


'''simple docstring'''






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

import torch_xla.distributed.xla_multiprocessing as xmp


def 					_snake_case   (     )						->    Tuple:
							lowerCAmelCase__          =	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=A ,    default=1 ,    help='''Number of TPU cores to use (1 or 8).'''       )

							# positional
							parser.add_argument(
							    '''training_script''' ,    type=A ,    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=A       )

							return parser.parse_args()


def 					_snake_case   (     )						->    Dict:
							lowerCAmelCase__          =	parse_args()

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

							# Patch sys.argv
							lowerCAmelCase__          =	[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'''
def 						A_(			A		:						list[list[int]]):
							if len(A) == 0 or not all(len(A) == 2 for pair in coordinates):
														raise ValueError('The program cannot work out a fitting polynomial.')

							if len({tuple(A) for pair in coordinates}) != len(A):
														raise ValueError('The program cannot work out a fitting polynomial.')

							UpperCamelCase					       =			{x for x, _ in coordinates}
							if len(A) == 1:
														return f'''x={coordinates[0][0]}'''

							if len(A) != len(A):
														raise ValueError('The program cannot work out a fitting polynomial.')

							UpperCamelCase					       =			len(A)

							UpperCamelCase					       =			0
							UpperCamelCase					       =			[]
							# put the x and x to the power values in a matrix
							while count_of_line < x:
														UpperCamelCase					       =			0
														UpperCamelCase					       =			coordinates[count_of_line][0]
														UpperCamelCase					       =			[]
														while count_in_line < x:
																					count_line.append(a ** (x - (count_in_line + 1)))
																					count_in_line += 1
														matrix.append(A)
														count_of_line += 1

							UpperCamelCase					       =			0
							# put the y values into a vector
							UpperCamelCase					       =			[]
							while count_of_line < x:
														vector.append(coordinates[count_of_line][1])
														count_of_line += 1

							UpperCamelCase					       =			0

							while count < x:
														UpperCamelCase					       =			0
														while zahlen < x:
																					if count == zahlen:
																												zahlen += 1
																					if zahlen == x:
																												break
																					UpperCamelCase					       =			matrix[zahlen][count] / matrix[count][count]
																					for counting_columns, item in enumerate(matrix[count]):
																												# manipulating all the values in the matrix
																												matrix[zahlen][counting_columns] -= item * bruch
																					# manipulating the values in the vector
																					vector[zahlen] -= vector[count] * bruch
																					zahlen += 1
														count += 1

							UpperCamelCase					       =			0
							# make solutions
							UpperCamelCase					       =			[]
							while count < x:
														solution.append(str(vector[count] / matrix[count][count]))
														count += 1

							UpperCamelCase					       =			0
							UpperCamelCase					       =			'f(x)='

							while count < x:
														UpperCamelCase					       =			solution[count].split('E')
														if len(A) > 1:
																					UpperCamelCase					       =			f'''{remove_e[0]}*10^{remove_e[1]}'''
														solved += f'''x^{x - (count + 1)}*{solution[count]}'''
														if count + 1 != x:
																					solved += "+"
														count += 1

							return solved


if __name__ == "__main__":
						print(points_to_polynomial([]))
						print(points_to_polynomial([[]]))
						print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
						print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
						print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
						print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))




