






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


def 							A						(				__snake_case: ndarray  )    ->		float:

       """simple docstring"""





       return np.dot(lowerCAmelCase_ ,     lowerCAmelCase_  )



class        UpperCamelCase__ :







    """simple docstring"""







    def __init__(		self :	Tuple				,    *,
        UpperCamelCase_ :	float = np.inf				,    UpperCamelCase_ :	str = "linear"				,    UpperCamelCase_ :	float = 0.0				,    ):





           '''simple docstring'''

           __magic_name__      				=    regularization
           __magic_name__      				=    gamma
           if kernel == "linear":
                  __magic_name__      				=    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__      				=    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__      				=    f"""Unknown kernel: {kernel}"""
                  raise ValueError(_lowerCAmelCase )







    def 				a__			(		self :	Optional[Any]				,    UpperCamelCase_ :	ndarray				,    UpperCamelCase_ :	ndarray ):





           '''simple docstring'''

           return np.dot(_lowerCAmelCase				,    _lowerCAmelCase )







    def 				a__			(		self :	Optional[Any]				,    UpperCamelCase_ :	ndarray				,    UpperCamelCase_ :	ndarray ):





           '''simple docstring'''

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







    def 				a__			(		self :	Tuple				,    UpperCamelCase_ :	list[ndarray]				,    UpperCamelCase_ :	ndarray ):





           '''simple docstring'''

           __magic_name__      				=    observations
           __magic_name__      				=    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__     )				,       )      				=    np.shape(_lowerCAmelCase )

           def to_minimize(UpperCamelCase_ :	ndarray ) -> float:
                  __magic_name__      				=    0
                  ((__magic_name__     )				,       )      				=    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__      				=    LinearConstraint(_lowerCAmelCase				,    0				,    0 )
           __magic_name__      				=    Bounds(0				,    self.regularization )

           __magic_name__      				=    minimize(
               _lowerCAmelCase				,    np.ones(_lowerCAmelCase )				,    bounds=_lowerCAmelCase				,    constraints=[ly_contraint] ).x
           __magic_name__      				=    l_star

           # calculating mean offset of separation plane to points
           __magic_name__      				=    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__      				=    s / n







    def 				a__			(		self :	str				,    UpperCamelCase_ :	ndarray ):





           '''simple docstring'''

           __magic_name__      				=    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       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->int:
   '''simple docstring'''






   return int((input_a, input_a).count(0				) == 0				)



def       _lowerCAmelCase    (				)->None:
   '''simple docstring'''






   assert and_gate(0		,    0				) == 0
   assert and_gate(0		,    1				) == 0
   assert and_gate(1		,    0				) == 0
   assert and_gate(1		,    1				) == 1


if __name__ == "__main__":
   test_and_gate()
   print(and_gate(1, 0))
   print(and_gate(0, 0))
   print(and_gate(0, 1))
   print(and_gate(1, 1))




