




'''simple docstring'''





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

import torch_xla.distributed.xla_multiprocessing as xmp


def 					UpperCamelCase_(     ):

							'''simple docstring'''






							snake_case_      =				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=snake_case							,    default=1							,    help="Number of TPU cores to use (1 or 8)."					)

							# positional
							parser.add_argument(
							    "training_script"							,    type=snake_case							,    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=snake_case					)

							return parser.parse_args()


def 					UpperCamelCase_(     ):

							'''simple docstring'''






							snake_case_      =				parse_args()

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

							# Patch sys.argv
							snake_case_      =				[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 __future__ import annotations

import numpy as np


def 					UpperCamelCase_(     snake_case							:	np.ndarray					):

							'''simple docstring'''






							snake_case_ ,				snake_case_      =				np.shape(snake_case					)
							if rows != columns:
														snake_case_      =				(
														    "'table' has to be of square shaped array but got a "
														    f'{rows}x{columns} array:\n{table}'
														)
														raise ValueError(snake_case					)

							snake_case_      =				np.zeros((rows, columns)					)
							snake_case_      =				np.zeros((rows, columns)					)
							for i in range(snake_case					):
														for j in range(snake_case					):
																					snake_case_      =				sum(lower[i][k] * upper[k][j] for k in range(snake_case					)					)
																					if upper[j][j] == 0:
																												raise ArithmeticError("No LU decomposition exists"					)
																					snake_case_      =				(table[i][j] - total) / upper[j][j]
														snake_case_      =				1
														for j in range(snake_case							,    snake_case					):
																					snake_case_      =				sum(lower[i][k] * upper[k][j] for k in range(snake_case					)					)
																					snake_case_      =				table[i][j] - total
							return lower, upper


if __name__ == "__main__":
		import doctest

		doctest.testmod()




