





def   __lowerCamelCase   (				__a  :list[list]       )						->							list[list]:






		"""simple docstring"""

		A__     =  current_set.copy()
		for row_index, row in enumerate(__a       ):
				A__     =  row[0]
				for column_index, column in enumerate(__a       ):
						if magnitude == 0:
								A__     =  column
								continue
						A__     =  column / magnitude
    # Subtract to cancel term
		A__     =  current_set[0]
		A__     =  [first_row]
		A__     =  current_set[1::]
		for row in current_set:
				A__     =  []
				# 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:
				A__     =  final_set[0]
				A__     =  []
				A__     =  []
				for row in final_set[1::]:
						current_first_column.append(row[0]       )
						next_iteration.append(row[1::]       )
				A__     =  simplify(__a       )
				for i in range(len(__a       )       ):
						resultant[i].insert(0       ,	current_first_column[i]       )
				resultant.insert(0       ,	__a       )
				A__     =  resultant
		return final_set







def   __lowerCamelCase   (				__a  :list[list]       )						->							list:






		"""simple docstring"""

		if len(__a       ) == 0:
				raise IndexError("""solve_simultaneous() requires n lists of length n+1"""       )
		A__     =  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]]
		A__     =  equations.copy()
		if any(0 in row for row in data_set       ):
				A__     =  data_set.copy()
				A__     =  []
				for row_index, row in enumerate(__a       ):
						if 0 not in row:
								A__     =  data_set.pop(__a       )
								break
				if not full_row:
						raise ValueError("""solve_simultaneous() requires at least 1 full equation"""       )
				data_set.insert(0       ,	__a       )
		A__     =  data_set.copy()
		A__     =  simplify(__a       )
		A__     =  simplified[::-1]
		A__     =  []
		for row in simplified:
				A__     =  row[-1]
				if not solutions:
						if row[-2] == 0:
								solutions.append(0       )
								continue
						solutions.append(current_solution / row[-2]       )
						continue
				A__     =  row.copy()[: len(__a       ) - 1 :]
				while temp_row[0] == 0:
						temp_row.pop(0       )
				if len(__a       ) == 0:
						solutions.append(0       )
						continue
				A__     =  temp_row[1::]
				A__     =  temp_row[::-1]
				for column_index, column in enumerate(__a       ):
						current_solution -= column * solutions[column_index]
				solutions.append(__a       )
		A__     =  []
		for item in solutions:
				final.append(float(round(__a       ,	5       )       )       )
		return final[::-1]


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					A       :   int					= [
					    [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]]))










import multiprocessing
from typing import TYPE_CHECKING, Optional, Union

from .. import Dataset, Features, config
from ..formatting import query_table
from ..packaged_modules.sql.sql import Sql
from ..utils import logging
from .abc import AbstractDatasetInputStream


if TYPE_CHECKING:
					import sqlitea

					import sqlalchemy


class     A     (SCREAMING_SNAKE_CASE       ):
			'''simple docstring'''




			def __init__(     self  :       Any				,      __lowerCAmelCase  :       Union[str, "sqlalchemy.sql.Selectable"]				,      __lowerCAmelCase  :       Union[str, "sqlalchemy.engine.Connection", "sqlalchemy.engine.Engine", "sqlite3.Connection"]				,      __lowerCAmelCase  :       Optional[Features] = None				,      __lowerCAmelCase  :       str = None				,      __lowerCAmelCase  :       bool = False				,      **__lowerCAmelCase  :       Dict				,      )      ->      Any:







					"""simple docstring"""






					super().__init__(features=__lowerCAmelCase				,      cache_dir=__lowerCAmelCase				,      keep_in_memory=__lowerCAmelCase				,      **__lowerCAmelCase  )
					A__     =  Sql(
					    cache_dir=__lowerCAmelCase				,      features=__lowerCAmelCase				,      sql=__lowerCAmelCase				,      con=__lowerCAmelCase				,      **__lowerCAmelCase				,      )







			def   a_			(     self  :       Optional[int]  )      ->      Optional[int]:







					"""simple docstring"""






					A__     =  None
					A__     =  None
					A__     =  None
					A__     =  None

					self.builder.download_and_prepare(
					    download_config=__lowerCAmelCase				,      download_mode=__lowerCAmelCase				,      verification_mode=__lowerCAmelCase				,      base_path=__lowerCAmelCase				,      )

					# Build dataset for splits
					A__     =  self.builder.as_dataset(
					    split="""train"""				,      verification_mode=__lowerCAmelCase				,      in_memory=self.keep_in_memory  )
					return dataset


class     A     :
			'''simple docstring'''




			def __init__(     self  :       Optional[int]				,      __lowerCAmelCase  :       Dataset				,      __lowerCAmelCase  :       str				,      __lowerCAmelCase  :       Union[str, "sqlalchemy.engine.Connection", "sqlalchemy.engine.Engine", "sqlite3.Connection"]				,      __lowerCAmelCase  :       Optional[int] = None				,      __lowerCAmelCase  :       Optional[int] = None				,      **__lowerCAmelCase  :       List[Any]				,      )      ->      Any:







					"""simple docstring"""






					if num_proc is not None and num_proc <= 0:
							raise ValueError(f'num_proc {num_proc} must be an integer > 0.'  )

					A__     =  dataset
					A__     =  name
					A__     =  con
					A__     =  batch_size if batch_size else config.DEFAULT_MAX_BATCH_SIZE
					A__     =  num_proc
					A__     =  to_sql_kwargs






			def   a_			(     self  :       Any  )      ->      int:







					"""simple docstring"""






					A__     =  self.to_sql_kwargs.pop("""sql"""				,      __lowerCAmelCase  )
					A__     =  self.to_sql_kwargs.pop("""con"""				,      __lowerCAmelCase  )
					A__     =  self.to_sql_kwargs.pop("""index"""				,      __lowerCAmelCase  )

					A__     =  self._write(index=__lowerCAmelCase				,      **self.to_sql_kwargs  )
					return written






			def   a_			(     self  :       Union[str, Any]				,      __lowerCAmelCase  :       Optional[Any]  )      ->      Optional[Any]:







					"""simple docstring"""






					A__ ,     A__ ,     A__     =  args
					A__     =  {**to_sql_kwargs, """if_exists""": """append"""} if offset > 0 else to_sql_kwargs
					A__     =  query_table(
					    table=self.dataset.data				,      key=slice(__lowerCAmelCase				,      offset + self.batch_size  )				,      indices=self.dataset._indices				,      )
					A__     =  batch.to_pandas()
					A__     =  df.to_sql(self.name				,      self.con				,      index=__lowerCAmelCase				,      **__lowerCAmelCase  )
					return num_rows or len(__lowerCAmelCase  )







			def   a_			(     self  :       Optional[int]				,      __lowerCAmelCase  :       Tuple				,      **__lowerCAmelCase  :       Dict  )      ->      int:







					"""simple docstring"""






					A__     =  0

					if self.num_proc is None or self.num_proc == 1:
							for offset in logging.tqdm(
							    range(0				,      len(self.dataset  )				,      self.batch_size  )				,      unit="""ba"""				,      disable=not logging.is_progress_bar_enabled()				,      desc="""Creating SQL from Arrow format"""				,      ):
									written += self._batch_sql((offset, index, to_sql_kwargs)  )
					else:
							A__ ,     A__     =  len(self.dataset  ), self.batch_size
							with multiprocessing.Pool(self.num_proc  ) as pool:
									for num_rows in logging.tqdm(
									    pool.imap(
									        self._batch_sql				,      [(offset, index, to_sql_kwargs) for offset in range(0				,      __lowerCAmelCase				,      __lowerCAmelCase  )]				,      )				,      total=(num_rows // batch_size) + 1 if num_rows % batch_size else num_rows // batch_size				,      unit="""ba"""				,      disable=not logging.is_progress_bar_enabled()				,      desc="""Creating SQL from Arrow format"""				,      ):
											written += num_rows

					return written



