code: 
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__		):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						if not isinstance(lowercase_       ,    lowercase_		):
  												raise ValueError("""Input series is not valid, valid series - [2, 4, 8]"""		)
  						if len(lowercase_		) == 0:
  												raise ValueError("""Input list must be a non empty list"""		)
  						if len(lowercase_		) == 1:
  												return True
  						try:
  												a_					=		series[1] / series[0]
  												for index in range(len(lowercase_		) - 1		):
  																		if series[index + 1] / series[index] != common_ratio:
  																								return False
  						except ZeroDivisionError:
  												return False
  						return True
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__		):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						if not isinstance(lowercase_       ,    lowercase_		):
  												raise ValueError("""Input series is not valid, valid series - [2, 4, 8]"""		)
  						if len(lowercase_		) == 0:
  												raise ValueError("""Input list must be a non empty list"""		)
  						a_					=		1
  						for value in series:
  												answer *= value
  						return pow(lowercase_       ,    1 / len(lowercase_		)		)
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
style_context: 
  
  
  import importlib
  import sys
  from argparse import REMAINDER, ArgumentParser
  from pathlib import Path
  
  import torch_xla.distributed.xla_multiprocessing as xmp
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		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=UpperCAmelCase__       ,    default=1       ,    help="""Number of TPU cores to use (1 or 8)."""      )
  
  						# positional
  						parser.add_argument(
  						    """training_script"""       ,    type=UpperCAmelCase__       ,    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=UpperCAmelCase__      )
  
  						return parser.parse_args()
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		parse_args()
  
  						# Import training_script as a module.
  						a_					=		Path(args.training_script      )
  						sys.path.append(str(script_fpath.parent.resolve()      )      )
  						a_					=		script_fpath.stem
  						a_					=		importlib.import_module(UpperCAmelCase__      )
  
  						# Patch sys.argv
  						a_					=		[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()