






import unittest

import numpy as np





def 						__UpperCAmelCase			(     a_							,     a_							,     a_							,     a_ = None							,     ):
							snake_case_				=							np.shape(a__)
							snake_case_				=							np.shape(a__)
							snake_case_				=							np.shape(a__)

							if shape_a[0] != shape_b[0]:
														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(a__)

							if shape_b[1] != shape_c[1]:
														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(a__)

							snake_case_				=							pseudo_inv
							if a_inv is None:
														try:
																					snake_case_				=							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  UpperCamelCase_      (			unittest.TestCase				):



	'''simple docstring'''




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

								snake_case_				=							schur_complement(_snake_case       ,			_snake_case       ,			_snake_case					)

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

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

								self.assertAlmostEqual(_snake_case       ,			det_a * det_s					)




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

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






	def 							_UpperCamelCase			(       self					)       ->    None:
								snake_case_				=							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
								snake_case_				=							np.array([[0, 3], [3, 0], [2, 3]]					)
								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()







from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Features, Value
from .base import TaskTemplate







@dataclass(frozen=a			)
class 			__A( a			):
				snake_case_						   =    field(default='''language-modeling'''  ,   metadata={'''include_in_asdict_even_if_is_default''': True}			)

				snake_case_						   =    Features({'''text''': Value('''string'''			)}			)
				snake_case_						   =    Features({}			)
				snake_case_						   =    "text"




				@property
				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      Dict[str, str]:


								'''simple docstring'''




								return {self.text_column: "text"}