


'''simple docstring'''





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


def        a__     (					UpperCamelCase_						:      Optional[int]						):
   return np.dot(_A,   _A						)




class 				UpperCAmelCase			:


 def __init__(      self							:	Union[str, Any]			,       *,
     __lowerCamelCase							:	float = np.inf			,       __lowerCamelCase							:	str = "linear"			,       __lowerCamelCase							:	float = 0.0			,       ):
    UpperCAmelCase__	:Dict      =      regularization
    UpperCAmelCase__	:Optional[int]      =      gamma
    if kernel == "linear":
       UpperCAmelCase__	:List[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''' )
       UpperCAmelCase__	:Union[str, 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(__lowerCamelCase )


 def        __SCREAMING_SNAKE_CASE					(      self							:	Dict			,       __lowerCamelCase							:	ndarray			,       __lowerCamelCase							:	ndarray ):
    return np.dot(__lowerCamelCase			,       __lowerCamelCase )


 def        __SCREAMING_SNAKE_CASE					(      self							:	List[Any]			,       __lowerCamelCase							:	ndarray			,       __lowerCamelCase							:	ndarray ):
    return np.exp(-(self.gamma * norm_squared(vectora - vectora )) )


 def        __SCREAMING_SNAKE_CASE					(      self							:	int			,       __lowerCamelCase							:	list[ndarray]			,       __lowerCamelCase							:	ndarray ):
    UpperCAmelCase__	:Optional[Any]      =      observations
    UpperCAmelCase__	:str      =      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(__lowerCamelCase )

    def to_minimize(__lowerCamelCase							:	ndarray ) -> float:
       UpperCAmelCase__	:Optional[int]      =      0
       (UpperCAmelCase__      )	:Union[str, Any]      =      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 )

    UpperCAmelCase__	:List[Any]      =      LinearConstraint(__lowerCamelCase			,       0			,       0 )
    UpperCAmelCase__	:Optional[int]      =      Bounds(0			,       self.regularization )

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

    # calculating mean offset of separation plane to points
    UpperCAmelCase__	:Optional[Any]      =      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] )
    UpperCAmelCase__	:List[str]      =      s / n





 def        __SCREAMING_SNAKE_CASE					(      self							:	Any			,       __lowerCamelCase							:	ndarray ):
    UpperCAmelCase__	:List[str]      =      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"""







def      UpperCamelCase       ( _A  ,				_A )     ->       None:
				lowercase    :      List[Any]       = len(_A )
				print("""The following activities are selected:""" )

				# The first activity is always selected
				lowercase    :      Optional[int]       = 0
				print(_A  ,				end=""",""" )

				# Consider rest of the activities
				for j in range(_A ):
								# If this activity has start time greater than
								# or equal to the finish time of previously
								# selected activity, then select it
								if start[j] >= finish[i]:
												print(_A  ,				end=""",""" )
												lowercase    :      str       = j


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				_lowerCAmelCase            =	[1, 3, 0, 5, 8, 5]
				_lowerCAmelCase            =	[2, 4, 6, 7, 9, 9]
				print_max_activities(start, finish)
