






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


def 				snake_case__							(							UpperCAmelCase							:  ndarray       ):
    return np.dot(UpperCAmelCase    ,			UpperCAmelCase       )







class 	_UpperCAmelCase  :




      """simple docstring"""



      def __init__(   self    ,	*,
          _lowerCAmelCase = np.inf    ,	_lowerCAmelCase = "linear"    ,	_lowerCAmelCase = 0.0    ,	):



          '''simple docstring'''
          lowerCAmelCase__   :int      							=				regularization
          lowerCAmelCase__   :Dict      							=				gamma
          if kernel == "linear":
              lowerCAmelCase__   :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"		)
              lowerCAmelCase__   :Optional[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__   :str      							=				f'''Unknown kernel: {kernel}'''
              raise ValueError(_lowerCAmelCase		)
      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          return np.dot(_lowerCAmelCase    ,	_lowerCAmelCase		)
      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          return np.exp(-(self.gamma * norm_squared(vectora - vectora		))		)
      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :List[str]      							=				observations
          lowerCAmelCase__   :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__)							,)   :Tuple      							=				np.shape(_lowerCAmelCase		)

          def to_minimize(_lowerCAmelCase		) -> float:
              lowerCAmelCase__   :int      							=				0
              ((lowerCAmelCase__)							,)   :Tuple      							=				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		)

          lowerCAmelCase__   :List[Any]      							=				LinearConstraint(_lowerCAmelCase    ,	0    ,	0		)
          lowerCAmelCase__   :Dict      							=				Bounds(0    ,	self.regularization		)

          lowerCAmelCase__   :List[str]      							=				minimize(
              _lowerCAmelCase    ,	np.ones(_lowerCAmelCase		)    ,	bounds=_lowerCAmelCase    ,	constraints=[ly_contraint]		).x
          lowerCAmelCase__   :List[str]      							=				l_star

          # calculating mean offset of separation plane to points
          lowerCAmelCase__   :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]		)
          lowerCAmelCase__   :int      							=				s / n



      def 			snake_case_      (   self    ,	_lowerCAmelCase		):



          '''simple docstring'''
          lowerCAmelCase__   :List[Any]      							=				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 				snake_case__							(							UpperCAmelCase							:  float       ):

    if edge <= 0 or not isinstance(UpperCAmelCase    ,			UpperCAmelCase       ):
        raise ValueError("Length must be a positive."       )
    return 3 * ((2_5 + 1_0 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)


def 				snake_case__							(							UpperCAmelCase							:  float       ):

    if edge <= 0 or not isinstance(UpperCAmelCase    ,			UpperCAmelCase       ):
        raise ValueError("Length must be a positive."       )
    return ((1_5 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
 import doctest

 doctest.testmod()



