")






@dataclass(frozen=a__  )
class      UpperCamelCase_  (abc.ABC  ):







						"""simple docstring"""


						_lowerCAmelCase         =       42
						_lowerCAmelCase         =       42
						_lowerCAmelCase         =       42







						def    _a     (  self   :							T				,			_lowerCamelCase   :							Features     ):





											"""simple docstring"""







											return copy.deepcopy(self     )







						@property
						def    _a     (  self   :							List[str]     ):





											"""simple docstring"""







											return Features(**self.input_schema				,			**self.label_schema     )







						@property
						@abc.abstractmethod
						def    _a     (  self   :							int     ):





											"""simple docstring"""







											raise NotImplementedError







						@classmethod
						def    _a     (  cls   :							Type[T]				,			_lowerCamelCase   :							dict     ):





											"""simple docstring"""







											A_			:  Dict			=				{f.name for f in dataclasses.fields(cls     )}
											return cls(**{k: v for k, v in template_dict.items() if k in field_names}     )



