from __future__ import annotations

from scipy.special import comb  # type: ignore


class 						a__							:



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



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

								__a		 =       self.basis_function(UpperCAmelCase   )
								__a		 =       0.0
								__a		 =       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 __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase = 0.01   )			->   Optional[Any]:
								from matplotlib import pyplot as plt  # type: ignore

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

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

								__a		 =       [i[0] for i in self.list_of_points]
								__a		 =       [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





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


lowerCamelCase_    :		Optional[Any]							=	{
    """configuration_roberta_prelayernorm""": [
        """ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """RobertaPreLayerNormConfig""",
        """RobertaPreLayerNormOnnxConfig""",
    ],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	lowerCamelCase_    :		Dict							=	[
	    """ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """RobertaPreLayerNormForCausalLM""",
	    """RobertaPreLayerNormForMaskedLM""",
	    """RobertaPreLayerNormForMultipleChoice""",
	    """RobertaPreLayerNormForQuestionAnswering""",
	    """RobertaPreLayerNormForSequenceClassification""",
	    """RobertaPreLayerNormForTokenClassification""",
	    """RobertaPreLayerNormModel""",
	    """RobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	lowerCamelCase_    :		Any							=	[
	    """TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """TFRobertaPreLayerNormForCausalLM""",
	    """TFRobertaPreLayerNormForMaskedLM""",
	    """TFRobertaPreLayerNormForMultipleChoice""",
	    """TFRobertaPreLayerNormForQuestionAnswering""",
	    """TFRobertaPreLayerNormForSequenceClassification""",
	    """TFRobertaPreLayerNormForTokenClassification""",
	    """TFRobertaPreLayerNormMainLayer""",
	    """TFRobertaPreLayerNormModel""",
	    """TFRobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	lowerCamelCase_    :		Any							=	[
	    """FlaxRobertaPreLayerNormForCausalLM""",
	    """FlaxRobertaPreLayerNormForMaskedLM""",
	    """FlaxRobertaPreLayerNormForMultipleChoice""",
	    """FlaxRobertaPreLayerNormForQuestionAnswering""",
	    """FlaxRobertaPreLayerNormForSequenceClassification""",
	    """FlaxRobertaPreLayerNormForTokenClassification""",
	    """FlaxRobertaPreLayerNormModel""",
	    """FlaxRobertaPreLayerNormPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_roberta_prelayernorm import (
	    ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    RobertaPreLayerNormConfig,
	    RobertaPreLayerNormOnnxConfig,
	)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_roberta_prelayernorm import (
		    ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    RobertaPreLayerNormForCausalLM,
		    RobertaPreLayerNormForMaskedLM,
		    RobertaPreLayerNormForMultipleChoice,
		    RobertaPreLayerNormForQuestionAnswering,
		    RobertaPreLayerNormForSequenceClassification,
		    RobertaPreLayerNormForTokenClassification,
		    RobertaPreLayerNormModel,
		    RobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_roberta_prelayernorm import (
		    TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TFRobertaPreLayerNormForCausalLM,
		    TFRobertaPreLayerNormForMaskedLM,
		    TFRobertaPreLayerNormForMultipleChoice,
		    TFRobertaPreLayerNormForQuestionAnswering,
		    TFRobertaPreLayerNormForSequenceClassification,
		    TFRobertaPreLayerNormForTokenClassification,
		    TFRobertaPreLayerNormMainLayer,
		    TFRobertaPreLayerNormModel,
		    TFRobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_roberta_prelayernorm import (
		    FlaxRobertaPreLayerNormForCausalLM,
		    FlaxRobertaPreLayerNormForMaskedLM,
		    FlaxRobertaPreLayerNormForMultipleChoice,
		    FlaxRobertaPreLayerNormForQuestionAnswering,
		    FlaxRobertaPreLayerNormForSequenceClassification,
		    FlaxRobertaPreLayerNormForTokenClassification,
		    FlaxRobertaPreLayerNormModel,
		    FlaxRobertaPreLayerNormPreTrainedModel,
		)

else:
	import sys

	lowerCamelCase_    :		Optional[int]							=	_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)




