


# 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 ,						__lowerCamelCase ,						__lowerCamelCase ,						__lowerCamelCase = True ,						__lowerCamelCase = False)			->				Dict:
            _A      :       Dict				    = scheduler
            _A      :       Union[str, Any]				    = optimizers if isinstance(__lowerCamelCase ,						(list, tuple)) else [optimizers]
            _A      :       int				    = split_batches
            _A      :       int				    = step_with_optimizer
            _A      :       Any				    = GradientState()


     def  _lowerCamelCase (						self ,						*__lowerCamelCase ,						**__lowerCamelCase)			->				str:
            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      :       List[Any]				    = 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)			->				Union[str, Any]:
            return self.scheduler.get_last_lr()


     def  _lowerCamelCase (						self)			->				Optional[Any]:
            return self.scheduler.state_dict()


     def  _lowerCamelCase (						self ,						__lowerCamelCase)			->				Union[str, Any]:
            self.scheduler.load_state_dict(__lowerCamelCase)


     def  _lowerCamelCase (						self)			->				Tuple:
            return self.scheduler.get_lr()


     def  _lowerCamelCase (						self ,						*__lowerCamelCase ,						**__lowerCamelCase)			->				str:
            return self.scheduler.print_lr(*__lowerCamelCase ,						**__lowerCamelCase)


"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np



class 	lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__=None   ,       SCREAMING_SNAKE_CASE__=None    )					->		Dict:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   list(poly_a or [0]    )[:]
											SCREAMING_SNAKE_CASE__						:       Tuple           =   list(poly_b or [0]    )[:]

											# Remove leading zero coefficients
											while self.polyA[-1] == 0:
																		self.polyA.pop()
											SCREAMING_SNAKE_CASE__						:       int           =   len(self.polyA    )

											while self.polyB[-1] == 0:
																		self.polyB.pop()
											SCREAMING_SNAKE_CASE__						:       List[str]           =   len(self.polyB    )

											# Add 0 to make lengths equal a power of 2
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   int(
											    2 ** np.ceil(np.loga(len(self.polyA    ) + len(self.polyB    ) - 1    )    )    )

											while len(self.polyA    ) < self.c_max_length:
																		self.polyA.append(0    )
											while len(self.polyB    ) < self.c_max_length:
																		self.polyB.append(0    )
											# A complex root used for the fourier transform
											SCREAMING_SNAKE_CASE__						:       List[str]           =   complex(mpmath.root(x=1   ,       n=self.c_max_length   ,       k=1    )    )

											# The product
											SCREAMING_SNAKE_CASE__						:       Tuple           =   self.__multiply()



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Union[str, Any]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       str           =   [[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
											# Corner case
											if len(SCREAMING_SNAKE_CASE__    ) <= 1:
																		return dft[0]
											#
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   self.c_max_length // 2
											while next_ncol > 0:
																		SCREAMING_SNAKE_CASE__						:       Any           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root**next_ncol

																		# First half of next step
																		SCREAMING_SNAKE_CASE__						:       str           =   1
																		for j in range(self.c_max_length // (next_ncol * 2)    ):
																									for i in range(SCREAMING_SNAKE_CASE__    ):
																																new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]    )
																									current_root *= root
																		# Second half of next step
																		SCREAMING_SNAKE_CASE__						:       int           =   1
																		for j in range(self.c_max_length // (next_ncol * 2)    ):
																									for i in range(SCREAMING_SNAKE_CASE__    ):
																																new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]    )
																									current_root *= root
																		# Update
																		SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   new_dft
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   next_ncol // 2
											return dft[0]



				def 	__magic_name__    (self    )					->		int:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self.__dft("""A"""    )
											SCREAMING_SNAKE_CASE__						:       Dict           =   self.__dft("""B"""    )
											SCREAMING_SNAKE_CASE__						:       List[Any]           =   [[dft_a[i] * dft_b[i] for i in range(self.c_max_length    )]]
											del dft_a
											del dft_b

											# Corner Case
											if len(inverce_c[0]    ) <= 1:
																		return inverce_c[0]
											# Inverse DFT
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   2
											while next_ncol <= self.c_max_length:
																		SCREAMING_SNAKE_CASE__						:       List[str]           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root ** (next_ncol // 2)
																		SCREAMING_SNAKE_CASE__						:       Any           =   1
																		# First half of next step
																		for j in range(self.c_max_length // next_ncol    ):
																									for i in range(next_ncol // 2    ):
																																# Even positions
																																new_inverse_c[i].append(
																																    (
																																        inverce_c[i][j]
																																        + inverce_c[i][j + self.c_max_length // next_ncol]
																																    )
																																    / 2    )
																																# Odd positions
																																new_inverse_c[i + next_ncol // 2].append(
																																    (
																																        inverce_c[i][j]
																																        - inverce_c[i][j + self.c_max_length // next_ncol]
																																    )
																																    / (2 * current_root)    )
																									current_root *= root
																		# Update
																		SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   new_inverse_c
																		next_ncol *= 2
											# Unpack
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   [round(x[0].real   ,       8    ) + round(x[0].imag   ,       8    ) * 1j for x in inverce_c]

											# Remove leading 0's
											while inverce_c[-1] == 0:
																		inverce_c.pop()
											return inverce_c



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



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[str]           =   """A = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   """B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
											SCREAMING_SNAKE_CASE__						:       int           =   """A*B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.product    )    )

											return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
					import doctest

					doctest.testmod()




