



"""simple docstring"""







def       _lowerCamelCase				(							UpperCAmelCase_ :       str,	UpperCAmelCase_ :       Optional[int]     )	-> str:






	"""simple docstring"""





	if a < 0 or b < 0:
		raise ValueError("the value of both inputs must be positive"     )

	A__											=					str(bin(UpperCAmelCase_     )     )[2:]  # remove the leading "0b"
	A__											=					str(bin(UpperCAmelCase_     )     )[2:]  # remove the leading "0b"

	A__											=					max(len(UpperCAmelCase_     ),	len(UpperCAmelCase_     )     )

	return "0b" + "".join(
	    str(int(char_a != char_b     )     )
	    for char_a, char_b in zip(a_binary.zfill(UpperCAmelCase_     ),	b_binary.zfill(UpperCAmelCase_     )     )     )


if __name__ == "__main__":
			import doctest

			doctest.testmod()










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


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



class    lowercase_		:



						def __init__(			self	:   int					,							*,
						    snake_case__	:   float = np.inf					,							snake_case__	:   str = "linear"					,							snake_case__	:   float = 0.0					,							):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							regularization
								SCREAMING_SNAKE_CASE_					      =							gamma
								if kernel == "linear":
										SCREAMING_SNAKE_CASE_					      =							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'  )
										SCREAMING_SNAKE_CASE_					      =							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:
										SCREAMING_SNAKE_CASE_					      =							f'''Unknown kernel: {kernel}'''
										raise ValueError(snake_case__  )



						def 	__a					(			self	:   Tuple					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								return np.dot(snake_case__					,							snake_case__  )



						def 	__a					(			self	:   int					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								return np.exp(-(self.gamma * norm_squared(vectora - vectora  ))  )



						def 	__a					(			self	:   int					,							snake_case__	:   list[ndarray]					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							observations
								SCREAMING_SNAKE_CASE_					      =							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

								((SCREAMING_SNAKE_CASE_)      ,				)					      =							np.shape(snake_case__  )

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

								SCREAMING_SNAKE_CASE_					      =							LinearConstraint(snake_case__					,							0					,							0  )
								SCREAMING_SNAKE_CASE_					      =							Bounds(0					,							self.regularization  )

								SCREAMING_SNAKE_CASE_					      =							minimize(
								    snake_case__					,							np.ones(snake_case__  )					,							bounds=snake_case__					,							constraints=[ly_contraint]  ).x
								SCREAMING_SNAKE_CASE_					      =							l_star

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






						def 	__a					(			self	:   Any					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sum(
								    self.optimum[n]
								    * self.classes[n]
								    * self.kernel(self.observations[n]					,							snake_case__  )
								    for n in range(len(self.classes  )  )  )
								return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()