UpperCAmelCase					      =							[
    "Audio",
    "Array2D",
    "Array3D",
    "Array4D",
    "Array5D",
    "ClassLabel",
    "Features",
    "Sequence",
    "Value",
    "Image",
    "Translation",
    "TranslationVariableLanguages",
]
from .audio import Audio
from .features import ArrayaD, ArrayaD, ArrayaD, ArrayaD, ClassLabel, Features, Sequence, Value
from .image import Image
from .translation import Translation, TranslationVariableLanguages











import unittest

import numpy as np






def 	UpperCamelCase	(							snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray | None = None						,):




     '''simple docstring'''






     __snake_case      :Any 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)

     if shape_a[0] != shape_b[0]:
          __snake_case      :int 							=    (
              """Expected the same number of rows for A and B. """
              f'''Instead found A of size {shape_a} and B of size {shape_b}'''
          )
          raise ValueError(snake_case__	)

     if shape_b[1] != shape_c[1]:
          __snake_case      :List[str] 							=    (
              """Expected the same number of columns for B and C. """
              f'''Instead found B of size {shape_b} and C of size {shape_c}'''
          )
          raise ValueError(snake_case__	)

     __snake_case      :Any 							=    pseudo_inv
     if a_inv is None:
          try:
               __snake_case      :Optional[Any] 							=    np.linalg.inv(snake_case__	)
          except np.linalg.LinAlgError:
               raise ValueError(
                   """Input matrix A is not invertible. Cannot compute Schur complement."""	)

     return mat_c - mat_b.T @ a_inv @ mat_b




class       snake_case__ (				unittest.TestCase):

       '''simple docstring'''



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[str] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1], [6, 3]]     )

            __snake_case      :int 							=    schur_complement(a__      ,    a__      ,    a__     )

            __snake_case      :Union[str, Any] 							=    np.block([[a, b], [b.T, c]]     )

            __snake_case      :Dict 							=    np.linalg.det(a__     )
            __snake_case      :Tuple 							=    np.linalg.det(a__     )
            __snake_case      :List[Any] 							=    np.linalg.det(a__     )

            self.assertAlmostEqual(a__      ,    det_a * det_s     )



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :Optional[int] 							=    np.array([[2, 1], [6, 3]]     )

            with self.assertRaises(a__     ):
                 schur_complement(a__      ,    a__      ,    a__     )



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :Optional[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :List[str] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1, 3], [6, 3, 5]]     )

            with self.assertRaises(a__     ):
                 schur_complement(a__      ,    a__      ,    a__     )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     unittest.main()


