"""simple docstring"""






import unittest

import numpy as np




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase = None  ,					)							->   np.ndarray:
				SCREAMING_SNAKE_CASE__		  =				np.shape(__UpperCAmelCase       )
				SCREAMING_SNAKE_CASE__		  =				np.shape(__UpperCAmelCase       )
				SCREAMING_SNAKE_CASE__		  =				np.shape(__UpperCAmelCase       )

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

				SCREAMING_SNAKE_CASE__		  =				pseudo_inv
				if a_inv is None:
								try:
												SCREAMING_SNAKE_CASE__		  =				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 			lowerCAmelCase_					(						self			:				Dict		)							->       None:
									SCREAMING_SNAKE_CASE__		  =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
									SCREAMING_SNAKE_CASE__		  =				np.array([[0, 3], [3, 0], [2, 3]]		)
									SCREAMING_SNAKE_CASE__		  =				np.array([[2, 1], [6, 3]]		)

									SCREAMING_SNAKE_CASE__		  =				schur_complement(_snake_case   , _snake_case   , _snake_case		)

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

									SCREAMING_SNAKE_CASE__		  =				np.linalg.det(_snake_case		)
									SCREAMING_SNAKE_CASE__		  =				np.linalg.det(_snake_case		)
									SCREAMING_SNAKE_CASE__		  =				np.linalg.det(_snake_case		)

									self.assertAlmostEqual(_snake_case   , det_a * det_s		)



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

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



					def 			lowerCAmelCase_					(						self			:				Any		)							->       None:
									SCREAMING_SNAKE_CASE__		  =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
									SCREAMING_SNAKE_CASE__		  =				np.array([[0, 3], [3, 0], [2, 3]]		)
									SCREAMING_SNAKE_CASE__		  =				np.array([[2, 1, 3], [6, 3, 5]]		)

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						unittest.main()





"""simple docstring"""






def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   int:

				if not isinstance(__UpperCAmelCase  ,					__UpperCAmelCase       ):
								raise ValueError("multiplicative_persistence() only accepts integral values"       )
				if num < 0:
								raise ValueError("multiplicative_persistence() does not accept negative values"       )

				SCREAMING_SNAKE_CASE__		  =				0
				SCREAMING_SNAKE_CASE__		  =				str(__UpperCAmelCase       )

				while len(__UpperCAmelCase       ) != 1:
								SCREAMING_SNAKE_CASE__		  =				[int(__UpperCAmelCase       ) for i in num_string]

								SCREAMING_SNAKE_CASE__		  =				1
								for i in range(0  ,					len(__UpperCAmelCase       )       ):
												total *= numbers[i]

								SCREAMING_SNAKE_CASE__		  =				str(__UpperCAmelCase       )

								steps += 1
				return steps




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   int:

				if not isinstance(__UpperCAmelCase  ,					__UpperCAmelCase       ):
								raise ValueError("additive_persistence() only accepts integral values"       )
				if num < 0:
								raise ValueError("additive_persistence() does not accept negative values"       )

				SCREAMING_SNAKE_CASE__		  =				0
				SCREAMING_SNAKE_CASE__		  =				str(__UpperCAmelCase       )

				while len(__UpperCAmelCase       ) != 1:
								SCREAMING_SNAKE_CASE__		  =				[int(__UpperCAmelCase       ) for i in num_string]

								SCREAMING_SNAKE_CASE__		  =				0
								for i in range(0  ,					len(__UpperCAmelCase       )       ):
												total += numbers[i]

								SCREAMING_SNAKE_CASE__		  =				str(__UpperCAmelCase       )

								steps += 1
				return steps


if __name__ == "__main__":
						import doctest

						doctest.testmod()




