



from __future__ import annotations

from typing import Any

class 							a__:







    def __init__(				self			:  Union[str, Any]						,      __snake_case			:  int						,      __snake_case			:  int						,      __snake_case			:  float = 0     ):
      a						: Any					       =					row, column
      a						: int					       =					[[default_value for c in range(__snake_case     )] for r in range(__snake_case     )]







    def __str__(				self			:  Any     ):
      a						: Dict					       =					F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

      # Make string identifier
      a						: Optional[int]					       =					0
      for row_vector in self.array:
        for obj in row_vector:
          a						: Union[str, Any]					       =					max(__snake_case						,      len(str(__snake_case     )     )     )
      a						: Optional[Any]					       =					F"""%{max_element_length}s"""

      # Make string and return
      def single_line(__snake_case			:  list[float]     ) -> str:
        nonlocal string_format_identifier
        a						: int					       =					'['
        line += ", ".join(string_format_identifier % (obj,) for obj in row_vector     )
        line += "]"
        return line

      s += "\n".join(single_line(__snake_case     ) for row_vector in self.array     )
      return s







    def __repr__(				self			:  Any     ):
      return str(self     )







    def       lowercase_	(				self			:  List[Any]						,      __snake_case			:  tuple[int, int]     ):
      if not (isinstance(__snake_case						,      (list, tuple)     ) and len(__snake_case     ) == 2):
        return False
      elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
        return False
      else:
        return True







    def __getitem__(				self			:  Union[str, Any]						,      __snake_case			:  tuple[int, int]     ):
      assert self.validate_indicies(__snake_case     )
      return self.array[loc[0]][loc[1]]







    def __setitem__(				self			:  List[str]						,      __snake_case			:  tuple[int, int]						,      __snake_case			:  float     ):
      assert self.validate_indicies(__snake_case     )
      a						: Dict					       =					value







    def __add__(				self			:  List[str]						,      __snake_case			:  Matrix     ):
      assert isinstance(__snake_case						,      __snake_case     )
      assert self.row == another.row and self.column == another.column

      # Add
      a						: Tuple					       =					Matrix(self.row						,      self.column     )
      for r in range(self.row     ):
        for c in range(self.column     ):
          a						: Optional[Any]					       =					self[r, c] + another[r, c]
      return result







    def __neg__(				self			:  Any     ):
      a						: Any					       =					Matrix(self.row						,      self.column     )
      for r in range(self.row     ):
        for c in range(self.column     ):
          a						: List[str]					       =					-self[r, c]
      return result







    def __sub__(				self			:  Optional[Any]						,      __snake_case			:  Matrix     ):
      return self + (-another)







    def __mul__(				self			:  List[Any]						,      __snake_case			:  int | float | Matrix     ):

      if isinstance(__snake_case						,      (int, float)     ):  # Scalar multiplication
        a						: List[str]					       =					Matrix(self.row						,      self.column     )
        for r in range(self.row     ):
          for c in range(self.column     ):
            a						: List[Any]					       =					self[r, c] * another
        return result
      elif isinstance(__snake_case						,      __snake_case     ):  # Matrix multiplication
        assert self.column == another.row
        a						: List[Any]					       =					Matrix(self.row						,      another.column     )
        for r in range(self.row     ):
          for c in range(another.column     ):
            for i in range(self.column     ):
              result[r, c] += self[r, i] * another[i, c]
        return result
      else:
        a						: Optional[Any]					       =					F"""Unsupported type given for another ({type(__snake_case     )})"""
        raise TypeError(__snake_case     )







    def       lowercase_	(				self			:  Any     ):
      a						: Tuple					       =					Matrix(self.column						,      self.row     )
      for r in range(self.row     ):
        for c in range(self.column     ):
          a						: List[Any]					       =					self[r, c]
      return result







    def       lowercase_	(				self			:  Any						,      __snake_case			:  Matrix						,      __snake_case			:  Matrix     ):
      assert isinstance(__snake_case						,      __snake_case     ) and isinstance(__snake_case						,      __snake_case     )
      assert self.row == self.column == u.row == v.row  # u, v should be column vector
      assert u.column == v.column == 1  # u, v should be column vector

      # Calculate
      a						: Union[str, Any]					       =					v.transpose()
      a						: int					       =					(v_t * self * u)[0, 0] + 1
      if numerator_factor == 0:
        return None  # It's not invertable
      return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":
     def 				lowerCamelCase__	(						):
       # a^(-1)
       a						: Tuple					       =					Matrix(3			,      3			,      0    )
       for i in range(3    ):
         a						: List[Any]					       =					1
       print(f"""a^(-1) is {ainv}"""    )
       # u, v
       a						: List[Any]					       =					Matrix(3			,      1			,      0    )
       a						: Optional[int]					       =					1, 2, -3
       a						: Optional[int]					       =					Matrix(3			,      1			,      0    )
       a						: Optional[int]					       =					4, -2, 5
       print(f"""u is {u}"""    )
       print(f"""v is {v}"""    )
       print(f"""uv^T is {u * v.transpose()}"""    )
       # Sherman Morrison
       print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(_A			,      _A    )}"""    )
     def 				lowerCamelCase__	(						):
       import doctest

       doctest.testmod()

     testa()




'''simple docstring'''






import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase: Any							=						logging.get_logger(__name__)

class 							a__( lowerCamelCase__     ):
    lowercase__			=   """encoder-decoder"""
    lowercase__			=   True







    def __init__(				self			:  Dict						,      **__snake_case			:  Union[str, Any]     ):
      super().__init__(**__snake_case     )
      assert (
          "encoder" in kwargs and "decoder" in kwargs
      ), "Config has to be initialized with encoder and decoder config"
      a						: List[str]					       =					kwargs.pop('encoder'     )
      a						: Optional[Any]					       =					encoder_config.pop('model_type'     )
      a						: Tuple					       =					kwargs.pop('decoder'     )
      a						: Optional[int]					       =					decoder_config.pop('model_type'     )

      from ..auto.configuration_auto import AutoConfig

      a						: Any					       =					AutoConfig.for_model(__snake_case						,      **__snake_case     )
      a						: Optional[int]					       =					AutoConfig.for_model(__snake_case						,      **__snake_case     )
      a						: Tuple					       =					True







    @classmethod
    def       lowercase_	(				cls			:  int						,      __snake_case			:  PretrainedConfig						,      __snake_case			:  PretrainedConfig						,      **__snake_case			:  Union[str, Any]     ):
      logger.info('Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config'     )
      a						: List[Any]					       =					True
      a						: Tuple					       =					True

      return cls(encoder=encoder_config.to_dict()						,      decoder=decoder_config.to_dict()						,      **__snake_case     )







    def       lowercase_	(				self			:  List[Any]     ):
      a						: int					       =					copy.deepcopy(self.__dict__     )
      a						: List[str]					       =					self.encoder.to_dict()
      a						: Optional[int]					       =					self.decoder.to_dict()
      a						: Optional[Any]					       =					self.__class__.model_type
      return output