


'''simple docstring'''






from __future__ import annotations

from scipy.special import comb  # type: ignore
class 						__UpperCamelCase      :





							def __init__(  self		:Optional[int]  ,_UpperCamelCase		:list[tuple[float, float]]			):
									snake_case_		:							List[str]			       =						list_of_points
									# Degree determines the flexibility of the curve.
									# Degree = 1 will produce a straight line.
									snake_case_		:							Optional[int]			       =						len(_UpperCamelCase			) - 1





							def 		a__   (  self		:Optional[int]  ,_UpperCamelCase		:float			):
									assert 0 <= t <= 1, "Time t must be between 0 and 1."
									snake_case_		:							list[float]			       =						[]
									for i in range(len(self.list_of_points			)			):
											# basis function for each i
											output_values.append(
											    comb(self.degree  ,_UpperCamelCase			) * ((1 - t) ** (self.degree - i)) * (t**i)			)
									# the basis must sum up to 1 for it to produce a valid Bezier curve.
									assert round(sum(_UpperCamelCase			)  ,5			) == 1
									return output_values





							def 		a__   (  self		:Any  ,_UpperCamelCase		:float			):
									assert 0 <= t <= 1, "Time t must be between 0 and 1."

									snake_case_		:							Any			       =						self.basis_function(_UpperCamelCase			)
									snake_case_		:							Optional[int]			       =						0.0
									snake_case_		:							Union[str, Any]			       =						0.0
									for i in range(len(self.list_of_points			)			):
											# For all points, sum up the product of i-th basis function and i-th point.
											x += basis_function[i] * self.list_of_points[i][0]
											y += basis_function[i] * self.list_of_points[i][1]
									return (x, y)





							def 		a__   (  self		:int  ,_UpperCamelCase		:float = 0.01			):
									from matplotlib import pyplot as plt  # type: ignore

									snake_case_		:							list[float]			       =						[]  # x coordinates of points to plot
									snake_case_		:							list[float]			       =						[]  # y coordinates of points to plot

									snake_case_		:							Optional[Any]			       =						0.0
									while t <= 1:
											snake_case_		:							Optional[int]			       =						self.bezier_curve_function(_UpperCamelCase			)
											to_plot_x.append(value[0]			)
											to_plot_y.append(value[1]			)
											t += step_size

									snake_case_		:							Dict			       =						[i[0] for i in self.list_of_points]
									snake_case_		:							Tuple			       =						[i[1] for i in self.list_of_points]

									plt.plot(
									    _UpperCamelCase  ,_UpperCamelCase  ,color="""blue"""  ,label="""Curve of Degree """ + str(self.degree			)  ,)
									plt.scatter(_UpperCamelCase  ,_UpperCamelCase  ,color="""red"""  ,label="""Control Points"""			)
									plt.legend()
									plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
							BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
							BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3



'''simple docstring'''






import torch

from transformers import AutoModel
class 						__UpperCamelCase	(						torch.nn.Module							):





							def __init__(  self		:Union[str, Any]  ,_UpperCamelCase		:Tuple="sayef/fsner-bert-base-uncased"			):
									super(_UpperCamelCase  ,self			).__init__()

									snake_case_		:							Dict			       =						AutoModel.from_pretrained(_UpperCamelCase  ,return_dict=_UpperCamelCase			)
									snake_case_		:							Dict			       =						torch.nn.CosineSimilarity(3  ,1E-0_8			)
									snake_case_		:							int			       =						torch.nn.Softmax(dim=1			)





							def 		a__   (  self		:Optional[Any]  ,**_UpperCamelCase		:Optional[Any]			):
									return self.bert(**_UpperCamelCase			).last_hidden_state





							def 		a__   (  self		:List[Any]  ,_UpperCamelCase		:Dict			):
									return token_embeddings.sum(2  ,keepdim=_UpperCamelCase			)





							def 		a__   (  self		:Optional[Any]  ,_UpperCamelCase		:List[str]  ,_UpperCamelCase		:List[str]  ,_UpperCamelCase		:List[str]=1			):
									return self.softmax(T * self.cos(_UpperCamelCase  ,_UpperCamelCase			)			)





							def 		a__   (  self		:Optional[Any]  ,_UpperCamelCase		:Optional[Any]  ,_UpperCamelCase		:int			):
									snake_case_		:							Union[str, Any]			       =						W_supports["""sizes"""].tolist()
									snake_case_		:							Dict			       =						W_supports["""start_token_id"""].item()
									snake_case_		:							int			       =						W_supports["""end_token_id"""].item()

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

									snake_case_		:							int			       =						self.BERT(**_UpperCamelCase			)
									snake_case_		:							int			       =						self.BERT(**_UpperCamelCase			)

									snake_case_		:							Any			       =						None
									snake_case_		:							Any			       =						None

									snake_case_		:							Union[str, Any]			       =						W_supports["""input_ids"""] == start_token_id
									snake_case_		:							Tuple			       =						W_supports["""input_ids"""] == end_token_id

									for i, size in enumerate(_UpperCamelCase			):
											if i == 0:
													snake_case_		:							str			       =						0
											else:
													snake_case_		:							Optional[Any]			       =						support_sizes[i - 1]

											snake_case_		:							Dict			       =						S[s : s + size][start_token_masks[s : s + size]]
											snake_case_		:							Optional[Any]			       =						S[s : s + size][end_token_masks[s : s + size]]

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

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

									return p_starts, p_ends