




'''simple docstring'''


import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize
def 	snake_case_					(UpperCamelCase :						ndarray   ):





							'''simple docstring'''


							return np.dot(UpperCamelCase				,		UpperCamelCase   )

class     A					:







							def __init__(						self :						Any							,    *,
							    lowerCAmelCase_ :						float = np.inf							,    lowerCAmelCase_ :						str = "linear"							,    lowerCAmelCase_ :						float = 0.0							,    )    ->							None:


														"""simple docstring"""


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







							def      __lowerCAmelCase    (						self :						Tuple							,    lowerCAmelCase_ :						ndarray							,    lowerCAmelCase_ :						ndarray      )    ->							float:


														"""simple docstring"""


														return np.dot(lowerCAmelCase_							,    lowerCAmelCase_      )







							def      __lowerCAmelCase    (						self :						Optional[int]							,    lowerCAmelCase_ :						ndarray							,    lowerCAmelCase_ :						ndarray      )    ->							float:


														"""simple docstring"""


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







							def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						list[ndarray]							,    lowerCAmelCase_ :						ndarray      )    ->							None:


														"""simple docstring"""


														_a			  =       observations
														_a			  =       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

														((_a)  ,							)			  =       np.shape(lowerCAmelCase_      )

														def to_minimize(lowerCAmelCase_ :						ndarray      ) -> float:
																					_a			  =       0
																					((_a)  ,							)			  =       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_      )

														_a			  =       LinearConstraint(lowerCAmelCase_							,    0							,    0      )
														_a			  =       Bounds(0							,    self.regularization      )

														_a			  =       minimize(
														    lowerCAmelCase_							,    np.ones(lowerCAmelCase_      )							,    bounds=lowerCAmelCase_							,    constraints=[ly_contraint]      ).x
														_a			  =       l_star

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







							def      __lowerCAmelCase    (						self :						List[Any]							,    lowerCAmelCase_ :						ndarray      )    ->							int:


														"""simple docstring"""


														_a			  =       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     A					(	metaclass=_a					):
							lowercase_           =       ['torch', 'torchsde']







							def __init__(						self :						Optional[Any]							,    *lowerCAmelCase_ :						Any							,    **lowerCAmelCase_ :						Tuple      )    ->							Dict:


														"""simple docstring"""


														requires_backends(self							,    ['''torch''', '''torchsde''']      )







							@classmethod
							def      __lowerCAmelCase    (						cls :						Dict							,    *lowerCAmelCase_ :						Optional[int]							,    **lowerCAmelCase_ :						Optional[Any]      )    ->							int:


														"""simple docstring"""


														requires_backends(cls							,    ['''torch''', '''torchsde''']      )







							@classmethod
							def      __lowerCAmelCase    (						cls :						List[str]							,    *lowerCAmelCase_ :						str							,    **lowerCAmelCase_ :						Optional[Any]      )    ->							Any:


														"""simple docstring"""


														requires_backends(cls							,    ['''torch''', '''torchsde''']      )

