





'''simple docstring'''


from __future__ import annotations

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





     def __init__( self		:					Optional[int]	,      lowercase		:					list[tuple[float, float]]						):





        """simple docstring"""




        lowercase_			:Optional[Any]    			= list_of_points
        # Degree determines the flexibility of the curve.
        # Degree = 1 will produce a straight line.
        lowercase_			:Union[str, Any]    			= len(lowercase						) - 1





     def 							lowercase__      ( self		:					Dict	,      lowercase		:					float						):





        """simple docstring"""




        assert 0 <= t <= 1, "Time t must be between 0 and 1."
        lowercase_			:list[float]    			= []
        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 							lowercase__      ( self		:					Optional[Any]	,      lowercase		:					float						):





        """simple docstring"""




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

        lowercase_			:Union[str, Any]    			= self.basis_function(lowercase						)
        lowercase_			:Optional[Any]    			= 0.0
        lowercase_			: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 							lowercase__      ( self		:					Tuple	,      lowercase		:					float = 0.01						):





        """simple docstring"""




        from matplotlib import pyplot as plt  # type: ignore

        lowercase_			:list[float]    			= []  # x coordinates of points to plot
        lowercase_			:list[float]    			= []  # y coordinates of points to plot

        lowercase_			:Optional[Any]    			= 0.0
        while t <= 1:
           lowercase_			:Union[str, Any]    			= self.bezier_curve_function(lowercase						)
           to_plot_x.append(value[0]						)
           to_plot_y.append(value[1]						)
           t += step_size

        lowercase_			:Optional[Any]    			= [i[0] for i in self.list_of_points]
        lowercase_			:Tuple    			= [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









'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase					:     Optional[Any]												={
    '''configuration_nllb_moe''': [
        '''NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''NllbMoeConfig''',
    ]
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase					:     Tuple												=[
     '''NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''NllbMoeForConditionalGeneration''',
     '''NllbMoeModel''',
     '''NllbMoePreTrainedModel''',
     '''NllbMoeTop2Router''',
     '''NllbMoeSparseMLP''',
 ]


if TYPE_CHECKING:
 from .configuration_nllb_moe import (
     NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
     NllbMoeConfig,
 )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_nllb_moe import (
      NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
      NllbMoeForConditionalGeneration,
      NllbMoeModel,
      NllbMoePreTrainedModel,
      NllbMoeSparseMLP,
      NllbMoeTopaRouter,
  )


else:
 import sys

 lowerCAmelCase					:     Tuple												=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


