






"""simple docstring"""







def      UpperCamelCase       ( _A )     ->       list[list]:
				lowercase    :      List[Any]       = current_set.copy()
				for row_index, row in enumerate(_A ):
								lowercase    :      str       = row[0]
								for column_index, column in enumerate(_A ):
												if magnitude == 0:
																lowercase    :      Tuple       = column
																continue
												lowercase    :      Optional[int]       = column / magnitude
    # Subtract to cancel term
				lowercase    :      Dict       = current_set[0]
				lowercase    :      Any       = [first_row]
				lowercase    :      int       = current_set[1::]
				for row in current_set:
								lowercase    :      List[str]       = []
								# If first term is 0, it is already in form we want, so we preserve it
								if row[0] == 0:
												final_set.append(_A )
												continue
								for column_index in range(len(_A ) ):
												temp_row.append(first_row[column_index] - row[column_index] )
								final_set.append(_A )
				# Create next recursion iteration set
				if len(final_set[0] ) != 3:
								lowercase    :      Union[str, Any]       = final_set[0]
								lowercase    :      str       = []
								lowercase    :      str       = []
								for row in final_set[1::]:
												current_first_column.append(row[0] )
												next_iteration.append(row[1::] )
								lowercase    :      str       = simplify(_A )
								for i in range(len(_A ) ):
												resultant[i].insert(0  ,				current_first_column[i] )
								resultant.insert(0  ,				_A )
								lowercase    :      List[str]       = resultant
				return final_set


def      UpperCamelCase       ( _A )     ->       list:
				if len(_A ) == 0:
								raise IndexError("""solve_simultaneous() requires n lists of length n+1""" )
				lowercase    :      List[Any]       = len(_A ) + 1
				if any(len(_A ) != _length for item in equations ):
								raise IndexError("""solve_simultaneous() requires n lists of length n+1""" )
				for row in equations:
								if any(not isinstance(_A  ,				(int, float) ) for column in row ):
												raise ValueError("""solve_simultaneous() requires lists of integers""" )
				if len(_A ) == 1:
								return [equations[0][-1] / equations[0][0]]
				lowercase    :      int       = equations.copy()
				if any(0 in row for row in data_set ):
								lowercase    :      Union[str, Any]       = data_set.copy()
								lowercase    :      int       = []
								for row_index, row in enumerate(_A ):
												if 0 not in row:
																lowercase    :      List[str]       = data_set.pop(_A )
																break
								if not full_row:
												raise ValueError("""solve_simultaneous() requires at least 1 full equation""" )
								data_set.insert(0  ,				_A )
				lowercase    :      Any       = data_set.copy()
				lowercase    :      List[Any]       = simplify(_A )
				lowercase    :      List[Any]       = simplified[::-1]
				lowercase    :      list       = []
				for row in simplified:
								lowercase    :      Optional[int]       = row[-1]
								if not solutions:
												if row[-2] == 0:
																solutions.append(0 )
																continue
												solutions.append(current_solution / row[-2] )
												continue
								lowercase    :      List[str]       = row.copy()[: len(_A ) - 1 :]
								while temp_row[0] == 0:
												temp_row.pop(0 )
								if len(_A ) == 0:
												solutions.append(0 )
												continue
								lowercase    :      Optional[int]       = temp_row[1::]
								lowercase    :      List[Any]       = temp_row[::-1]
								for column_index, column in enumerate(_A ):
												current_solution -= column * solutions[column_index]
								solutions.append(_A )
				lowercase    :      List[str]       = []
				for item in solutions:
								final.append(float(round(_A  ,				5 ) ) )
				return final[::-1]


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				_lowerCAmelCase            =	[
				    [2, 1, 1, 1, 1, 4],
				    [1, 2, 1, 1, 1, 5],
				    [1, 1, 2, 1, 1, 6],
				    [1, 1, 1, 2, 1, 7],
				    [1, 1, 1, 1, 2, 8],
				]
				print(solve_simultaneous(eq))
				print(solve_simultaneous([[4, 2]]))








"""simple docstring"""







from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
				import torch

if is_torch_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm


_lowerCAmelCase            =	logging.get_logger(__name__)


@dataclass
class      UpperCamelCase		(__snake_case     ):
						_SCREAMING_SNAKE_CASE  : str												=		[
						    """no_inference""",
						    """no_cuda""",
						    """no_tpu""",
						    """no_speed""",
						    """no_memory""",
						    """no_env_print""",
						    """no_multi_process""",
						]






						def __init__(		self  :Union[str, Any]			, **__magic_name__  :int				)      ->Any:
										for deprecated_arg in self.deprecated_args:
														if deprecated_arg in kwargs:
																		lowercase    :      int       = deprecated_arg[3:]
																		setattr(self			, __magic_name__			, not kwargs.pop(__magic_name__				)				)
																		logger.warning(
																		    f"""{deprecated_arg} is depreciated. Please use --no_{positive_arg} or"""
																		    f""" {positive_arg}={kwargs[positive_arg]}"""				)

										lowercase    :      List[str]       = kwargs.pop("""torchscript"""			, self.torchscript				)
										lowercase    :      Any       = kwargs.pop("""torch_xla_tpu_print_metrics"""			, self.torch_xla_tpu_print_metrics				)
										lowercase    :      Union[str, Any]       = kwargs.pop("""fp16_opt_level"""			, self.fpaa_opt_level				)
										super().__init__(**__magic_name__				)

						_SCREAMING_SNAKE_CASE  : bool												=		field(default=__snake_case						,						metadata={"""help""": """Trace the models using torchscript"""}     )
						_SCREAMING_SNAKE_CASE  : bool												=		field(default=__snake_case						,						metadata={"""help""": """Print Xla/PyTorch tpu metrics"""}     )
						_SCREAMING_SNAKE_CASE  : str												=		field(
						    default="""O1"""						,						metadata={
						        """help""": (
						            """For fp16: Apex AMP optimization level selected in ['O0', 'O1', 'O2', and 'O3']. """
						            """See details at https://nvidia.github.io/apex/amp.html"""
						        )
						    }						,						)






						@cached_property
						def      __snake_case      (		self  :Optional[int]				)      ->Tuple["torch.device", int]:
										requires_backends(self			, ["""torch"""]				)
										logger.info("""PyTorch: setting up devices"""				)
										if not self.cuda:
														lowercase    :      Optional[Any]       = torch.device("""cpu"""				)
														lowercase    :      int       = 0
										elif is_torch_tpu_available():
														lowercase    :      Any       = xm.xla_device()
														lowercase    :      List[str]       = 0
										else:
														lowercase    :      int       = torch.device("""cuda""" if torch.cuda.is_available() else """cpu"""				)
														lowercase    :      Any       = torch.cuda.device_count()
										return device, n_gpu






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->Union[str, Any]:
										return is_torch_tpu_available() and self.tpu






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->int:
										requires_backends(self			, ["""torch"""]				)
										# TODO(PVP): currently only single GPU is supported
										return torch.cuda.current_device()






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->"torch.device":
										requires_backends(self			, ["""torch"""]				)
										return self._setup_devices[0]






						@property
						def      __snake_case      (		self  :Optional[Any]				)      ->str:
										requires_backends(self			, ["""torch"""]				)
										return self._setup_devices[1]






						@property
						def      __snake_case      (		self  :int				)      ->List[str]:
										return self.n_gpu > 0
