


"""simple docstring"""

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"""







 __lowercase									=	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"""







 __lowercase									=	parse_args()

 # Import training_script as a module.
 __lowercase									=	Path(args.training_script )
 sys.path.append(str(script_fpath.parent.resolve() ) )
 __lowercase									=	script_fpath.stem
 __lowercase									=	importlib.import_module(UpperCamelCase__ )

 # Patch sys.argv
 __lowercase									=	[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()




"""simple docstring"""

from collections.abc import Callable

import numpy as np


def lowerCAmelCase_      (				UpperCamelCase__	: Callable				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float ):






 """simple docstring"""







 __lowercase									=	int(np.ceil((x_end - xa) / step_size ) )
 __lowercase									=	np.zeros((n + 1,) )
 __lowercase									=	ya
 __lowercase									=	xa

 for k in range(UpperCamelCase__ ):
  __lowercase									=	y[k] + step_size * ode_func(UpperCamelCase__				,   y[k] )
  x += step_size

 return y


if __name__ == "__main__":
       import doctest

       doctest.testmod()
