





from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def      _UpperCamelCase  (a__ :int							):






							"""simple docstring"""





							def is_in_circle(a__ :float ,      a__ :float							) -> bool:
														UpperCamelCase__					  =      sqrt((x**2) + (y**2)							)
														# Our circle has a radius of 1, so a distance
														# greater than 1 would land outside the circle.
														return distance_from_centre <= 1

							# The proportion of guesses that landed in the circle
							UpperCamelCase__					  =      mean(
							    int(is_in_circle(uniform(-1.0 ,      1.0							) ,      uniform(-1.0 ,      1.0							)							)							)
							    for _ in range(a__							)							)
							# The ratio of the area for circle to square is pi/4.
							UpperCamelCase__					  =      proportion * 4
							print(f"""The estimated value of pi is {pi_estimate}"""							)
							print(f"""The numpy value of pi is {pi}"""							)
							print(f"""The total error is {abs(pi - pi_estimate							)}"""							)





def      _UpperCamelCase  (a__ :int ,      a__ :Callable[[float], float] ,      a__ :float = 0.0 ,      a__ :float = 1.0 ,      ):






							"""simple docstring"""





							return mean(
							    function_to_integrate(uniform(a__ ,      a__							)							) for _ in range(a__							)							) * (max_value - min_value)





def      _UpperCamelCase  (a__ :int ,      a__ :float = 0.0 ,      a__ :float = 1.0							):






							"""simple docstring"""





							def identity_function(a__ :float							) -> float:
														return x

							UpperCamelCase__					  =      area_under_curve_estimator(
							    a__ ,      a__ ,      a__ ,      a__							)
							UpperCamelCase__					  =      (max_value * max_value - min_value * min_value) / 2

							print("""******************"""							)
							print(f"""Estimating area under y=x where x varies from {min_value} to {max_value}"""							)
							print(f"""Estimated value is {estimated_value}"""							)
							print(f"""Expected value is {expected_value}"""							)
							print(f"""Total error is {abs(estimated_value - expected_value							)}"""							)
							print("""******************"""							)





def      _UpperCamelCase  (a__ :int							):






							"""simple docstring"""





							def function_to_integrate(a__ :float							) -> float:
														return sqrt(4.0 - x * x							)

							UpperCamelCase__					  =      area_under_curve_estimator(
							    a__ ,      a__ ,      0.0 ,      2.0							)

							print("""******************"""							)
							print("""Estimating pi using area_under_curve_estimator"""							)
							print(f"""Estimated value is {estimated_value}"""							)
							print(f"""Expected value is {pi}"""							)
							print(f"""Total error is {abs(estimated_value - pi							)}"""							)
							print("""******************"""							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()











# 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 							__SCREAMING_SNAKE_CASE       :






							def __init__(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase = True	,			__lowerCAmelCase = False	):
														UpperCamelCase__					  =      scheduler
														UpperCamelCase__					  =      optimizers if isinstance(__lowerCAmelCase	,			(list, tuple)	) else [optimizers]
														UpperCamelCase__					  =      split_batches
														UpperCamelCase__					  =      step_with_optimizer
														UpperCamelCase__					  =      GradientState()






							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														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
																					UpperCamelCase__					  =      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 					_lowerCamelCase		(    self	):
														return self.scheduler.get_last_lr()






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.state_dict()






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														self.scheduler.load_state_dict(__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.get_lr()







							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														return self.scheduler.print_lr(*__lowerCAmelCase	,			**__lowerCAmelCase	)




