


'''simple docstring'''







from __future__ import annotations

import numpy as np



def     _UpperCamelCase				(			UpperCamelCase__		):






				"""simple docstring"""



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

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()






'''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"""]    )






