import sys
import turtle




def       lowerCAmelCase_     (		lowercase:							Tuple  ,					lowercase:							Tuple		):







 '''simple docstring'''
 return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2




def       lowerCAmelCase_     (		lowercase:							int  ,					lowercase:							Any  ,					lowercase:							int  ,					lowercase:							Any  ,					):







 '''simple docstring'''
 my_pen.up()
 my_pen.goto(vertexa[0]  ,					vertexa[1]		)
 my_pen.down()
 my_pen.goto(vertexa[0]  ,					vertexa[1]		)
 my_pen.goto(vertexa[0]  ,					vertexa[1]		)
 my_pen.goto(vertexa[0]  ,					vertexa[1]		)

 if depth == 0:
  return

 triangle(_lowerCAmelCase  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					depth - 1		)
 triangle(_lowerCAmelCase  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					depth - 1		)
 triangle(_lowerCAmelCase  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					get_mid(_lowerCAmelCase  ,					_lowerCAmelCase		)  ,					depth - 1		)


if __name__ == "__main__":
  if len(sys.argv) != 2:
    raise ValueError(
        '''Correct format for using this script: '''
        '''python fractals.py <int:depth_for_fractal>'''
    )
  UpperCAmelCase_			    =							turtle.Turtle()
  my_pen.ht()
  my_pen.speed(5)
  my_pen.pencolor('''red''')

  UpperCAmelCase_			    =							[(-1_7_5, -1_2_5), (0, 1_7_5), (1_7_5, -1_2_5)]  # vertices of triangle
  triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))
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()