





'''simple docstring'''






from ..utils import DummyObject, requires_backends




class 					UpperCAmelCase	(     metaclass=snake_case_  ):
      _lowercase:     List[Any]			=  ['''torch''', '''scipy''']




      def __init__(     self     :					Tuple     ,     *__snake_case     :					Dict     ,     **__snake_case     :					List[str]    )							-> str:
            requires_backends(self     ,     ["""torch""", """scipy"""]    )




      @classmethod
      def 							lowercase__       (     cls     :					str     ,     *__snake_case     :					List[str]     ,     **__snake_case     :					str    )							-> Tuple:
            requires_backends(cls     ,     ["""torch""", """scipy"""]    )




      @classmethod
      def 							lowercase__       (     cls     :					Optional[int]     ,     *__snake_case     :					int     ,     **__snake_case     :					Union[str, Any]    )							-> Optional[int]:
            requires_backends(cls     ,     ["""torch""", """scipy"""]    )













'''simple docstring'''






from __future__ import annotations

import numpy as np
def   UpperCamelCase__ (						lowerCAmelCase    ):





      """simple docstring"""


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

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()






