from __future__ import annotations

from scipy.special import comb  # type: ignore




class  __magic_name__  :





   """simple docstring"""




   def __init__(	self					:  Optional[Any]		,  _lowercase					:  list[tuple[float, float]]							):



    """simple docstring"""



    _UpperCamelCase:     Optional[Any]							= list_of_points
    # Degree determines the flexibility of the curve.
    # Degree = 1 will produce a straight line.
    _UpperCamelCase:     Optional[int]							= len(_lowercase							) - 1



   def   lowerCAmelCase						(	self					:  Any		,  _lowercase					:  float							):



    """simple docstring"""



    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		,  _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   lowerCAmelCase						(	self					:  Optional[Any]		,  _lowercase					:  float							):



    """simple docstring"""



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

    _UpperCamelCase:     Dict							= self.basis_function(_lowercase							)
    _UpperCamelCase:     Optional[Any]							= 0.0
    _UpperCamelCase:     Union[str, Any]							= 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   lowerCAmelCase						(	self					:  Union[str, Any]		,  _lowercase					:  float = 0.01							):



    """simple docstring"""



    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:     Any							= 0.0
    while t <= 1:
     _UpperCamelCase:     Dict							= self.bezier_curve_function(_lowercase							)
     to_plot_x.append(value[0]							)
     to_plot_y.append(value[1]							)
     t += step_size

    _UpperCamelCase:     Union[str, Any]							= [i[0] for i in self.list_of_points]
    _UpperCamelCase:     Dict							= [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
import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize




def       lowerCAmelCase_     (		lowercase:							ndarray		)    ->				float:







 '''simple docstring'''
 return np.dot(lowercase  ,					lowercase		)




class  __magic_name__  :





   """simple docstring"""




   def __init__(	self					:  int		,  *,
       _lowercase					:  float = np.inf		,  _lowercase					:  str = "linear"		,  _lowercase					:  float = 0.0		,  ):



    """simple docstring"""



    _UpperCamelCase:     int							= regularization
    _UpperCamelCase:     Optional[int]							= gamma
    if kernel == "linear":
     _UpperCamelCase:     Optional[Any]							= self.__linear
    elif kernel == "rbf":
     if self.gamma == 0:
      raise ValueError('''rbf kernel requires gamma'''							)
     if not isinstance(self.gamma		,  (float, int)							):
      raise ValueError('''gamma must be float or int'''							)
     if not self.gamma > 0:
      raise ValueError('''gamma must be > 0'''							)
     _UpperCamelCase:     Optional[Any]							= self.__rbf
     # in the future, there could be a default value like in sklearn
     # sklear: def_gamma = 1/(n_features * X.var()) (wiki)
     # previously it was 1/(n_features)
    else:
     _UpperCamelCase:     Optional[int]							= f"""Unknown kernel: {kernel}"""
     raise ValueError(_lowercase							)



   def   lowerCAmelCase						(	self					:  Union[str, Any]		,  _lowercase					:  ndarray		,  _lowercase					:  ndarray							):



    """simple docstring"""



    return np.dot(_lowercase		,  _lowercase							)



   def   lowerCAmelCase						(	self					:  str		,  _lowercase					:  ndarray		,  _lowercase					:  ndarray							):



    """simple docstring"""



    return np.exp(-(self.gamma * norm_squared(vectora - vectora							))							)



   def   lowerCAmelCase						(	self					:  str		,  _lowercase					:  list[ndarray]		,  _lowercase					:  ndarray							):



    """simple docstring"""



    _UpperCamelCase:     List[str]							= observations
    _UpperCamelCase:     Optional[int]							= classes

    # using Wolfe's Dual to calculate w.
    # Primal problem: minimize 1/2*norm_squared(w)
    #   constraint: yn(w . xn + b) >= 1
    #
    # With l a vector
    # Dual problem: maximize sum_n(ln) -
    #       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
    #   constraint: self.C >= ln >= 0
    #           and sum_n(ln*yn) = 0
    # Then we get w using w = sum_n(ln*yn*xn)
    # At the end we can get b ~= mean(yn - w . xn)
    #
    # Since we use kernels, we only need l_star to calculate b
    # and to classify observations

    ((_UpperCamelCase)	,							):     Any							= np.shape(_lowercase							)

    def to_minimize(_lowercase					:  ndarray							) -> float:
     _UpperCamelCase:     Optional[int]							= 0
     ((_UpperCamelCase)	,							):     str							= np.shape(_lowercase							)
     for i in range(_lowercase							):
      for j in range(_lowercase							):
       s += (
           candidate[i]
           * candidate[j]
           * classes[i]
           * classes[j]
           * self.kernel(observations[i]		,  observations[j]							)
       )
     return 1 / 2 * s - sum(_lowercase							)

    _UpperCamelCase:     Optional[Any]							= LinearConstraint(_lowercase		,  0		,  0							)
    _UpperCamelCase:     Optional[int]							= Bounds(0		,  self.regularization							)

    _UpperCamelCase:     Dict							= minimize(
        _lowercase		,  np.ones(_lowercase							)		,  bounds=_lowercase		,  constraints=[ly_contraint]							).x
    _UpperCamelCase:     Union[str, Any]							= l_star

    # calculating mean offset of separation plane to points
    _UpperCamelCase:     List[str]							= 0
    for i in range(_lowercase							):
     for j in range(_lowercase							):
      s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
          observations[i]		,  observations[j]							)
    _UpperCamelCase:     str							= s / n



   def   lowerCAmelCase						(	self					:  Optional[Any]		,  _lowercase					:  ndarray							):



    """simple docstring"""



    _UpperCamelCase:     Optional[int]							= sum(
        self.optimum[n]
        * self.classes[n]
        * self.kernel(self.observations[n]		,  _lowercase							)
        for n in range(len(self.classes							)							)							)
    return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
  import doctest

  doctest.testmod()