



"""simple docstring"""






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






def   snake_case__     (	__lowerCamelCase       :					ndarray			):
			"""simple docstring"""
			return np.dot(__lowerCamelCase							,	__lowerCamelCase			)

class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					def __init__( self							:						List[str],						*,
					    lowerCamelCase							:						float = np.inf,						lowerCamelCase							:						str = "linear",						lowerCamelCase							:						float = 0.0,						)->      None:
								lowerCamelCase__	:	List[Any]				=regularization
								lowerCamelCase__	:	List[Any]				=gamma
								if kernel == "linear":
											lowerCamelCase__	:	Union[str, 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'''  )
											lowerCamelCase__	:	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:
											lowerCamelCase__	:	Dict				=F'''Unknown kernel: {kernel}'''
											raise ValueError(lowerCamelCase  )



					def 	snake_case ( self							:						Any,						lowerCamelCase							:						ndarray,						lowerCamelCase							:						ndarray  )->      float:
								return np.dot(lowerCamelCase,						lowerCamelCase  )



					def 	snake_case ( self							:						Optional[Any],						lowerCamelCase							:						ndarray,						lowerCamelCase							:						ndarray  )->      float:
								return np.exp(-(self.gamma * norm_squared(vectora - vectora  ))  )



					def 	snake_case ( self							:						Any,						lowerCamelCase							:						list[ndarray],						lowerCamelCase							:						ndarray  )->      None:
								lowerCamelCase__	:	int				=observations
								lowerCamelCase__	:	Dict				=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__)			,     )	:	Optional[Any]				=np.shape(lowerCamelCase  )

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

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

								lowerCamelCase__	:	str				=minimize(
								    lowerCamelCase,						np.ones(lowerCamelCase  ),						bounds=lowerCamelCase,						constraints=[ly_contraint]  ).x
								lowerCamelCase__	:	int				=l_star

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




					def 	snake_case ( self							:						Dict,						lowerCamelCase							:						ndarray  )->      int:
								lowerCamelCase__	:	int				=sum(
								    self.optimum[n]
								    * self.classes[n]
								    * self.kernel(self.observations[n],						lowerCamelCase  )
								    for n in range(len(self.classes  )  )  )
								return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
		import doctest

		doctest.testmod()









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					int = 4000000			):
			"""simple docstring"""
			lowerCamelCase__	:	Dict				=[]
			lowerCamelCase__			,     lowerCamelCase__	:	Union[str, Any]				=0, 1
			while b <= n:
						if b % 2 == 0:
									even_fibs.append(__lowerCamelCase			)
						lowerCamelCase__			,     lowerCamelCase__	:	Union[str, Any]				=b, a + b
			return sum(__lowerCamelCase			)


if __name__ == "__main__":
		print(f'{solution() = }')




