




'''simple docstring'''





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


def 					SCREAMING_SNAKE_CASE__(     snake_case							:	ndarray					):

							'''simple docstring'''






							return np.dot(snake_case							,    snake_case					)




class 			_snake_case		:




			def __init__( self    ,							*,
			    a__ = np.inf    ,							a__ = "linear"    ,							a__ = 0.0    ,							)    ->    Tuple:

										'''simple docstring'''




										snake_case_      =				regularization
										snake_case_      =				gamma
										if kernel == "linear":
																	snake_case_      =				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"							)
																	snake_case_      =				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:
																	snake_case_      =				F'Unknown kernel: {kernel}'
																	raise ValueError(lowerCamelCase_							)




			def        lowerCAmelCase__    ( self    ,							a__    ,							a__							)    ->    List[Any]:

										'''simple docstring'''




										return np.dot(lowerCamelCase_    ,							lowerCamelCase_							)




			def        lowerCAmelCase__    ( self    ,							a__    ,							a__							)    ->    List[str]:

										'''simple docstring'''




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




			def        lowerCAmelCase__    ( self    ,							a__    ,							a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										snake_case_      =				observations
										snake_case_      =				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

										((snake_case_    ) ,				    )      =				np.shape(lowerCamelCase_							)

										def to_minimize(a__							) -> float:
																	snake_case_      =				0
																	((snake_case_    ) ,				    )      =				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_							)

										snake_case_      =				LinearConstraint(lowerCamelCase_    ,							0    ,							0							)
										snake_case_      =				Bounds(0    ,							self.regularization							)

										snake_case_      =				minimize(
										    lowerCamelCase_    ,							np.ones(lowerCamelCase_							)    ,							bounds=lowerCamelCase_    ,							constraints=[ly_contraint]							).x
										snake_case_      =				l_star

										# calculating mean offset of separation plane to points
										snake_case_      =				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]							)
										snake_case_      =				s / n




			def        lowerCAmelCase__    ( self    ,							a__							)    ->    int:

										'''simple docstring'''




										snake_case_      =				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'''





from ..utils import DummyObject, requires_backends




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Dict							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    List[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    str:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Dict							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Dict:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[str]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Optional[Any]							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    str:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[int]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[str]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Optional[Any]							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[str]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Dict:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				List[str]							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[int]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				int							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    List[str]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Any:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Optional[Any]							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Any:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    int:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Dict							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[int]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    List[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				List[str]							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Dict:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				int							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Dict:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    int:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Any							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Tuple:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    str:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				str							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    List[str]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Union[str, Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




class 			_snake_case		(     metaclass=lowercase_							):
			lowerCAmelCase_					:				Tuple							=   ["flax"]




			def __init__( self    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(self    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    int:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




			@classmethod
			def        lowerCAmelCase__    ( cls    ,							*a__    ,							**a__							)    ->    Optional[Any]:

										'''simple docstring'''




										requires_backends(cls    ,							["flax"]							)




