






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

def    UpperCamelCase						(	_A			):






						"""simple docstring"""







						return np.dot(_A,   _A			)





class 	snake_case__ :
	def __init__(    self      ,       *,
	    lowerCAmelCase__ = np.inf      ,       lowerCAmelCase__ = "linear"      ,       lowerCAmelCase__ = 0.0      ,       )							->				None:
							__magic_name__      :       Optional[int]       						= regularization
							__magic_name__      :       Dict       						= gamma
							if kernel == "linear":
													__magic_name__      :       str       						= 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"""			)
													__magic_name__      :       Optional[int]       						= 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:
													__magic_name__      :       Tuple       						= F'Unknown kernel: {kernel}'
													raise ValueError(lowerCAmelCase__			)
	def       __magic_name__    (    self      ,       lowerCAmelCase__      ,       lowerCAmelCase__			)							->				float:
							return np.dot(lowerCAmelCase__      ,       lowerCAmelCase__			)
	def       __magic_name__    (    self      ,       lowerCAmelCase__      ,       lowerCAmelCase__			)							->				float:
							return np.exp(-(self.gamma * norm_squared(vectora - vectora			))			)
	def       __magic_name__    (    self      ,       lowerCAmelCase__      ,       lowerCAmelCase__			)							->				None:
							__magic_name__      :       Union[str, Any]       						= observations
							__magic_name__      :       Tuple       						= 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

							((__magic_name__)						,)      :       int       						= np.shape(lowerCAmelCase__			)

							def to_minimize(lowerCAmelCase__			) -> float:
													__magic_name__      :       List[Any]       						= 0
													((__magic_name__)						,)      :       int       						= 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__			)

							__magic_name__      :       Tuple       						= LinearConstraint(lowerCAmelCase__      ,       0      ,       0			)
							__magic_name__      :       Optional[Any]       						= Bounds(0      ,       self.regularization			)

							__magic_name__      :       Tuple       						= minimize(
							    lowerCAmelCase__      ,       np.ones(lowerCAmelCase__			)      ,       bounds=lowerCAmelCase__      ,       constraints=[ly_contraint]			).x
							__magic_name__      :       Union[str, Any]       						= l_star

							# calculating mean offset of separation plane to points
							__magic_name__      :       Tuple       						= 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]			)
							__magic_name__      :       Dict       						= s / n







	def       __magic_name__    (    self      ,       lowerCAmelCase__			)							->				int:
							__magic_name__      :       Optional[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()








def    UpperCamelCase						(	_A = 1,   _A = 1000			):






						"""simple docstring"""







						__magic_name__      :       Optional[int]       						= 1
						__magic_name__      :       Dict       						= 0

						for divide_by_number in range(_A,   digit + 1			):
												__magic_name__      :       list[int]       						= []
												__magic_name__      :       Any       						= numerator
												for _ in range(1,   digit + 1			):
																		if now_divide in has_been_divided:
																								if longest_list_length < len(_A			):
																														__magic_name__      :       int       						= len(_A			)
																														__magic_name__      :       Dict       						= divide_by_number
																		else:
																								has_been_divided.append(_A			)
																								__magic_name__      :       Optional[int]       						= now_divide * 10 % divide_by_number

						return the_digit


# Tests
if __name__ == "__main__":
		import doctest

		doctest.testmod()
