




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







def 				lowerCAmelCase_	(     snake_case_     ):
      return np.dot(snake_case_,snake_case_     )







class 						lowercase							:

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

     def 					a__	(  self		,     _a		,     _a				)						->							float:
           return np.dot(_a		,     _a				)

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

     def 					a__	(  self		,     _a		,     _a				)						->							None:
           _A							:     List[Any]			=						observations
           _A							:     Optional[int]			=						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

           ((_A)			,   )							:     Union[str, Any]			=						np.shape(_a				)

           def to_minimize(_a				) -> float:
                 _A							:     str			=						0
                 ((_A)			,   )							:     Optional[int]			=						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				)

           _A							:     Optional[int]			=						LinearConstraint(_a		,     0		,     0				)
           _A							:     List[str]			=						Bounds(0		,     self.regularization				)

           _A							:     Dict			=						minimize(
               _a		,     np.ones(_a				)		,     bounds=_a		,     constraints=[ly_contraint]				).x
           _A							:     Union[str, Any]			=						l_star

           # calculating mean offset of separation plane to points
           _A							:     Optional[int]			=						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]				)
           _A							:     str			=						s / n



     def 					a__	(  self		,     _a				)						->							int:
           _A							:     Union[str, 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()







from math import asin, atan, cos, radians, sin, sqrt, tan

_snake_case										=       6_3_7_8_1_3_7.0
_snake_case										=       6_3_5_6_7_5_2.3_1_4_2_4_5
_snake_case										=       6378137







def 				lowerCAmelCase_	(     snake_case_,snake_case_,snake_case_,snake_case_     ):
      _A							:     Any			=						(AXIS_A - AXIS_B) / AXIS_A
      _A							:     Optional[int]			=						atan((1 - flattening) * tan(radians(snake_case_     )     )     )
      _A							:     List[str]			=						atan((1 - flattening) * tan(radians(snake_case_     )     )     )
      _A							:     Optional[Any]			=						radians(snake_case_     )
      _A							:     str			=						radians(snake_case_     )
      # Equation
      _A							:     Dict			=						sin((phi_a - phi_a) / 2     )
      _A							:     List[str]			=						sin((lambda_a - lambda_a) / 2     )
      # Square both values
      sin_sq_phi *= sin_sq_phi
      sin_sq_lambda *= sin_sq_lambda
      _A							:     Optional[int]			=						sqrt(sin_sq_phi + (cos(snake_case_     ) * cos(snake_case_     ) * sin_sq_lambda)     )
      return 2 * RADIUS * asin(snake_case_     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

