
'''simple docstring'''







import unittest

import numpy as np
def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: np.ndarray      ,      __SCREAMING_SNAKE_CASE					: np.ndarray      ,      __SCREAMING_SNAKE_CASE					: np.ndarray      ,      __SCREAMING_SNAKE_CASE					: np.ndarray | None = None      ,      ):



						"""simple docstring"""





						lowercase_	:     Dict													=       np.shape(__SCREAMING_SNAKE_CASE							)
						lowercase_	:     str													=       np.shape(__SCREAMING_SNAKE_CASE							)
						lowercase_	:     int													=       np.shape(__SCREAMING_SNAKE_CASE							)

						if shape_a[0] != shape_b[0]:
												lowercase_	:     Optional[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(__SCREAMING_SNAKE_CASE							)

						if shape_b[1] != shape_c[1]:
												lowercase_	:     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(__SCREAMING_SNAKE_CASE							)

						lowercase_	:     int													=       pseudo_inv
						if a_inv is None:
												try:
																		lowercase_	:     str													=       np.linalg.inv(__SCREAMING_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  lowerCAmelCase__   (  unittest.TestCase     ):






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     Optional[Any]													=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
											lowercase_	:     Any													=       np.array([[0, 3], [3, 0], [2, 3]]		)
											lowercase_	:     int													=       np.array([[2, 1], [6, 3]]		)

											lowercase_	:     Tuple													=       schur_complement(__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		)

											lowercase_	:     int													=       np.block([[a, b], [b.T, c]]		)

											lowercase_	:     int													=       np.linalg.det(__SCREAMING_SNAKE_CASE		)
											lowercase_	:     List[str]													=       np.linalg.det(__SCREAMING_SNAKE_CASE		)
											lowercase_	:     Optional[int]													=       np.linalg.det(__SCREAMING_SNAKE_CASE		)

											self.assertAlmostEqual(__SCREAMING_SNAKE_CASE				,							det_a * det_s		)






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     Optional[Any]													=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
											lowercase_	:     List[Any]													=       np.array([[0, 3], [3, 0], [2, 3]]		)
											lowercase_	:     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 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     Dict													=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
											lowercase_	:     int													=       np.array([[0, 3], [3, 0], [2, 3]]		)
											lowercase_	:     List[str]													=       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'''


def 			snake_case_   (  SCREAMING_SNAKE_CASE__     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       int     		=      0
				while len(SCREAMING_SNAKE_CASE__     ) > 1:
								_SCREAMING_SNAKE_CASE :       Any     		=      0
								# Consider two files with minimum cost to be merged
								for _ in range(2     ):
												_SCREAMING_SNAKE_CASE :       Optional[int]     		=      files.index(min(SCREAMING_SNAKE_CASE__     )     )
												temp += files[min_index]
												files.pop(SCREAMING_SNAKE_CASE__     )
								files.append(SCREAMING_SNAKE_CASE__     )
								optimal_merge_cost += temp
				return optimal_merge_cost


if __name__ == "__main__":
				import doctest

				doctest.testmod()




