





from __future__ import annotations

from decimal import Decimal

from numpy import array


def _A       (   __magic_name__	):
   lowercase__			       =  Decimal

   # Check if the provided matrix has 2 rows and 2 columns
   # since this implementation only works for 2x2 matrices
   if len(__magic_name__	) == 2 and len(matrix[0]	) == 2 and len(matrix[1]	) == 2:
      # Calculate the determinant of the matrix
      lowercase__			       =  float(
          d(matrix[0][0]	) * d(matrix[1][1]	) - d(matrix[1][0]	) * d(matrix[0][1]	)	)
      if determinant == 0:
         raise ValueError("This matrix has no inverse."	)

      # Creates a copy of the matrix with swapped positions of the elements
      lowercase__			       =  [[0.0, 0.0], [0.0, 0.0]]
      lowercase__       ,							lowercase__			       =  matrix[1][1], matrix[0][0]
      lowercase__       ,							lowercase__			       =  -matrix[1][0], -matrix[0][1]

      # Calculate the inverse of the matrix
      return [
          [(float(d(__magic_name__	)	) / determinant) or 0.0 for n in row] for row in swapped_matrix
      ]
   elif (
       len(__magic_name__	) == 3
       and len(matrix[0]	) == 3
       and len(matrix[1]	) == 3
       and len(matrix[2]	) == 3
   ):
      # Calculate the determinant of the matrix using Sarrus rule
      lowercase__			       =  float(
          (
              (d(matrix[0][0]	) * d(matrix[1][1]	) * d(matrix[2][2]	))
              + (d(matrix[0][1]	) * d(matrix[1][2]	) * d(matrix[2][0]	))
              + (d(matrix[0][2]	) * d(matrix[1][0]	) * d(matrix[2][1]	))
          )
          - (
              (d(matrix[0][2]	) * d(matrix[1][1]	) * d(matrix[2][0]	))
              + (d(matrix[0][1]	) * d(matrix[1][0]	) * d(matrix[2][2]	))
              + (d(matrix[0][0]	) * d(matrix[1][2]	) * d(matrix[2][1]	))
          )	)
      if determinant == 0:
         raise ValueError("This matrix has no inverse."	)

      # Creating cofactor matrix
      lowercase__			       =  [
          [d(0.0	), d(0.0	), d(0.0	)],
          [d(0.0	), d(0.0	), d(0.0	)],
          [d(0.0	), d(0.0	), d(0.0	)],
      ]
      lowercase__			       =  (d(matrix[1][1]	) * d(matrix[2][2]	)) - (
          d(matrix[1][2]	) * d(matrix[2][1]	)
      )
      lowercase__			       =  -(
          (d(matrix[1][0]	) * d(matrix[2][2]	)) - (d(matrix[1][2]	) * d(matrix[2][0]	))
      )
      lowercase__			       =  (d(matrix[1][0]	) * d(matrix[2][1]	)) - (
          d(matrix[1][1]	) * d(matrix[2][0]	)
      )
      lowercase__			       =  -(
          (d(matrix[0][1]	) * d(matrix[2][2]	)) - (d(matrix[0][2]	) * d(matrix[2][1]	))
      )
      lowercase__			       =  (d(matrix[0][0]	) * d(matrix[2][2]	)) - (
          d(matrix[0][2]	) * d(matrix[2][0]	)
      )
      lowercase__			       =  -(
          (d(matrix[0][0]	) * d(matrix[2][1]	)) - (d(matrix[0][1]	) * d(matrix[2][0]	))
      )
      lowercase__			       =  (d(matrix[0][1]	) * d(matrix[1][2]	)) - (
          d(matrix[0][2]	) * d(matrix[1][1]	)
      )
      lowercase__			       =  -(
          (d(matrix[0][0]	) * d(matrix[1][2]	)) - (d(matrix[0][2]	) * d(matrix[1][0]	))
      )
      lowercase__			       =  (d(matrix[0][0]	) * d(matrix[1][1]	)) - (
          d(matrix[0][1]	) * d(matrix[1][0]	)
      )

      # Transpose the cofactor matrix (Adjoint matrix)
      lowercase__			       =  array(__magic_name__	)
      for i in range(3	):
         for j in range(3	):
            lowercase__			       =  cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
      lowercase__			       =  array(__magic_name__	)
      for i in range(3	):
         for j in range(3	):
            inverse_matrix[i][j] /= d(__magic_name__	)

        # Calculate the inverse of the matrix
      return [[float(d(__magic_name__	)	) or 0.0 for n in row] for row in inverse_matrix]
   raise ValueError("Please provide a matrix of size 2x2 or 3x3."	)













from abc import ABC, abstractmethod
from typing import Optional, Union

from .. import Dataset, DatasetDict, Features, IterableDataset, IterableDatasetDict, NamedSplit
from ..utils.typing import NestedDataStructureLike, PathLike





class  lowerCAmelCase							(       lowercase_ ):







  def __init__(      self  :str   ,							_lowercase  :Optional[NestedDataStructureLike[PathLike]] = None   ,							_lowercase  :Optional[NamedSplit] = None   ,							_lowercase  :Optional[Features] = None   ,							_lowercase  :str = None   ,							_lowercase  :bool = False   ,							_lowercase  :bool = False   ,							_lowercase  :Optional[int] = None   ,							**_lowercase  :Tuple   ,							):






     '''simple docstring'''





     lowercase__			       =  path_or_paths
     lowercase__			       =  split if split or isinstance(_lowercase   ,							_lowercase ) else "train"
     lowercase__			       =  features
     lowercase__			       =  cache_dir
     lowercase__			       =  keep_in_memory
     lowercase__			       =  streaming
     lowercase__			       =  num_proc
     lowercase__			       =  kwargs







  @abstractmethod
  def   UpperCAmelCase					(      self  :Any ):






     '''simple docstring'''





     pass





class  lowerCAmelCase							(       lowercase_ ):







  def __init__(      self  :List[Any]   ,							_lowercase  :Optional[Features] = None   ,							_lowercase  :str = None   ,							_lowercase  :bool = False   ,							_lowercase  :bool = False   ,							_lowercase  :Optional[int] = None   ,							**_lowercase  :Optional[int]   ,							):






     '''simple docstring'''





     lowercase__			       =  features
     lowercase__			       =  cache_dir
     lowercase__			       =  keep_in_memory
     lowercase__			       =  streaming
     lowercase__			       =  num_proc
     lowercase__			       =  kwargs







  @abstractmethod
  def   UpperCAmelCase					(      self  :int ):






     '''simple docstring'''





     pass






