



'''simple docstring'''


from __future__ import annotations

from scipy.special import comb  # type: ignore







class 	UpperCAmelCase	:


 '''simple docstring'''




 def __init__(   self							,  lowerCAmelCase_) ->      List[Any]:



      """simple docstring"""







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




 def       lowercase_  (   self							,  lowerCAmelCase_) ->      list[float]:



      """simple docstring"""







      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							,  lowerCAmelCase_) * ((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(lowerCAmelCase_)							,  5) == 1
      return output_values




 def       lowercase_  (   self							,  lowerCAmelCase_) ->      tuple[float, float]:



      """simple docstring"""







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

      a_       		=self.basis_function(lowerCAmelCase_)
      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       lowercase_  (   self							,  lowerCAmelCase_ = 0.0_1) ->      Optional[int]:



      """simple docstring"""







      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(lowerCAmelCase_)
           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(
          lowerCAmelCase_							,  lowerCAmelCase_							,  color="blue"							,  label="Curve of Degree " + str(self.degree)							,  )
      plt.scatter(lowerCAmelCase_							,  lowerCAmelCase_							,  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_tf_available, is_torch_available


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

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

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase							       =			[
      '''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

  lowercase							       =			_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


