


'''simple docstring'''






import unittest

import numpy as np






def 		_A (lowerCAmelCase__     :np.ndarray ,  lowerCAmelCase__     :np.ndarray ,  lowerCAmelCase__     :np.ndarray ,  lowerCAmelCase__     :np.ndarray | None = None ,  )      ->     Union[str, Any]:




     '''simple docstring'''



     _a						=							np.shape(__SCREAMING_SNAKE_CASE						)
     _a						=							np.shape(__SCREAMING_SNAKE_CASE						)
     _a						=							np.shape(__SCREAMING_SNAKE_CASE						)

     if shape_a[0] != shape_b[0]:
          _a						=							(
              '''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]:
          _a						=							(
              '''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						)

     _a						=							pseudo_inv
     if a_inv is None:
          try:
               _a						=							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        a   (   unittest.TestCase				):
 def 							__UpperCAmelCase						(       self  )    ->							Tuple:
      _a						=							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]  )
      _a						=							np.array([[0, 3], [3, 0], [2, 3]]  )
      _a						=							np.array([[2, 1], [6, 3]]  )

      _a						=							schur_complement(__SCREAMING_SNAKE_CASE					, __SCREAMING_SNAKE_CASE					, __SCREAMING_SNAKE_CASE  )

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

      _a						=							np.linalg.det(__SCREAMING_SNAKE_CASE  )
      _a						=							np.linalg.det(__SCREAMING_SNAKE_CASE  )
      _a						=							np.linalg.det(__SCREAMING_SNAKE_CASE  )

      self.assertAlmostEqual(__SCREAMING_SNAKE_CASE					, det_a * det_s  )
 def 							__UpperCAmelCase						(       self  )    ->							int:
      _a						=							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]  )
      _a						=							np.array([[0, 3], [3, 0], [2, 3]]  )
      _a						=							np.array([[2, 1], [6, 3]]  )

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




 def 							__UpperCAmelCase						(       self  )    ->							Any:
      _a						=							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]  )
      _a						=							np.array([[0, 3], [3, 0], [2, 3]]  )
      _a						=							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'''







import torch

from transformers import AutoModel






class  lowerCAmelCase__   (  torch.nn.Module     ):






					def __init__(   self				,							__SCREAMING_SNAKE_CASE="sayef/fsner-bert-base-uncased"		):


											"""simple docstring"""





											super(__SCREAMING_SNAKE_CASE				,							self		).__init__()

											lowercase_	:     Tuple													=       AutoModel.from_pretrained(__SCREAMING_SNAKE_CASE				,							return_dict=__SCREAMING_SNAKE_CASE		)
											lowercase_	:     Optional[Any]													=       torch.nn.CosineSimilarity(3				,							1E-0_8		)
											lowercase_	:     Optional[Any]													=       torch.nn.Softmax(dim=1		)






					def 	_snake_case    (   self				,							**__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											return self.bert(**__SCREAMING_SNAKE_CASE		).last_hidden_state






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											return token_embeddings.sum(2				,							keepdim=__SCREAMING_SNAKE_CASE		)






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE=1		):


											"""simple docstring"""





											return self.softmax(T * self.cos(__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		)		)






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     Optional[Any]													=       W_supports['''sizes'''].tolist()
											lowercase_	:     Dict													=       W_supports['''start_token_id'''].item()
											lowercase_	:     List[Any]													=       W_supports['''end_token_id'''].item()

											del W_supports["sizes"]
											del W_supports["start_token_id"]
											del W_supports["end_token_id"]

											lowercase_	:     List[str]													=       self.BERT(**__SCREAMING_SNAKE_CASE		)
											lowercase_	:     Optional[int]													=       self.BERT(**__SCREAMING_SNAKE_CASE		)

											lowercase_	:     str													=       None
											lowercase_	:     Dict													=       None

											lowercase_	:     Tuple													=       W_supports['''input_ids'''] == start_token_id
											lowercase_	:     Any													=       W_supports['''input_ids'''] == end_token_id

											for i, size in enumerate(__SCREAMING_SNAKE_CASE		):
																	if i == 0:
																							lowercase_	:     List[str]													=       0
																	else:
																							lowercase_	:     List[Any]													=       support_sizes[i - 1]

																	lowercase_	:     str													=       S[s : s + size][start_token_masks[s : s + size]]
																	lowercase_	:     Optional[int]													=       S[s : s + size][end_token_masks[s : s + size]]

																	lowercase_	:     List[str]													=       torch.matmul(q[i]				,							s_start.T		).sum(1		).softmax(0		)
																	lowercase_	:     List[str]													=       torch.matmul(q[i]				,							s_end.T		).sum(1		).softmax(0		)

																	if p_starts is not None:
																							lowercase_	:     Tuple													=       torch.vstack((p_starts, p_start)		)
																							lowercase_	:     Optional[Any]													=       torch.vstack((p_ends, p_end)		)
																	else:
																							lowercase_	:     str													=       p_start
																							lowercase_	:     int													=       p_end

											return p_starts, p_ends



