

"""simple docstring"""





import unittest

import numpy as np




def   _A  (  UpperCamelCase_     :       np.ndarray,			UpperCamelCase_     :       np.ndarray,			UpperCamelCase_     :       np.ndarray,			UpperCamelCase_     :       np.ndarray | None = None,			)	->						np.ndarray:
   '''simple docstring'''


   __lowercase								=						np.shape(UpperCamelCase_)
   __lowercase								=						np.shape(UpperCamelCase_)
   __lowercase								=						np.shape(UpperCamelCase_)

   if shape_a[0] != shape_b[0]:
      __lowercase								=						(
          "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]:
      __lowercase								=						(
          "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_)

   __lowercase								=						pseudo_inv
   if a_inv is None:
      try:
         __lowercase								=						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 					_lowerCAmelCase  (	unittest.TestCase   ):







 """simple docstring"""







 def 					_lowercase (			self							:			Optional[Any]	):
    __lowercase								=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
    __lowercase								=						np.array([[0, 3], [3, 0], [2, 3]]	)
    __lowercase								=						np.array([[2, 1], [6, 3]]	)

    __lowercase								=						schur_complement(UpperCAmelCase__,					UpperCAmelCase__,					UpperCAmelCase__	)

    __lowercase								=						np.block([[a, b], [b.T, c]]	)

    __lowercase								=						np.linalg.det(UpperCAmelCase__	)
    __lowercase								=						np.linalg.det(UpperCAmelCase__	)
    __lowercase								=						np.linalg.det(UpperCAmelCase__	)

    self.assertAlmostEqual(UpperCAmelCase__,					det_a * det_s	)


 def 					_lowercase (			self							:			Any	):
    __lowercase								=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
    __lowercase								=						np.array([[0, 3], [3, 0], [2, 3]]	)
    __lowercase								=						np.array([[2, 1], [6, 3]]	)

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



 def 					_lowercase (			self							:			Optional[Any]	):
    __lowercase								=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
    __lowercase								=						np.array([[0, 3], [3, 0], [2, 3]]	)
    __lowercase								=						np.array([[2, 1, 3], [6, 3, 5]]	)

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   unittest.main()







"""simple docstring"""





import baseaa




def   _A  (  UpperCamelCase_     :       str)	->						bytes:
   '''simple docstring'''


   return baseaa.baaencode(string.encode("utf-8"))




def   _A  (  UpperCamelCase_     :       bytes)	->						str:
   '''simple docstring'''


   return baseaa.baadecode(UpperCamelCase_).decode("utf-8")


if __name__ == "__main__":
   _a       =							'Hello World!'
   _a       =							baseaa_encode(test)
   print(encoded)

   _a       =							baseaa_decode(encoded)
   print(decoded)




