


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



def 				UpperCamelCase_(      lowerCamelCase_ )    ->						float:
    return np.dot(lowerCamelCase_							, lowerCamelCase_ )






class _lowerCamelCase:
       def __init__(					self,      *,
           lowerCamelCase = np.inf,      lowerCamelCase = "linear",      lowerCamelCase = 0.0,      )       ->   None:




           """simple docstring"""

           _lowercase       :							str      		=		regularization
           _lowercase       :							List[str]      		=		gamma
           if kernel == "linear":
               _lowercase       :							int      		=		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')
               _lowercase       :							Tuple      		=		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:
               _lowercase       :							Dict      		=		F'''Unknown kernel: {kernel}'''
               raise ValueError(lowerCamelCase)
       def 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase)       ->   float:




           """simple docstring"""

           return np.dot(lowerCamelCase,      lowerCamelCase)
       def 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase)       ->   float:




           """simple docstring"""

           return np.exp(-(self.gamma * norm_squared(vectora - vectora)))
       def 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase)       ->   None:




           """simple docstring"""

           _lowercase       :							int      		=		observations
           _lowercase       :							Optional[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

           ((_lowercase)		,				)       :							Tuple      		=		np.shape(lowerCamelCase)

           def to_minimize(lowerCamelCase) -> float:
               _lowercase       :							str      		=		0
               ((_lowercase)		,				)       :							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)

           _lowercase       :							Tuple      		=		LinearConstraint(lowerCamelCase,      0,      0)
           _lowercase       :							Dict      		=		Bounds(0,      self.regularization)

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

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




       def 			UpperCamelCase     (					self,      lowerCamelCase)       ->   int:




           """simple docstring"""

           _lowercase       :							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 				UpperCamelCase_(      lowerCamelCase_ )    ->						int:
    if not numbers:
        return 0

    if not isinstance(lowerCamelCase_							, (list, tuple) ) or not all(
        isinstance(lowerCamelCase_							, lowerCamelCase_ ) for number in numbers ):
        raise ValueError('numbers must be an iterable of integers' )

    _lowercase       :							int      		=		numbers[0]

    for i in range(1							, len(lowerCamelCase_ ) ):
        # update the maximum and minimum subarray products
        _lowercase       :							Union[str, Any]      		=		numbers[i]
        if number < 0:
            _lowercase		,				_lowercase       :							Any      		=		min_till_now, max_till_now
        _lowercase       :							Union[str, Any]      		=		max(lowerCamelCase_							, max_till_now * number )
        _lowercase       :							Union[str, Any]      		=		min(lowerCamelCase_							, min_till_now * number )

        # update the maximum product found till now
        _lowercase       :							Optional[Any]      		=		max(lowerCamelCase_							, lowerCamelCase_ )

    return max_prod


