



"""simple docstring"""







import math as m

def    __SCREAMING_SNAKE_CASE		( lowerCamelCase_:       Optional[int]    ,		lowerCamelCase_:       Optional[Any]    ,		lowerCamelCase_:       int=0.0_0_1   ):
						"""simple docstring"""






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

def    __SCREAMING_SNAKE_CASE		( lowerCamelCase_:       Optional[Any]    ,		lowerCamelCase_:       Optional[Any]=0    ,		lowerCamelCase_:       List[Any]=1_0_0    ,		lowerCamelCase_:       Optional[Any]=0.0_0_0_1    ,		lowerCamelCase_:       List[Any]=1e-6    ,		lowerCamelCase_:       Any=False   ):
						"""simple docstring"""






						snake_case      : List[str]							=   xa  # set the initial guess
						snake_case      : Optional[int]							=   [a]
						snake_case      : Union[str, Any]							=   abs(f(lowerCamelCase_   )   )
						snake_case      : 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"   )
												snake_case      : Tuple							=   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

			A    =	lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
			A  ,  A  ,  A    =	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"""







import random
from typing import List, Optional, Union

import numpy as np
import torch

from ..state import AcceleratorState
from .constants import CUDA_DISTRIBUTED_TYPES
from .dataclasses import DistributedType, RNGType
from .imports import is_npu_available, is_tpu_available, is_xpu_available


if is_tpu_available(check_device=False):
			import torch_xla.core.xla_model as xm

def    __SCREAMING_SNAKE_CASE		( lowerCamelCase_:       int    ,		lowerCamelCase_:       bool = False   ):
						"""simple docstring"""






						if device_specific:
												seed += AcceleratorState().process_index
						random.seed(lowerCamelCase_   )
						np.random.seed(lowerCamelCase_   )
						torch.manual_seed(lowerCamelCase_   )
						if is_xpu_available():
												torch.xpu.manual_seed_all(lowerCamelCase_   )
						elif is_npu_available():
												torch.npu.manual_seed_all(lowerCamelCase_   )
						else:
												torch.cuda.manual_seed_all(lowerCamelCase_   )
						# ^^ safe to call this function even if cuda is not available
						if is_tpu_available():
												xm.set_rng_state(lowerCamelCase_   )

def    __SCREAMING_SNAKE_CASE		( lowerCamelCase_:       Optional[RNGType] = None    ,		lowerCamelCase_:       Optional[torch.Generator] = None   ):
						"""simple docstring"""






						if rng_type == RNGType.TORCH:
												snake_case      : List[Any]							=   torch.get_rng_state()
						elif rng_type == RNGType.CUDA:
												snake_case      : Union[str, Any]							=   torch.cuda.get_rng_state()
						elif rng_type == RNGType.XLA:
												assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
												snake_case      : Optional[int]							=   torch.tensor(xm.get_rng_state()   )
						elif rng_type == RNGType.NPU:
												assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
												snake_case      : int							=   torch.npu.get_rng_state()
						elif rng_type == RNGType.XPU:
												assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
												snake_case      : int							=   torch.xpu.get_rng_state()
						elif rng_type == RNGType.GENERATOR:
												assert generator is not None, "Need a generator to synchronize its seed."
												snake_case      : List[Any]							=   generator.get_state()

						# Broadcast the rng state from device 0 to other devices
						snake_case      : Dict							=   AcceleratorState()
						if state.distributed_type == DistributedType.TPU:
												snake_case      : List[str]							=   rng_state.to(xm.xla_device()   )
												xm.collective_broadcast([rng_state]   )
												xm.mark_step()
												snake_case      : List[Any]							=   rng_state.cpu()
						elif (
						    state.distributed_type in CUDA_DISTRIBUTED_TYPES
						    or state.distributed_type == DistributedType.MULTI_NPU
						    or state.distributed_type == DistributedType.MULTI_XPU
						):
												snake_case      : str							=   rng_state.to(state.device   )
												torch.distributed.broadcast(lowerCamelCase_    ,		0   )
												snake_case      : Union[str, Any]							=   rng_state.cpu()
						elif state.distributed_type == DistributedType.MULTI_CPU:
												torch.distributed.broadcast(lowerCamelCase_    ,		0   )

						# Set the broadcast rng state
						if rng_type == RNGType.TORCH:
												torch.set_rng_state(lowerCamelCase_   )
						elif rng_type == RNGType.CUDA:
												torch.cuda.set_rng_state(lowerCamelCase_   )
						elif rng_type == RNGType.NPU:
												torch.npu.set_rng_state(lowerCamelCase_   )
						elif rng_type == RNGType.XPU:
												torch.xpu.set_rng_state(lowerCamelCase_   )
						elif rng_type == RNGType.XLA:
												xm.set_rng_state(rng_state.item()   )
						elif rng_type == RNGType.GENERATOR:
												generator.set_state(lowerCamelCase_   )

def    __SCREAMING_SNAKE_CASE		( lowerCamelCase_:       List[Union[str, RNGType]]    ,		lowerCamelCase_:       Optional[torch.Generator] = None   ):
						"""simple docstring"""






						for rng_type in rng_types:
												synchronize_rng_state(RNGType(lowerCamelCase_   )    ,		generator=lowerCamelCase_   )



