




'''simple docstring'''


from __future__ import annotations

from typing import Any







class      SCREAMING_SNAKE_CASE    :






      def __init__( self   :  Optional[Any]						,						lowercase__   :  int						,						lowercase__   :  int						,						lowercase__   :  float = 0       ):


           '''simple docstring'''

           a_						,     a_     :							Optional[Any]     						=  row, column
           a_     :							Optional[int]     						=  [[default_value for c in range(lowercase__       )] for r in range(lowercase__       )]






      def __str__( self   :  Optional[Any]       ):


           '''simple docstring'''

           a_     :							Tuple     						=  F"Matrix consist of {self.row} rows and {self.column} columns\n"

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

           # Make string and return
           def single_line(lowercase__   :  list[float]       ) -> str:
                nonlocal string_format_identifier
                a_     :							Union[str, Any]     						=  """["""
                line += ", ".join(string_format_identifier % (obj,) for obj in row_vector       )
                line += "]"
                return line

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






      def __repr__( self   :  Tuple       ):


           '''simple docstring'''

           return str(self       )






      def 							lowercase_						( self   :  List[Any]						,						lowercase__   :  tuple[int, int]       ):


           '''simple docstring'''

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






      def __getitem__( self   :  Any						,						lowercase__   :  tuple[int, int]       ):


           '''simple docstring'''

           assert self.validate_indicies(lowercase__       )
           return self.array[loc[0]][loc[1]]






      def __setitem__( self   :  Dict						,						lowercase__   :  tuple[int, int]						,						lowercase__   :  float       ):


           '''simple docstring'''

           assert self.validate_indicies(lowercase__       )
           a_     :							Optional[Any]     						=  value






      def __add__( self   :  Tuple						,						lowercase__   :  Matrix       ):


           '''simple docstring'''

           assert isinstance(lowercase__						,						lowercase__       )
           assert self.row == another.row and self.column == another.column

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






      def __neg__( self   :  List[str]       ):


           '''simple docstring'''

           a_     :							Union[str, 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   :  str						,						lowercase__   :  Matrix       ):


           '''simple docstring'''

           return self + (-another)






      def __mul__( self   :  List[str]						,						lowercase__   :  int | float | Matrix       ):


           '''simple docstring'''

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






      def 							lowercase_						( self   :  Union[str, Any]       ):


           '''simple docstring'''

           a_     :							List[str]     						=  Matrix(self.column						,						self.row       )
           for r in range(self.row       ):
                for c in range(self.column       ):
                     a_     :							Tuple     						=  self[r, c]
           return result






      def 							lowercase_						( self   :  List[Any]						,						lowercase__   :  Matrix						,						lowercase__   :  Matrix       ):


           '''simple docstring'''

           assert isinstance(lowercase__						,						lowercase__       ) and isinstance(lowercase__						,						lowercase__       )
           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_     :							Optional[int]     						=  v.transpose()
           a_     :							Union[str, Any]     						=  (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  _SCREAMING_SNAKE_CASE     (      ):




      """simple docstring"""


      a_     :							Optional[Any]     						=  Matrix(3 ,    3 ,    0				)
      for i in range(3				):
           a_     :							Dict     						=  1
      print(F"a^(-1) is {ainv}"				)
      # u, v
      a_     :							Optional[int]     						=  Matrix(3 ,    1 ,    0				)
      a_						,     a_						,     a_     :							List[Any]     						=  1, 2, -3
      a_     :							Optional[Any]     						=  Matrix(3 ,    1 ,    0				)
      a_						,     a_						,     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(UpperCamelCase__ ,    UpperCamelCase__				)}"				)



 def  _SCREAMING_SNAKE_CASE     (      ):




      """simple docstring"""


      import doctest

      doctest.testmod()


 testa()






'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


lowerCAmelCase_      :  Optional[Any]				     =  {}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase_      :  Any				     =  ['GPTSw3Tokenizer']


if TYPE_CHECKING:
 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_gpt_swa import GPTSwaTokenizer

else:
 import sys

 lowerCAmelCase_      :  int				     =  _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
