
"""simple docstring"""







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




def       A_      (       lowercase   )  ->				float:


     """simple docstring"""







     return np.dot(lowercase    ,			lowercase   )



class 		UpperCAmelCase_						:
 """simple docstring"""




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



      """simple docstring"""

      UpperCAmelCase_    :     Tuple            =	regularization
      UpperCAmelCase_    :     List[str]            =	gamma
      if kernel == "linear":
           UpperCAmelCase_    :     Tuple            =	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"""			)
           UpperCAmelCase_    :     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:
           UpperCAmelCase_    :     Union[str, Any]            =	f'''Unknown kernel: {kernel}'''
           raise ValueError(a_			)




 def 	a   (			self							:			Optional[int]  , a_							:			ndarray  , a_							:			ndarray			)->       float:



      """simple docstring"""

      return np.dot(a_  , a_			)




 def 	a   (			self							:			int  , a_							:			ndarray  , a_							:			ndarray			)->       float:



      """simple docstring"""

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




 def 	a   (			self							:			int  , a_							:			list[ndarray]  , a_							:			ndarray			)->       None:



      """simple docstring"""

      UpperCAmelCase_    :     List[Any]            =	observations
      UpperCAmelCase_    :     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

      ((UpperCAmelCase_)       ,)    :     str            =	np.shape(a_			)

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

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

      UpperCAmelCase_    :     Tuple            =	minimize(
          a_  , np.ones(a_			)  , bounds=a_  , constraints=[ly_contraint]			).x
      UpperCAmelCase_    :     int            =	l_star

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






 def 	a   (			self							:			Optional[int]  , a_							:			ndarray			)->       int:



      """simple docstring"""

      UpperCAmelCase_    :     Any            =	sum(
          self.optimum[n]
          * self.classes[n]
          * self.kernel(self.observations[n]  , a_			)
          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       A_      (       lowercase    ,			lowercase   )  ->				int:


     """simple docstring"""







     return number | (1 << position)




def       A_      (       lowercase    ,			lowercase   )  ->				int:


     """simple docstring"""







     return number & ~(1 << position)




def       A_      (       lowercase    ,			lowercase   )  ->				int:


     """simple docstring"""







     return number ^ (1 << position)




def       A_      (       lowercase    ,			lowercase   )  ->				bool:


     """simple docstring"""







     return ((number >> position) & 1) == 1




def       A_      (       lowercase    ,			lowercase   )  ->				int:


     """simple docstring"""







     return int((number & (1 << position)) != 0   )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

