





import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize





def 	lowerCAmelCase_					(			__a						)	->						float:







  """simple docstring"""





  return np.dot(__a      ,       __a						)



class   _SCREAMING_SNAKE_CASE		:







 '''simple docstring'''

 def __init__(self							:  List[str]			,					*,
     UpperCAmelCase_							:  float = np.inf			,					UpperCAmelCase_							:  str = "linear"			,					UpperCAmelCase_							:  float = 0.0			,					)			->None:



   '''simple docstring'''



   lowerCamelCase__: Dict         =regularization
   lowerCamelCase__: Any         =gamma
   if kernel == "linear":
     lowerCamelCase__: Dict         =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")
     lowerCamelCase__: Tuple         =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:
     lowerCamelCase__: Optional[Any]         =F"""Unknown kernel: {kernel}"""
     raise ValueError(UpperCAmelCase_)

 def 				SCREAMING_SNAKE_CASE_   (self							:  List[str]			,					UpperCAmelCase_							:  ndarray			,					UpperCAmelCase_							:  ndarray)			->float:



   '''simple docstring'''



   return np.dot(UpperCAmelCase_			,					UpperCAmelCase_)

 def 				SCREAMING_SNAKE_CASE_   (self							:  List[str]			,					UpperCAmelCase_							:  ndarray			,					UpperCAmelCase_							:  ndarray)			->float:



   '''simple docstring'''



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

 def 				SCREAMING_SNAKE_CASE_   (self							:  Tuple			,					UpperCAmelCase_							:  list[ndarray]			,					UpperCAmelCase_							:  ndarray)			->None:



   '''simple docstring'''



   lowerCamelCase__: Optional[Any]         =observations
   lowerCamelCase__: 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

   ((lowerCamelCase__)    ,   ): List[str]         =np.shape(UpperCAmelCase_)

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

   lowerCamelCase__: List[Any]         =LinearConstraint(UpperCAmelCase_			,					0			,					0)
   lowerCamelCase__: str         =Bounds(0			,					self.regularization)

   lowerCamelCase__: Union[str, Any]         =minimize(
       UpperCAmelCase_			,					np.ones(UpperCAmelCase_)			,					bounds=UpperCAmelCase_			,					constraints=[ly_contraint]).x
   lowerCamelCase__: str         =l_star

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







 def 				SCREAMING_SNAKE_CASE_   (self							:  Any			,					UpperCAmelCase_							:  ndarray)			->int:



   '''simple docstring'''



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


if __name__ == "__main__":
     import doctest

     doctest.testmod()





def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->str:
   '''simple docstring'''






   if not isinstance(lowerCAmelCase_		,    lowerCAmelCase_				):
      raise ValueError("iterations must be defined as integers"				)
   if not isinstance(lowerCAmelCase_		,    lowerCAmelCase_				) or not number >= 1:
      raise ValueError(
          "starting number must be\n                         and integer and be more than 0"				)
   if not iterations >= 1:
      raise ValueError("Iterations must be done more than 0 times to play FizzBuzz"				)

   snake_case_            =       ""
   while number <= iterations:
      if number % 3 == 0:
         out += "Fizz"
      if number % 5 == 0:
         out += "Buzz"
      if 0 not in (number % 3, number % 5):
         out += str(lowerCAmelCase_				)

      # print(out)
      number += 1
      out += " "
   return out


if __name__ == "__main__":
   import doctest

   doctest.testmod()




