


"""simple docstring"""



from unittest import TestCase

from datasets import Sequence, Value
from datasets.arrow_dataset import Dataset
class 					__magic_name__		(			__UpperCAmelCase     ):






       def  __snake_case						(   self  :    List[Any]				):

              '''simple docstring'''






              return [
                  {"col_1": 3, "col_2": "a"},
                  {"col_1": 2, "col_2": "b"},
                  {"col_1": 1, "col_2": "c"},
                  {"col_1": 0, "col_2": "d"},
              ]






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

              '''simple docstring'''






              lowercase		:Tuple       							=				{'''col_1''': [3, 2, 1, 0], '''col_2''': ['''a''', '''b''', '''c''', '''d''']}
              return Dataset.from_dict(snake_case__				)






       def  __snake_case						(   self  :    Optional[int]				):

              '''simple docstring'''






              lowercase		:Dict       							=				self._create_example_records()
              lowercase		:Optional[Any]       							=				Dataset.from_list(snake_case__				)
              self.assertListEqual(dset.column_names  ,     ['''col_1''', '''col_2''']				)
              for i, r in enumerate(snake_case__				):
                     self.assertDictEqual(snake_case__  ,     example_records[i]				)






       def  __snake_case						(   self  :    Tuple				):

              '''simple docstring'''






              lowercase		:Any       							=				self._create_example_records()
              lowercase		:Union[str, Any]       							=				Dataset.from_list(snake_case__				)
              lowercase		:Optional[int]       							=				Dataset.from_dict({k: [r[k] for r in example_records] for k in example_records[0]}				)
              self.assertEqual(dset.info  ,     dset_from_dict.info				)






       def  __snake_case						(   self  :    List[Any]				):  # checks what happens with missing columns

              '''simple docstring'''






              lowercase		:Optional[Any]       							=				[{'''col_1''': 1}, {'''col_2''': '''x'''}]
              lowercase		:str       							=				Dataset.from_list(snake_case__				)
              self.assertDictEqual(dset[0]  ,     {'''col_1''': 1}				)
              self.assertDictEqual(dset[1]  ,     {'''col_1''': None}				)  # NB: first record is used for columns






       def  __snake_case						(   self  :    Union[str, Any]				):  # checks if the type can be inferred from the second record

              '''simple docstring'''






              lowercase		:Dict       							=				[{'''col_1''': []}, {'''col_1''': [1, 2]}]
              lowercase		:Optional[int]       							=				Dataset.from_list(snake_case__				)
              self.assertEqual(dset.info.features['''col_1''']  ,     Sequence(Value('''int64'''				)				)				)







       def  __snake_case						(   self  :    List[str]				):

              '''simple docstring'''






              lowercase		:Tuple       							=				Dataset.from_list([]				)
              self.assertEqual(len(snake_case__				)  ,     0				)
              self.assertListEqual(dset.column_names  ,     []				)





"""simple docstring"""



from __future__ import annotations

from decimal import Decimal

from numpy import array






def       lowerCamelCase					(a_						:list[list[float]])     ->							list[list[float]]:
       lowercase		:List[str]       							=				Decimal

       # Check if the provided matrix has 2 rows and 2 columns
       # since this implementation only works for 2x2 matrices
       if len(a_) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
              # Calculate the determinant of the matrix
              lowercase		:List[str]       							=				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		:Optional[Any]       							=				[[0.0, 0.0], [0.0, 0.0]]
              lowercase							,  lowercase		:List[Any]       							=				matrix[1][1], matrix[0][0]
              lowercase							,  lowercase		:Union[str, Any]       							=				-matrix[1][0], -matrix[0][1]

              # Calculate the inverse of the matrix
              return [
                  [(float(d(a_)) / determinant) or 0.0 for n in row] for row in swapped_matrix
              ]
       elif (
           len(a_) == 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		:Any       							=				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		:Optional[Any]       							=				[
                  [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		:Optional[int]       							=				(d(matrix[1][1]) * d(matrix[2][2])) - (
                  d(matrix[1][2]) * d(matrix[2][1])
              )
              lowercase		:str       							=				-(
                  (d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[1][0]) * d(matrix[2][1])) - (
                  d(matrix[1][1]) * d(matrix[2][0])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][0]) * d(matrix[2][2])) - (
                  d(matrix[0][2]) * d(matrix[2][0])
              )
              lowercase		:List[str]       							=				-(
                  (d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][1]) * d(matrix[1][2])) - (
                  d(matrix[0][2]) * d(matrix[1][1])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
              )
              lowercase		:Any       							=				(d(matrix[0][0]) * d(matrix[1][1])) - (
                  d(matrix[0][1]) * d(matrix[1][0])
              )

              # Transpose the cofactor matrix (Adjoint matrix)
              lowercase		:Union[str, Any]       							=				array(a_)
              for i in range(3):
                     for j in range(3):
                            lowercase		:Any       							=				cofactor_matrix[j][i]

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

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

