

from __future__ import annotations

import numpy as np

def    A_  (							a  ):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_       ,						SCREAMING_SNAKE_CASE_				:  List[str]           =     np.shape(a  )
      if rows != columns:
            SCREAMING_SNAKE_CASE_				:  Optional[int]           =     (
                '\'table\' has to be of square shaped array but got a '
                f"{rows}x{columns} array:\n{table}"
            )
            raise ValueError(a  )

      SCREAMING_SNAKE_CASE_				:  List[str]           =     np.zeros((rows, columns)  )
      SCREAMING_SNAKE_CASE_				:  Optional[Any]           =     np.zeros((rows, columns)  )
      for i in range(a  ):
            for j in range(a  ):
                  SCREAMING_SNAKE_CASE_				:  Tuple           =     sum(lower[i][k] * upper[k][j] for k in range(a  )  )
                  if upper[j][j] == 0:
                        raise ArithmeticError('No LU decomposition exists'  )
                  SCREAMING_SNAKE_CASE_				:  List[Any]           =     (table[i][j] - total) / upper[j][j]
            SCREAMING_SNAKE_CASE_				:  Dict           =     1
            for j in range(a					,   a  ):
                  SCREAMING_SNAKE_CASE_				:  Any           =     sum(lower[i][k] * upper[k][j] for k in range(a  )  )
                  SCREAMING_SNAKE_CASE_				:  Optional[int]           =     table[i][j] - total
      return lower, upper


if __name__ == "__main__":
    import doctest

    doctest.testmod()









def    A_  (							a					,   a  ):

      """simple docstring"""



      return numa ^ numa < 0


if __name__ == "__main__":
    import doctest

    doctest.testmod()






