






import baseaa
import io
import json
import os
from copy import deepcopy

from ..optimizer import AcceleratedOptimizer
from ..scheduler import AcceleratedScheduler

class        lowerCAmelCase_				:







				"""simple docstring"""




				def __init__( self     :str  ,     lowerCamelCase__     :Dict     ):
					if isinstance(lowerCamelCase__  ,     lowerCamelCase__     ):
						# Don't modify user's data should they want to reuse it (e.g. in tests), because once we
						# modified it, it will not be accepted here again, since `auto` values would have been overridden
						UpperCamelCase__ :Optional[Any]						=      deepcopy(lowerCamelCase__     )
					elif os.path.exists(lowerCamelCase__     ):
						with io.open(lowerCamelCase__  ,     """r"""  ,     encoding="""utf-8"""     ) as f:
							UpperCamelCase__ :int						=      json.load(lowerCamelCase__     )
					else:
						try:
							UpperCamelCase__ :int						=      baseaa.urlsafe_baadecode(lowerCamelCase__     ).decode("""utf-8"""     )
							UpperCamelCase__ :Union[str, Any]						=      json.loads(lowerCamelCase__     )
						except (UnicodeDecodeError, AttributeError, ValueError):
							raise ValueError(
							    f"""Expected a string path to an existing deepspeed config, or a dictionary, or a base64 encoded string. Received: {config_file_or_dict}"""     )

					UpperCamelCase__ :Tuple						=      config

					self.set_stage_and_offload()







				def 				__a   ( self     :Tuple     ):
					# zero stage - this is done as early as possible, before model is created, to allow
					# ``is_deepspeed_zero3_enabled`` query and getting to the early deepspeed config object
					# during ``zero.Init()`` which needs to know the dtype, and some other hparams.
					UpperCamelCase__ :Dict						=      self.get_value("""zero_optimization.stage"""  ,     -1     )

					# offload
					UpperCamelCase__ :Tuple						=      False
					if self.is_zeroa() or self.is_zeroa():
						UpperCamelCase__ :Optional[int]						=      set(["""cpu""", """nvme"""]     )
						UpperCamelCase__ :Optional[Any]						=      set(
						    [
						        self.get_value("""zero_optimization.offload_optimizer.device"""     ),
						        self.get_value("""zero_optimization.offload_param.device"""     ),
						    ]     )
						if len(offload_devices & offload_devices_valid     ) > 0:
							UpperCamelCase__ :Optional[int]						=      True







				def 				__a   ( self     :Union[str, Any]  ,     lowerCamelCase__     :str     ):
					UpperCamelCase__ :Tuple						=      self.config

					# find the config node of interest if it exists
					UpperCamelCase__ :Any						=      ds_key_long.split("""."""     )
					UpperCamelCase__ :int						=      nodes.pop()
					for node in nodes:
						UpperCamelCase__ :Dict						=      config.get(lowerCamelCase__     )
						if config is None:
							return None, ds_key

					return config, ds_key







				def 				__a   ( self     :Dict  ,     lowerCamelCase__     :Optional[int]  ,     lowerCamelCase__     :Optional[Any]=None     ):
					UpperCamelCase__				,		UpperCamelCase__ :Dict						=      self.find_config_node(lowerCamelCase__     )
					if config is None:
						return default
					return config.get(lowerCamelCase__  ,     lowerCamelCase__     )







				def 				__a   ( self     :Tuple  ,     lowerCamelCase__     :str  ,     lowerCamelCase__     :Tuple=False     ):
					UpperCamelCase__ :Tuple						=      self.config

					# find the config node of interest if it exists
					UpperCamelCase__ :Optional[Any]						=      ds_key_long.split("""."""     )
					for node in nodes:
						UpperCamelCase__ :Any						=      config
						UpperCamelCase__ :Optional[Any]						=      config.get(lowerCamelCase__     )
						if config is None:
							if must_exist:
								raise ValueError(f"""Can't find {ds_key_long} entry in the config: {self.config}"""     )
							else:
								return

        # if found remove it
					if parent_config is not None:
						parent_config.pop(lowerCamelCase__     )







				def 				__a   ( self     :Any  ,     lowerCamelCase__     :str     ):
					UpperCamelCase__ :Any						=      self.get_value(lowerCamelCase__     )
					return False if value is None else bool(lowerCamelCase__     )







				def 				__a   ( self     :List[Any]  ,     lowerCamelCase__     :List[Any]     ):
					UpperCamelCase__ :Dict						=      self.get_value(lowerCamelCase__     )
					return False if value is None else not bool(lowerCamelCase__     )







				def 				__a   ( self     :Dict     ):
					return self._stage == 2







				def 				__a   ( self     :List[str]     ):
					return self._stage == 3







				def 				__a   ( self     :Optional[int]     ):
					return self._offload

class        lowerCAmelCase_				:







				"""simple docstring"""




				def __init__( self     :Union[str, Any]  ,     lowerCamelCase__     :int     ):
					UpperCamelCase__ :Union[str, Any]						=      engine







				def 				__a   ( self     :str  ,     lowerCamelCase__     :List[str]  ,     **lowerCamelCase__     :Optional[int]     ):
					# runs backpropagation and handles mixed precision
					self.engine.backward(lowerCamelCase__  ,     **lowerCamelCase__     )

					# Deepspeed's `engine.step` performs the following operations:
					# - gradient accumulation check
					# - gradient clipping
					# - optimizer step
					# - zero grad
					# - checking overflow
					# - lr_scheduler step (only if engine.lr_scheduler is not None)
					self.engine.step()
					# and this plugin overrides the above calls with no-ops when Accelerate runs under
					# Deepspeed, but allows normal functionality for non-Deepspeed cases thus enabling a simple
					# training loop that works transparently under many training regimes.

class        lowerCAmelCase_				(      lowercase	):







				"""simple docstring"""




				def __init__( self     :Dict  ,     lowerCamelCase__     :Tuple     ):
					super().__init__(lowerCamelCase__  ,     device_placement=lowerCamelCase__  ,     scaler=lowerCamelCase__     )
					UpperCamelCase__ :Union[str, Any]						=      hasattr(self.optimizer  ,     """overflow"""     )







				def 				__a   ( self     :int  ,     lowerCamelCase__     :str=None     ):
					pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







				def 				__a   ( self     :List[Any]     ):
					pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







				@property
				def 				__a   ( self     :List[Any]     ):
					if self.__has_overflow__:
						return self.optimizer.overflow
					return False

class        lowerCAmelCase_				(      lowercase	):







				"""simple docstring"""




				def __init__( self     :List[Any]  ,     lowerCamelCase__     :Any  ,     lowerCamelCase__     :Tuple     ):
					super().__init__(lowerCamelCase__  ,     lowerCamelCase__     )







				def 				__a   ( self     :Union[str, Any]     ):
					pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed

class        lowerCAmelCase_				:







				"""simple docstring"""




				def __init__( self     :Optional[Any]  ,     lowerCamelCase__     :List[str]  ,     lowerCamelCase__     :Dict=0.001  ,     lowerCamelCase__     :Optional[int]=0  ,     **lowerCamelCase__     :List[Any]     ):
					UpperCamelCase__ :Any						=      params
					UpperCamelCase__ :Tuple						=      lr
					UpperCamelCase__ :Optional[int]						=      weight_decay
					UpperCamelCase__ :Optional[Any]						=      kwargs

class        lowerCAmelCase_				:







				"""simple docstring"""




				def __init__( self     :Any  ,     lowerCamelCase__     :int  ,     lowerCamelCase__     :int=None  ,     lowerCamelCase__     :List[str]=0  ,     **lowerCamelCase__     :List[str]     ):
					UpperCamelCase__ :Optional[Any]						=      optimizer
					UpperCamelCase__ :List[Any]						=      total_num_steps
					UpperCamelCase__ :Any						=      warmup_num_steps
					UpperCamelCase__ :Any						=      kwargs


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str			,a__    :   complex			,a__    :   str = "x"			,a__    :   float = 10**-10			,a__    :   int = 1			,)					->				complex:
	__A :			Tuple		    =			symbols(a__       )
	__A :			List[str]		    =			lambdify(a__			,a__       )
	__A :			Any		    =			lambdify(a__			,diff(a__			,a__       )       )

	__A :			Dict		    =			starting_point

	while True:
		if diff_function(a__       ) != 0:
			__A :			Optional[int]		    =			prev_guess - multiplicity * func(a__       ) / diff_function(
			    a__       )
		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 :			List[Any]		    =			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)}""")





