




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

def      A      (      _SCREAMING_SNAKE_CASE    )	-> float:
       return np.dot(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )




class 		UpperCamelCase__	:

    '''simple docstring'''



    def __init__(    self     ,  *,
        UpperCamelCase__ = np.inf     ,  UpperCamelCase__ = "linear"     ,  UpperCamelCase__ = 0.0     ,  )     ->      None:
           lowerCamelCase   :      Tuple			 =					regularization
           lowerCamelCase   :      List[str]			 =					gamma
           if kernel == "linear":
                  lowerCamelCase   :      Optional[Any]			 =					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"     )
                  lowerCamelCase   :      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:
                  lowerCamelCase   :      Optional[int]			 =					F'''Unknown kernel: {kernel}'''
                  raise ValueError(UpperCamelCase__     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      float:
           return np.dot(UpperCamelCase__     ,  UpperCamelCase__     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      float:
           return np.exp(-(self.gamma * norm_squared(vectora - vectora     ))     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      None:
           lowerCamelCase   :      Dict			 =					observations
           lowerCamelCase   :      List[Any]			 =					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

           ((lowerCamelCase) ,      )   :      List[Any]			 =					np.shape(UpperCamelCase__     )

           def to_minimize(UpperCamelCase__     ) -> float:
                  lowerCamelCase   :      int			 =					0
                  ((lowerCamelCase) ,      )   :      Tuple			 =					np.shape(UpperCamelCase__     )
                  for i in range(UpperCamelCase__     ):
                         for j in range(UpperCamelCase__     ):
                                s += (
                                    candidate[i]
                                    * candidate[j]
                                    * classes[i]
                                    * classes[j]
                                    * self.kernel(observations[i]     ,  observations[j]     )
                                )
                  return 1 / 2 * s - sum(UpperCamelCase__     )

           lowerCamelCase   :      Dict			 =					LinearConstraint(UpperCamelCase__     ,  0     ,  0     )
           lowerCamelCase   :      Union[str, Any]			 =					Bounds(0     ,  self.regularization     )

           lowerCamelCase   :      Any			 =					minimize(
               UpperCamelCase__     ,  np.ones(UpperCamelCase__     )     ,  bounds=UpperCamelCase__     ,  constraints=[ly_contraint]     ).x
           lowerCamelCase   :      Any			 =					l_star

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







    def     _lowercase     (    self     ,  UpperCamelCase__     )     ->      int:
           lowerCamelCase   :      List[str]			 =					sum(
               self.optimum[n]
               * self.classes[n]
               * self.kernel(self.observations[n]     ,  UpperCamelCase__     )
               for n in range(len(self.classes     )     )     )
           return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
       import doctest

       doctest.testmod()












def      A      (      _SCREAMING_SNAKE_CASE    )	-> list:
       if n_term == "":
              return []
       lowerCamelCase   :      list			 =					[]
       for temp in range(int(_SCREAMING_SNAKE_CASE    )    ):
              series.append(f'''1/{temp + 1}''' if series else "1"    )
       return series


if __name__ == "__main__":
       SCREAMING_SNAKE_CASE__       :      Dict  =   input('Enter the last number (nth term) of the Harmonic Series')
       print('Formula of Harmonic Series => 1+1/2+1/3 ..... 1/n')
       print(harmonic_series(nth_term))






