



# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("""ignore""", category=UserWarning, module="""torch.optim.lr_scheduler""")

class 	lowerCamelCase_    :






						'''simple docstring'''







						def __init__(	self      :			Optional[Any]	,	__lowerCamelCase      :			str	,	__lowerCamelCase      :			List[str]	,	__lowerCamelCase      :			bool = True	,	__lowerCamelCase      :			bool = False )      ->				List[str]:
									A							:					List[Any]              =						scheduler
									A							:					int              =						optimizers if isinstance(__lowerCamelCase	,	(list, tuple) ) else [optimizers]
									A							:					Any              =						split_batches
									A							:					List[str]              =						step_with_optimizer
									A							:					Tuple              =						GradientState()







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Union[str, Any]	,	*__lowerCamelCase      :			int	,	**__lowerCamelCase      :			str )      ->				List[Any]:
									if not self.step_with_optimizer:
												# No link between scheduler and optimizer -> just step
												self.scheduler.step(*__lowerCamelCase	,	**__lowerCamelCase )
												return

									# Otherwise, first make sure the optimizer was stepped.
									if not self.gradient_state.sync_gradients:
												if self.gradient_state.adjust_scheduler:
															self.scheduler._step_count += 1
												return

									for opt in self.optimizers:
												if opt.step_was_skipped:
															return
									if self.split_batches:
												# Split batches -> the training dataloader batch size is not changed so one step per training step
												self.scheduler.step(*__lowerCamelCase	,	**__lowerCamelCase )
									else:
												# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
												# num_processes steps per training step
												A							:					str              =						AcceleratorState().num_processes
												for _ in range(__lowerCamelCase ):
															# Special case when using OneCycle and `drop_last` was not used
															if hasattr(self.scheduler	,	"total_steps" ):
																		if self.scheduler._step_count <= self.scheduler.total_steps:
																					self.scheduler.step(*__lowerCamelCase	,	**__lowerCamelCase )
															else:
																		self.scheduler.step(*__lowerCamelCase	,	**__lowerCamelCase )







						def 			SCREAMING_SNAKE_CASE__		(	self      :			List[str] )      ->				Any:
									return self.scheduler.get_last_lr()







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Any )      ->				Union[str, Any]:
									return self.scheduler.state_dict()







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Tuple	,	__lowerCamelCase      :			Optional[Any] )      ->				str:
									self.scheduler.load_state_dict(__lowerCamelCase )







						def 			SCREAMING_SNAKE_CASE__		(	self      :			List[Any] )      ->				Any:
									return self.scheduler.get_lr()







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Union[str, Any]	,	*__lowerCamelCase      :			str	,	**__lowerCamelCase      :			str )      ->				Tuple:
									return self.scheduler.print_lr(*__lowerCamelCase	,	**__lowerCamelCase )




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase = "x" ,    _lowerCamelCase = 10**-10 ,    _lowerCamelCase = 1 ,    ):
			A							:					str              =						symbols(_lowerCamelCase    )
			A							:					int              =						lambdify(_lowerCamelCase ,    _lowerCamelCase    )
			A							:					List[str]              =						lambdify(_lowerCamelCase ,    diff(_lowerCamelCase ,    _lowerCamelCase    )    )

			A							:					Optional[int]              =						starting_point

			while True:
						if diff_function(_lowerCamelCase    ) != 0:
									A							:					Optional[Any]              =						prev_guess - multiplicity * func(_lowerCamelCase    ) / diff_function(
									    _lowerCamelCase    )
						else:
									raise ZeroDivisionError("Could not find root"    ) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess    ) < precision:
									return next_guess

						A							:					int              =						next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(F"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}""")

							# Find value of e
							print(
							    """The root of log(y) - 1 = 0 is """,
							    F"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
							)

							# Exponential Roots
							print(
							    """The root of exp(x) - 1 = 0 is""",
							    F"""{newton_raphson('exp(x) - 1', 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(F"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")