






from __future__ import annotations

from scipy.special import comb  # type: ignore




class 		UpperCAmelCase_						:


						'''simple docstring'''




						def __init__(	self		,				_SCREAMING_SNAKE_CASE				) ->				str:
								snake_case_				:							Union[str, Any]						 =       list_of_points
								# Degree determines the flexibility of the curve.
								# Degree = 1 will produce a straight line.
								snake_case_				:							Any						 =       len(_SCREAMING_SNAKE_CASE				) - 1






						def       _lowerCAmelCase       (	self		,				_SCREAMING_SNAKE_CASE				) ->				list[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		,				_SCREAMING_SNAKE_CASE				) * ((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(_SCREAMING_SNAKE_CASE				)		,				5				) == 1
								return output_values






						def       _lowerCAmelCase       (	self		,				_SCREAMING_SNAKE_CASE				) ->				tuple[float, float]:
								assert 0 <= t <= 1, "Time t must be between 0 and 1."

								snake_case_				:							Dict						 =       self.basis_function(_SCREAMING_SNAKE_CASE				)
								snake_case_				:							Union[str, Any]						 =       0.0
								snake_case_				:							Tuple						 =       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       _lowerCAmelCase       (	self		,				_SCREAMING_SNAKE_CASE = 0.01				) ->				int:
								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[int]						 =       0.0
								while t <= 1:
										snake_case_				:							Dict						 =       self.bezier_curve_function(_SCREAMING_SNAKE_CASE				)
										to_plot_x.append(value[0]				)
										to_plot_y.append(value[1]				)
										t += step_size

								snake_case_				:							str						 =       [i[0] for i in self.list_of_points]
								snake_case_				:							Optional[Any]						 =       [i[1] for i in self.list_of_points]

								plt.plot(
								    _SCREAMING_SNAKE_CASE		,				_SCREAMING_SNAKE_CASE		,				color="blue"		,				label="Curve of Degree " + str(self.degree				)		,				)
								plt.scatter(_SCREAMING_SNAKE_CASE		,				_SCREAMING_SNAKE_CASE		,				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








import fire

from transformers import AutoConfig, AutoModelForSeqaSeqLM, AutoTokenizer

def      lowerCAmelCase__	(    _a       :			str  ,      _a       :			str  ,      **_a       :			Optional[int]    ):
		snake_case_				:							Any						 =       AutoConfig.from_pretrained(_a  ,      **_a    )
		snake_case_				:							str						 =       AutoModelForSeqaSeqLM.from_config(_a    )
		model.save_pretrained(_a    )
		AutoTokenizer.from_pretrained(_a    ).save_pretrained(_a    )
		return model


if __name__ == "__main__":
							fire.Fire(save_randomly_initialized_version)
