



"""simple docstring"""






import torch

from transformers import AutoModel



class     A__     (						torch.nn.Module							):




	'''simple docstring'''





	def __init__(  self:	Dict ,    _SCREAMING_SNAKE_CASE:	List[str]="sayef/fsner-bert-base-uncased")       -> str:

				"""simple docstring"""

				super(_SCREAMING_SNAKE_CASE ,    self).__init__()

				__lowerCAmelCase   :						str				= AutoModel.from_pretrained(_SCREAMING_SNAKE_CASE ,    return_dict=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase   :						Dict				= torch.nn.CosineSimilarity(3 ,    1e-08)
				__lowerCAmelCase   :						int				= torch.nn.Softmax(dim=1)

	def 							_SCREAMING_SNAKE_CASE     (  self:	Optional[int] ,    **_SCREAMING_SNAKE_CASE:	Tuple)       -> str:

				"""simple docstring"""

				return self.bert(**_SCREAMING_SNAKE_CASE).last_hidden_state

	def 							_SCREAMING_SNAKE_CASE     (  self:	str ,    _SCREAMING_SNAKE_CASE:	Any)       -> Dict:

				"""simple docstring"""

				return token_embeddings.sum(2 ,    keepdim=_SCREAMING_SNAKE_CASE)

	def 							_SCREAMING_SNAKE_CASE     (  self:	Dict ,    _SCREAMING_SNAKE_CASE:	List[Any] ,    _SCREAMING_SNAKE_CASE:	List[str] ,    _SCREAMING_SNAKE_CASE:	Dict=1)       -> Dict:

				"""simple docstring"""

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







	def 							_SCREAMING_SNAKE_CASE     (  self:	List[str] ,    _SCREAMING_SNAKE_CASE:	Any ,    _SCREAMING_SNAKE_CASE:	Tuple)       -> List[Any]:

				"""simple docstring"""

				__lowerCAmelCase   :						List[Any]				= W_supports["sizes"].tolist()
				__lowerCAmelCase   :						Tuple				= W_supports["start_token_id"].item()
				__lowerCAmelCase   :						Optional[int]				= W_supports["end_token_id"].item()

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

				__lowerCAmelCase   :						str				= self.BERT(**_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase   :						Any				= self.BERT(**_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase   :						int				= None
				__lowerCAmelCase   :						Dict				= None

				__lowerCAmelCase   :						str				= W_supports["input_ids"] == start_token_id
				__lowerCAmelCase   :						Any				= W_supports["input_ids"] == end_token_id

				for i, size in enumerate(_SCREAMING_SNAKE_CASE):
							if i == 0:
										__lowerCAmelCase   :						Optional[int]				= 0
							else:
										__lowerCAmelCase   :						Optional[Any]				= support_sizes[i - 1]

							__lowerCAmelCase   :						List[Any]				= S[s : s + size][start_token_masks[s : s + size]]
							__lowerCAmelCase   :						int				= S[s : s + size][end_token_masks[s : s + size]]

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

							if p_starts is not None:
										__lowerCAmelCase   :						Dict				= torch.vstack((p_starts, p_start))
										__lowerCAmelCase   :						Dict				= torch.vstack((p_ends, p_end))
							else:
										__lowerCAmelCase   :						Optional[Any]				= p_start
										__lowerCAmelCase   :						Optional[Any]				= p_end

				return p_starts, p_ends




"""simple docstring"""






import math


def     _lowercase       (						__snake_case      ,__snake_case			)		->     float:
			return math.pow(__snake_case      ,2			) - a


def     _lowercase       (						__snake_case			)		->     float:
			return 2 * x


def     _lowercase       (						__snake_case			)		->     float:
			__lowerCAmelCase   :						List[str]				= 2.0

			while start <= a:
						__lowerCAmelCase   :						Union[str, Any]				= math.pow(__snake_case      ,2			)

			return start


def     _lowercase       (						__snake_case      ,__snake_case = 9_999      ,__snake_case = 0.00000000000001			)		->     float:

			if a < 0:
						raise ValueError("math domain error"			)

			__lowerCAmelCase   :						List[Any]				= get_initial_point(__snake_case			)

			for _ in range(__snake_case			):
						__lowerCAmelCase   :						Union[str, Any]				= value
						__lowerCAmelCase   :						List[str]				= value - fx(__snake_case      ,__snake_case			) / fx_derivative(__snake_case			)
						if abs(prev_value - value			) < tolerance:
									return value

			return value


if __name__ == "__main__":
	from doctest import testmod

	testmod()