
import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp







def        A__					(						)  ->	Optional[int]:
				UpperCamelCase_:							Dict	=						ArgumentParser(
				    description=(
				        """PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"""
				    )						)

				# Optional arguments for the launch helper
				parser.add_argument("""--num_cores"""     ,    type=__lowerCAmelCase     ,    default=1     ,    help="""Number of TPU cores to use (1 or 8)."""						)

				# positional
				parser.add_argument(
				    """training_script"""     ,    type=__lowerCAmelCase     ,    help=(
				        """The full path to the single TPU training """
				        """program/script to be launched in parallel, """
				        """followed by all the arguments for the """
				        """training script"""
				    )     ,    )

				# rest from the training program
				parser.add_argument("""training_script_args"""     ,    nargs=__lowerCAmelCase						)

				return parser.parse_args()







def        A__					(						)  ->	List[Any]:
				UpperCamelCase_:							List[str]	=						parse_args()

				# Import training_script as a module.
				UpperCamelCase_:							Optional[Any]	=						Path(args.training_script						)
				sys.path.append(str(script_fpath.parent.resolve()						)						)
				UpperCamelCase_:							Any	=						script_fpath.stem
				UpperCamelCase_:							Tuple	=						importlib.import_module(__lowerCAmelCase						)

				# Patch sys.argv
				UpperCamelCase_:							Union[str, Any]	=						[args.training_script] + args.training_script_args + ["--tpu_num_cores", str(args.num_cores						)]

				xmp.spawn(mod._mp_fn     ,    args=()     ,    nprocs=args.num_cores						)


if __name__ == "__main__":
							main()






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







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = "x"     ,    lowerCamelCase = 10**-10     ,    lowerCamelCase = 1     ,    )  ->	complex:
				UpperCamelCase_:							Optional[Any]	=						symbols(lowerCamelCase						)
				UpperCamelCase_:							int	=						lambdify(lowerCamelCase     ,    lowerCamelCase						)
				UpperCamelCase_:							Optional[Any]	=						lambdify(lowerCamelCase     ,    diff(lowerCamelCase     ,    lowerCamelCase						)						)

				UpperCamelCase_:							Tuple	=						starting_point

				while True:
								if diff_function(lowerCamelCase						) != 0:
												UpperCamelCase_:							List[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

								UpperCamelCase_:							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)}""")






