


'''simple docstring'''



import unittest

import numpy as np



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				np.ndarray      ,    UpperCAmelCase_    :				np.ndarray      ,    UpperCAmelCase_    :				np.ndarray      ,    UpperCAmelCase_    :				np.ndarray | None = None      ,    )     ->		np.ndarray:
     __lowerCamelCase   :	Union[str, Any]								=		np.shape(UpperCAmelCase_							)
     __lowerCamelCase   :	Optional[int]								=		np.shape(UpperCAmelCase_							)
     __lowerCamelCase   :	Union[str, Any]								=		np.shape(UpperCAmelCase_							)

     if shape_a[0] != shape_b[0]:
          __lowerCamelCase   :	Optional[Any]								=		(
              '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(UpperCAmelCase_							)

     if shape_b[1] != shape_c[1]:
          __lowerCamelCase   :	Optional[int]								=		(
              '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(UpperCAmelCase_							)

     __lowerCamelCase   :	int								=		pseudo_inv
     if a_inv is None:
          try:
               __lowerCamelCase   :	Union[str, Any]								=		np.linalg.inv(UpperCAmelCase_							)
          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    UpperCAmelCase_  (unittest.TestCase  ):





    """simple docstring"""






    def       lowercase_				(							self	)				->     None:
         __lowerCamelCase   :	str								=		np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
         __lowerCamelCase   :	Tuple								=		np.array([[0, 3], [3, 0], [2, 3]]	)
         __lowerCamelCase   :	Optional[int]								=		np.array([[2, 1], [6, 3]]	)

         __lowerCamelCase   :	int								=		schur_complement(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)

         __lowerCamelCase   :	str								=		np.block([[a, b], [b.T, c]]	)

         __lowerCamelCase   :	List[str]								=		np.linalg.det(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	List[str]								=		np.linalg.det(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	Tuple								=		np.linalg.det(SCREAMING_SNAKE_CASE_	)

         self.assertAlmostEqual(SCREAMING_SNAKE_CASE_			,     det_a * det_s	)







    def       lowercase_				(							self	)				->     None:
         __lowerCamelCase   :	Optional[int]								=		np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
         __lowerCamelCase   :	Optional[Any]								=		np.array([[0, 3], [3, 0], [2, 3]]	)
         __lowerCamelCase   :	Optional[int]								=		np.array([[2, 1], [6, 3]]	)

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







    def       lowercase_				(							self	)				->     None:
         __lowerCamelCase   :	List[Any]								=		np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
         __lowerCamelCase   :	Optional[Any]								=		np.array([[0, 3], [3, 0], [2, 3]]	)
         __lowerCamelCase   :	Optional[int]								=		np.array([[2, 1, 3], [6, 3, 5]]	)

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      unittest.main()










'''simple docstring'''



A__		:					Optional[int]												=  """ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"""



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				bytes							)     ->		bytes:
     # Make sure the supplied data is a bytes-like object
     if not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          __lowerCamelCase   :	Dict								=		F'a bytes-like object is required, not \'{data.__class__.__name__}\''
          raise TypeError(UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		''.join(bin(UpperCAmelCase_							)[2:].zfill(8							) for byte in data							)

     __lowerCamelCase   :	Any								=		len(UpperCAmelCase_							) % 6 != 0

     if padding_needed:
          # The padding that will be added later
          __lowerCamelCase   :	int								=		B'=' * ((6 - len(UpperCAmelCase_							) % 6) // 2)

          # Append binary_stream with arbitrary binary digits (0's by default) to make its
          # length a multiple of 6.
          binary_stream += "0" * (6 - len(UpperCAmelCase_							) % 6)
     else:
          __lowerCamelCase   :	str								=		B''

     # Encode every 6 binary digits to their corresponding Base64 character
     return (
         "".join(
             B64_CHARSET[int(binary_stream[index : index + 6]      ,    2							)]
             for index in range(0      ,    len(UpperCAmelCase_							)      ,    6							)							).encode()
         + padding
     )



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		bytes:
     # Make sure encoded_data is either a string or a bytes-like object
     if not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							) and not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          __lowerCamelCase   :	Dict								=		(
              'argument should be a bytes-like object or ASCII string, '
              F'not \'{encoded_data.__class__.__name__}\''
          )
          raise TypeError(UpperCAmelCase_							)

     # In case encoded_data is a bytes-like object, make sure it contains only
     # ASCII characters so we convert it to a string object
     if isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          try:
               __lowerCamelCase   :	int								=		encoded_data.decode('utf-8'							)
          except UnicodeDecodeError:
               raise ValueError('base64 encoded data should only contain ASCII characters'							)

     __lowerCamelCase   :	Union[str, Any]								=		encoded_data.count('='							)

     # Check if the encoded string contains non base64 characters
     if padding:
          assert all(
              char in B64_CHARSET for char in encoded_data[:-padding]							), "Invalid base64 character(s) found."
     else:
          assert all(
              char in B64_CHARSET for char in encoded_data							), "Invalid base64 character(s) found."

     # Check the padding
     assert len(UpperCAmelCase_							) % 4 == 0 and padding < 3, "Incorrect padding"

     if padding:
          # Remove padding if there is one
          __lowerCamelCase   :	Any								=		encoded_data[:-padding]

          __lowerCamelCase   :	Optional[Any]								=		''.join(
              bin(B64_CHARSET.index(UpperCAmelCase_							)							)[2:].zfill(6							) for char in encoded_data							)[: -padding * 2]
     else:
          __lowerCamelCase   :	Any								=		''.join(
              bin(B64_CHARSET.index(UpperCAmelCase_							)							)[2:].zfill(6							) for char in encoded_data							)

     __lowerCamelCase   :	str								=		[
         int(binary_stream[index : index + 8]      ,    2							)
         for index in range(0      ,    len(UpperCAmelCase_							)      ,    8							)
     ]

     return bytes(UpperCAmelCase_							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()






