





import unittest

import numpy as np





def 						lowerCamelCase__     (     UpperCamelCase__			:       Any       ,    UpperCamelCase__			:       Union[str, Any]       ,    UpperCamelCase__			:       Tuple       ,    UpperCamelCase__			:       Any = None       ,    )			-> Optional[int]:



					'''simple docstring'''




					_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					):




					def 	lowerCAmelCase			(		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(lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__  )

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

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

										self.assertAlmostEqual(lowerCAmelCase__				,						det_a * det_s  )




					def 	lowerCAmelCase			(		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(lowerCAmelCase__  ):
															schur_complement(lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__  )






					def 	lowerCAmelCase			(		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(lowerCAmelCase__  ):
															schur_complement(lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__  )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					unittest.main()










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase_      							=     {
    """configuration_luke""": ["""LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LukeConfig"""],
    """tokenization_luke""": ["""LukeTokenizer"""],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCAmelCase_      							=     [
					    """LUKE_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """LukeForEntityClassification""",
					    """LukeForEntityPairClassification""",
					    """LukeForEntitySpanClassification""",
					    """LukeForMultipleChoice""",
					    """LukeForQuestionAnswering""",
					    """LukeForSequenceClassification""",
					    """LukeForTokenClassification""",
					    """LukeForMaskedLM""",
					    """LukeModel""",
					    """LukePreTrainedModel""",
					]


if TYPE_CHECKING:
					from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
					from .tokenization_luke import LukeTokenizer

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_luke import (
										    LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
										    LukeForEntityClassification,
										    LukeForEntityPairClassification,
										    LukeForEntitySpanClassification,
										    LukeForMaskedLM,
										    LukeForMultipleChoice,
										    LukeForQuestionAnswering,
										    LukeForSequenceClassification,
										    LukeForTokenClassification,
										    LukeModel,
										    LukePreTrainedModel,
										)

else:
					import sys

					UpperCAmelCase_      							=     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



