



'''simple docstring'''






import torch

from accelerate import Accelerator, DistributedType

class 	_lowerCAmelCase     :






		'''simple docstring'''
		def __enter__(						self							:       Optional[int]		)      ->			str:







									'''simple docstring'''





									if self.enabled:
																_lowercase							:		Union[str, Any]				=   self.model.no_sync()
																self.model_sync_obj.__enter__()

									return self
		def __exit__(						self							:       Tuple      ,		UpperCamelCase_							:       int      ,		UpperCamelCase_							:       Union[str, Any]      ,		UpperCamelCase_							:       List[Any]		)      ->			List[str]:







									'''simple docstring'''





									if self.enabled:
																# Average all models on exit
																self._sync_and_avg_model_params()
																self.model_sync_obj.__exit__(UpperCamelCase_      ,		UpperCamelCase_      ,		UpperCamelCase_		)
		def __init__(						self							:       Optional[int]      ,		UpperCamelCase_							:       Accelerator      ,		UpperCamelCase_							:       torch.nn.Module      ,		UpperCamelCase_							:       int      ,		UpperCamelCase_							:       bool = True		)      ->			List[Any]:







									'''simple docstring'''





									if accelerator.distributed_type not in [
									    DistributedType.NO,
									    DistributedType.MULTI_CPU,
									    DistributedType.MULTI_GPU,
									]:
																raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'''		)
									_lowercase							:		List[str]				=   enabled and accelerator.distributed_type != DistributedType.NO
									_lowercase							:		List[str]				=   0
									if self.enabled:
																_lowercase							:		Tuple				=   accelerator
																_lowercase							:		Union[str, Any]				=   model
																_lowercase							:		Tuple				=   local_sgd_steps
		def 						__lowercase      (						self							:       List[str]		)      ->			int:







									'''simple docstring'''





									self.num_steps += 1
									if not self.enabled:
																return

									if self.num_steps % self.local_sgd_steps == 0:
																self._sync_and_avg_model_params()





		def 						__lowercase      (						self							:       List[str]		)      ->			List[str]:







									'''simple docstring'''





									self.accelerator.wait_for_everyone()
									with self.accelerator.autocast():
																for param in self.model.parameters():
																							_lowercase							:		Optional[int]				=   self.accelerator.reduce(param.data      ,		reduction='''mean'''		)








'''simple docstring'''






import math as m





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Union[str, Any] ,       snake_case_    :     int ,       snake_case_    :     Optional[Any]=0.0_0_1  )		->Tuple:






							'''simple docstring'''
							return (f(a + h  ) - f(a - h  )) / (2 * h)





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Dict ,       snake_case_    :     List[Any]=0 ,       snake_case_    :     Dict=1_00 ,       snake_case_    :     List[str]=0.0_0_0_1 ,       snake_case_    :     str=1E-6 ,       snake_case_    :     Tuple=False  )		->List[Any]:






							'''simple docstring'''
							_lowercase							:		Tuple				=   xa  # set the initial guess
							_lowercase							:		List[str]				=   [a]
							_lowercase							:		str				=   abs(f(snake_case_  )  )
							_lowercase							:		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'''  )
														_lowercase							:		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

						lowerCamelCase__	  =		lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
						lowerCamelCase__  ,      lowerCamelCase__  ,      lowerCamelCase__	  =		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}}}''')



