






from __future__ import annotations

from scipy.special import comb  # type: ignore




class     _lowerCAmelCase:





       """simple docstring"""







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





       def       _a   ( self  ,      _lowerCamelCase							):
         assert 0 <= t <= 1, "Time t must be between 0 and 1."
         UpperCamelCase_: list[float]   				=    []
         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       _a   ( self  ,      _lowerCamelCase							):
         assert 0 <= t <= 1, "Time t must be between 0 and 1."

         UpperCamelCase_: Optional[int]   				=    self.basis_function(_lowerCamelCase							)
         UpperCamelCase_: List[Any]   				=    0.0
         UpperCamelCase_: int   				=    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       _a   ( self  ,      _lowerCamelCase = 0.0_1							):
         from matplotlib import pyplot as plt  # type: ignore

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

         UpperCamelCase_: Dict   				=    0.0
         while t <= 1:
           UpperCamelCase_: Tuple   				=    self.bezier_curve_function(_lowerCamelCase							)
           to_plot_x.append(value[0]							)
           to_plot_y.append(value[1]							)
           t += step_size

         UpperCamelCase_: Dict   				=    [i[0] for i in self.list_of_points]
         UpperCamelCase_: str   				=    [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







from typing import TYPE_CHECKING

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


A_		:		Tuple		     =			{
    'configuration_funnel': ['FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP', 'FunnelConfig'],
    'convert_funnel_original_tf_checkpoint_to_pytorch': [],
    'tokenization_funnel': ['FunnelTokenizer'],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_		:		List[str]		     =			['FunnelTokenizerFast']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_		:		List[str]		     =			[
       'FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST',
       'FunnelBaseModel',
       'FunnelForMaskedLM',
       'FunnelForMultipleChoice',
       'FunnelForPreTraining',
       'FunnelForQuestionAnswering',
       'FunnelForSequenceClassification',
       'FunnelForTokenClassification',
       'FunnelModel',
       'FunnelPreTrainedModel',
       'load_tf_weights_in_funnel',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_		:		str		     =			[
       'TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFFunnelBaseModel',
       'TFFunnelForMaskedLM',
       'TFFunnelForMultipleChoice',
       'TFFunnelForPreTraining',
       'TFFunnelForQuestionAnswering',
       'TFFunnelForSequenceClassification',
       'TFFunnelForTokenClassification',
       'TFFunnelModel',
       'TFFunnelPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_funnel import FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP, FunnelConfig
   from .tokenization_funnel import FunnelTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_funnel_fast import FunnelTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_funnel import (
          FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
          FunnelBaseModel,
          FunnelForMaskedLM,
          FunnelForMultipleChoice,
          FunnelForPreTraining,
          FunnelForQuestionAnswering,
          FunnelForSequenceClassification,
          FunnelForTokenClassification,
          FunnelModel,
          FunnelPreTrainedModel,
          load_tf_weights_in_funnel,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_funnel import (
          TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFFunnelBaseModel,
          TFFunnelForMaskedLM,
          TFFunnelForMultipleChoice,
          TFFunnelForPreTraining,
          TFFunnelForQuestionAnswering,
          TFFunnelForSequenceClassification,
          TFFunnelForTokenClassification,
          TFFunnelModel,
          TFFunnelPreTrainedModel,
      )

else:
   import sys

   A_		:		Any		     =			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)