



from __future__ import annotations

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






			"""simple docstring"""





			def __init__(				self	:       Tuple			,     lowercase	:       list[tuple[float, float]]   )						->					List[str]:
									"""simple docstring"""







									__lowercase					=				list_of_points
									# Degree determines the flexibility of the curve.
									# Degree = 1 will produce a straight line.
									__lowercase					=				len(lowercase   ) - 1





			def 		snake_case__			(				self	:       Optional[Any]			,     lowercase	:       float   )						->					list[float]:
									"""simple docstring"""







									assert 0 <= t <= 1, "Time t must be between 0 and 1."
									__lowercase					=				[]
									for i in range(len(self.list_of_points   )   ):
															# basis function for each i
															output_values.append(
															    comb(self.degree			,     lowercase   ) * ((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(lowercase   )			,     5   ) == 1
									return output_values





			def 		snake_case__			(				self	:       List[str]			,     lowercase	:       float   )						->					tuple[float, float]:
									"""simple docstring"""







									assert 0 <= t <= 1, "Time t must be between 0 and 1."

									__lowercase					=				self.basis_function(lowercase   )
									__lowercase					=				0.0
									__lowercase					=				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 		snake_case__			(				self	:       Optional[Any]			,     lowercase	:       float = 0.01   )						->					Any:
									"""simple docstring"""







									from matplotlib import pyplot as plt  # type: ignore

									__lowercase					=				[]  # x coordinates of points to plot
									__lowercase					=				[]  # y coordinates of points to plot

									__lowercase					=				0.0
									while t <= 1:
															__lowercase					=				self.bezier_curve_function(lowercase   )
															to_plot_x.append(value[0]   )
															to_plot_y.append(value[1]   )
															t += step_size

									__lowercase					=				[i[0] for i in self.list_of_points]
									__lowercase					=				[i[1] for i in self.list_of_points]

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










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCamelCase__ =						{
    "configuration_luke": ["LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP", "LukeConfig"],
    "tokenization_luke": ["LukeTokenizer"],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCamelCase__ =						[
			    "LUKE_PRETRAINED_MODEL_ARCHIVE_LIST",
			    "LukeForEntityClassification",
			    "LukeForEntityPairClassification",
			    "LukeForEntitySpanClassification",
			    "LukeForMultipleChoice",
			    "LukeForQuestionAnswering",
			    "LukeForSequenceClassification",
			    "LukeForTokenClassification",
			    "LukeForMaskedLM",
			    "LukeModel",
			    "LukePreTrainedModel",
			]


if TYPE_CHECKING:
			from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
			from .tokenization_luke import LukeTokenizer

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_luke import (
						    LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
						    LukeForEntityClassification,
						    LukeForEntityPairClassification,
						    LukeForEntitySpanClassification,
						    LukeForMaskedLM,
						    LukeForMultipleChoice,
						    LukeForQuestionAnswering,
						    LukeForSequenceClassification,
						    LukeForTokenClassification,
						    LukeModel,
						    LukePreTrainedModel,
						)

else:
			import sys

			UpperCamelCase__ =						_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





