






"""simple docstring"""

import unittest

import numpy as np






def _lowerCAmelCase	(  __lowerCamelCase:List[Any] ,						__lowerCamelCase:Dict ,						__lowerCamelCase:Dict ,						__lowerCamelCase:List[Any] = None ,						):

						'''simple docstring'''






						__magic_name__            =     np.shape(__A   )
						__magic_name__            =     np.shape(__A   )
						__magic_name__            =     np.shape(__A   )

						if shape_a[0] != shape_b[0]:
												__magic_name__            =     (
												    "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(__A   )

						if shape_b[1] != shape_c[1]:
												__magic_name__            =     (
												    "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(__A   )

						__magic_name__            =     pseudo_inv
						if a_inv is None:
												try:
																		__magic_name__            =     np.linalg.inv(__A   )
												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 						A_							(      unittest.TestCase  ):







				def     _snake_case					(							self							:						List[str]	)				->					None:
										__magic_name__            =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
										__magic_name__            =     np.array([[0, 3], [3, 0], [2, 3]]	)
										__magic_name__            =     np.array([[2, 1], [6, 3]]	)

										__magic_name__            =     schur_complement(lowerCAmelCase__						,    lowerCAmelCase__						,    lowerCAmelCase__	)

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

										__magic_name__            =     np.linalg.det(lowerCAmelCase__	)
										__magic_name__            =     np.linalg.det(lowerCAmelCase__	)
										__magic_name__            =     np.linalg.det(lowerCAmelCase__	)

										self.assertAlmostEqual(lowerCAmelCase__						,    det_a * det_s	)







				def     _snake_case					(							self							:						str	)				->					None:
										__magic_name__            =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
										__magic_name__            =     np.array([[0, 3], [3, 0], [2, 3]]	)
										__magic_name__            =     np.array([[2, 1], [6, 3]]	)

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







				def     _snake_case					(							self							:						Dict	)				->					None:
										__magic_name__            =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
										__magic_name__            =     np.array([[0, 3], [3, 0], [2, 3]]	)
										__magic_name__            =     np.array([[2, 1, 3], [6, 3, 5]]	)

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			unittest.main()











"""simple docstring"""

def _lowerCAmelCase	(  __lowerCamelCase:int   ):

						'''simple docstring'''






						if number < 0:
												raise ValueError("number must not be negative"   )
						return number & (number - 1) == 0


if __name__ == "__main__":
			import doctest

			doctest.testmod()



