"""simple docstring"""




from __future__ import annotations

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






     def __init__(		self    ,					a__  ):
       _lowerCAmelCase						:	Dict        =					list_of_points
       # Degree determines the flexibility of the curve.
       # Degree = 1 will produce a straight line.
       _lowerCAmelCase						:	Optional[int]        =					len(__UpperCAmelCase  ) - 1






     def    __A  (		self    ,					a__  ):
       assert 0 <= t <= 1, "Time t must be between 0 and 1."
       _lowerCAmelCase						:	Optional[Any]        =					[]
       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    ,					a__  ):
       assert 0 <= t <= 1, "Time t must be between 0 and 1."

       _lowerCAmelCase						:	List[Any]        =					self.basis_function(__UpperCAmelCase  )
       _lowerCAmelCase						:	List[Any]        =					0.0
       _lowerCAmelCase						:	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    ,					a__ = 0.0_1  ):
       from matplotlib import pyplot as plt  # type: ignore

       _lowerCAmelCase						:	Any        =					[]  # x coordinates of points to plot
       _lowerCAmelCase						:	List[str]        =					[]  # y coordinates of points to plot

       _lowerCAmelCase						:	List[str]        =					0.0
       while t <= 1:
         _lowerCAmelCase						:	str        =					self.bezier_curve_function(__UpperCAmelCase  )
         to_plot_x.append(value[0]  )
         to_plot_y.append(value[1]  )
         t += step_size

       _lowerCAmelCase						:	Optional[Any]        =					[i[0] for i in self.list_of_points]
       _lowerCAmelCase						:	Any        =					[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"""




from dataclasses import dataclass
from typing import Optional, Tuple

import torch
from torch import nn
from transformers import RobertaPreTrainedModel, XLMRobertaConfig, XLMRobertaModel
from transformers.utils import ModelOutput
@dataclass
class 						__A							(			SCREAMING_SNAKE_CASE_		):
     _UpperCamelCase							:      Optional[torch.FloatTensor]		 =		None
     _UpperCamelCase							:      torch.FloatTensor		 =		None
     _UpperCamelCase							:      Optional[Tuple[torch.FloatTensor]]		 =		None
     _UpperCamelCase							:      Optional[Tuple[torch.FloatTensor]]		 =		None







class 						__A							(			SCREAMING_SNAKE_CASE_		):






     def __init__(		self    ,					a__=1    ,					a__=0    ,					a__=2    ,					a__=512    ,					a__="cls"    ,					a__=False    ,					a__=True    ,					**a__    ,					):
       super().__init__(pad_token_id=a__    ,					bos_token_id=a__    ,					eos_token_id=a__    ,					**a__  )
       _lowerCAmelCase						:	Optional[Any]        =					project_dim
       _lowerCAmelCase						:	List[str]        =					pooler_fn
       _lowerCAmelCase						:	Any        =					learn_encoder
       _lowerCAmelCase						:	Optional[int]        =					use_attention_mask







class 						__A							(			SCREAMING_SNAKE_CASE_		):
     _UpperCamelCase							:      Optional[int]		 =		[R"pooler", R"logit_scale"]
     _UpperCamelCase							:      List[Any]		 =		[R"position_ids", R"predictions.decoder.bias"]
     _UpperCamelCase							:      List[Any]		 =		"roberta"
     _UpperCamelCase							:      Optional[int]		 =		RobertaSeriesConfig






     def __init__(		self    ,					a__  ):
       super().__init__(a__  )
       _lowerCAmelCase						:	str        =					XLMRobertaModel(a__  )
       _lowerCAmelCase						:	Optional[Any]        =					nn.Linear(config.hidden_size    ,					config.project_dim  )
       _lowerCAmelCase						:	List[Any]        =					getattr(a__    ,					"""has_pre_transformation"""    ,					a__  )
       if self.has_pre_transformation:
         _lowerCAmelCase						:	List[str]        =					nn.Linear(config.hidden_size    ,					config.project_dim  )
         _lowerCAmelCase						:	Optional[int]        =					nn.LayerNorm(config.hidden_size    ,					eps=config.layer_norm_eps  )
       self.post_init()






     def    __A  (		self    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					a__ = None    ,					):
       _lowerCAmelCase						:	List[str]        =					return_dict if return_dict is not None else self.config.use_return_dict

       _lowerCAmelCase						:	Optional[int]        =					self.base_model(
           input_ids=a__    ,					attention_mask=a__    ,					token_type_ids=a__    ,					position_ids=a__    ,					head_mask=a__    ,					inputs_embeds=a__    ,					encoder_hidden_states=a__    ,					encoder_attention_mask=a__    ,					output_attentions=a__    ,					output_hidden_states=True if self.has_pre_transformation else output_hidden_states    ,					return_dict=a__    ,					)

       if self.has_pre_transformation:
         _lowerCAmelCase						:	Optional[Any]        =					outputs["""hidden_states"""][-2]
         _lowerCAmelCase						:	Optional[Any]        =					self.pre_LN(a__  )
         _lowerCAmelCase						:	int        =					self.transformation_pre(a__  )

         return TransformationModelOutput(
             projection_state=a__    ,					last_hidden_state=outputs.last_hidden_state    ,					hidden_states=outputs.hidden_states    ,					attentions=outputs.attentions    ,					)
       else:
         _lowerCAmelCase						:	Union[str, Any]        =					self.transformation(outputs.last_hidden_state  )
         return TransformationModelOutput(
             projection_state=a__    ,					last_hidden_state=outputs.last_hidden_state    ,					hidden_states=outputs.hidden_states    ,					attentions=outputs.attentions    ,					)




