
from __future__ import annotations

from scipy.special import comb  # type: ignore





class 							UpperCAmelCase				:




	'''simple docstring'''





	def __init__(	self :			Dict							,A :			list[tuple[float, float]]			):
					__A             =			list_of_points
					# Degree determines the flexibility of the curve.
					# Degree = 1 will produce a straight line.
					__A             =			len(A			) - 1






	def     UpperCamelCase_  (	self :			Any							,A :			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							,A			) * ((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(A			)							,5			) == 1
					return output_values






	def     UpperCamelCase_  (	self :			Union[str, Any]							,A :			float			):
					assert 0 <= t <= 1, "Time t must be between 0 and 1."

					__A             =			self.basis_function(A			)
					__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     UpperCamelCase_  (	self :			Optional[int]							,A :			float = 0.01			):
					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(A			)
									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(
					    A							,A							,color="blue"							,label="Curve of Degree " + str(self.degree			)							,)
					plt.scatter(A							,A							,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_tf_available, is_torch_available


SCREAMING_SNAKE_CASE							:Any										=    {
    'configuration_rag': ['RagConfig'],
    'retrieval_rag': ['RagRetriever'],
    'tokenization_rag': ['RagTokenizer'],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					SCREAMING_SNAKE_CASE							:List[Any]										=    [
					    'RagModel',
					    'RagPreTrainedModel',
					    'RagSequenceForGeneration',
					    'RagTokenForGeneration',
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					SCREAMING_SNAKE_CASE							:Any										=    [
					    'TFRagModel',
					    'TFRagPreTrainedModel',
					    'TFRagSequenceForGeneration',
					    'TFRagTokenForGeneration',
					]


if TYPE_CHECKING:
					from .configuration_rag import RagConfig
					from .retrieval_rag import RagRetriever
					from .tokenization_rag import RagTokenizer

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_rag import RagModel, RagPreTrainedModel, RagSequenceForGeneration, RagTokenForGeneration

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_rag import (
										    TFRagModel,
										    TFRagPreTrainedModel,
										    TFRagSequenceForGeneration,
										    TFRagTokenForGeneration,
										)

else:
					import sys

					SCREAMING_SNAKE_CASE							:int										=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
