





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




def       __UpperCamelCase  (_SCREAMING_SNAKE_CASE		)    ->       float:
  return np.dot(_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		)
class     SCREAMING_SNAKE_CASE       :


   def __init__(   self      :    Optional[Any]      ,					*,
       a      :    float = np.inf      ,					a      :    str = "linear"      ,					a      :    float = 0.0      ,					)->       None:





     """simple docstring"""







     lowercase__           =  regularization
     lowercase__           =  gamma
     if kernel == "linear":
       lowercase__           =  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__           =  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__           =  f"""Unknown kernel: {kernel}"""
       raise ValueError(a	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Dict      ,					a      :    ndarray      ,					a      :    ndarray	)->       float:





     """simple docstring"""







     return np.dot(a      ,					a	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    List[Any]      ,					a      :    ndarray      ,					a      :    ndarray	)->       float:





     """simple docstring"""







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


   def 	SCREAMING_SNAKE_CASE_							(   self      :    str      ,					a      :    list[ndarray]      ,					a      :    ndarray	)->       None:





     """simple docstring"""







     lowercase__           =  observations
     lowercase__           =  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__)      ,   )           =  np.shape(a	)

     def to_minimize(a      :    ndarray	) -> float:
       lowercase__           =  0
       ((lowercase__)      ,   )           =  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	)

     lowercase__           =  LinearConstraint(a      ,					0      ,					0	)
     lowercase__           =  Bounds(0      ,					self.regularization	)

     lowercase__           =  minimize(
         a      ,					np.ones(a	)      ,					bounds=a      ,					constraints=[ly_contraint]	).x
     lowercase__           =  l_star

     # calculating mean offset of separation plane to points
     lowercase__           =  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]	)
     lowercase__           =  s / n


   def 	SCREAMING_SNAKE_CASE_							(   self      :    List[str]      ,					a      :    ndarray	)->       int:





     """simple docstring"""







     lowercase__           =  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 collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

lowercase_          =		TypeVar("""KEY""")
lowercase_          =		TypeVar("""VAL""")
@dataclass(frozen=UpperCAmelCase      ,     slots=UpperCAmelCase				)
class     SCREAMING_SNAKE_CASE       (Generic[KEY, VAL]				):
   _UpperCamelCase   :		KEY
   _UpperCamelCase   :		VAL






class     SCREAMING_SNAKE_CASE       (_Item				):


   def __init__(   self      :    Optional[int]	)->       None:





     """simple docstring"""







     super().__init__(a      ,					a	)


   def __bool__(   self      :    str	)->       bool:





     """simple docstring"""







     return False






lowercase_          =		_DeletedItem()
class     SCREAMING_SNAKE_CASE       (MutableMapping[KEY, VAL]				):


   def __init__(   self      :    Tuple      ,					a      :    int = 8      ,					a      :    float = 0.75	)->       None:





     """simple docstring"""







     lowercase__           =  initial_block_size
     lowercase__           =  [None] * initial_block_size
     assert 0.0 < capacity_factor < 1.0
     lowercase__           =  capacity_factor
     lowercase__           =  0


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Any      ,					a      :    KEY	)->       int:





     """simple docstring"""







     return hash(a	) % len(self._buckets	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Optional[Any]      ,					a      :    int	)->       int:





     """simple docstring"""







     return (ind + 1) % len(self._buckets	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Any      ,					a      :    int      ,					a      :    KEY      ,					a      :    VAL	)->       bool:





     """simple docstring"""







     lowercase__           =  self._buckets[ind]
     if not stored:
       lowercase__           =  _Item(a      ,					a	)
       self._len += 1
       return True
     elif stored.key == key:
       lowercase__           =  _Item(a      ,					a	)
       return True
     else:
       return False


   def 	SCREAMING_SNAKE_CASE_							(   self      :    str	)->       bool:





     """simple docstring"""







     lowercase__           =  len(self._buckets	) * self._capacity_factor
     return len(self	) >= int(a	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Tuple	)->       bool:





     """simple docstring"""







     if len(self._buckets	) <= self._initial_block_size:
       return False
     lowercase__           =  len(self._buckets	) * self._capacity_factor / 2
     return len(self	) < limit


   def 	SCREAMING_SNAKE_CASE_							(   self      :    List[str]      ,					a      :    int	)->       None:





     """simple docstring"""







     lowercase__           =  self._buckets
     lowercase__           =  [None] * new_size
     lowercase__           =  0
     for item in old_buckets:
       if item:
         self._add_item(item.key      ,					item.val	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Optional[int]	)->       None:





     """simple docstring"""







     self._resize(len(self._buckets	) * 2	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Optional[int]	)->       None:





     """simple docstring"""







     self._resize(len(self._buckets	) // 2	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Any      ,					a      :    KEY	)->       Iterator[int]:





     """simple docstring"""







     lowercase__           =  self._get_bucket_index(a	)
     for _ in range(len(self._buckets	)	):
       yield ind
       lowercase__           =  self._get_next_ind(a	)


   def 	SCREAMING_SNAKE_CASE_							(   self      :    Tuple      ,					a      :    KEY      ,					a      :    VAL	)->       None:





     """simple docstring"""







     for ind in self._iterate_buckets(a	):
       if self._try_set(a      ,					a      ,					a	):
         break


   def __setitem__(   self      :    List[Any]      ,					a      :    KEY      ,					a      :    VAL	)->       None:





     """simple docstring"""







     if self._is_full():
       self._size_up()

     self._add_item(a      ,					a	)


   def __delitem__(   self      :    str      ,					a      :    KEY	)->       None:





     """simple docstring"""







     for ind in self._iterate_buckets(a	):
       lowercase__           =  self._buckets[ind]
       if item is None:
         raise KeyError(a	)
       if item is _deleted:
         continue
       if item.key == key:
         lowercase__           =  _deleted
         self._len -= 1
         break
     if self._is_sparse():
       self._size_down()


   def __getitem__(   self      :    List[str]      ,					a      :    KEY	)->       VAL:





     """simple docstring"""







     for ind in self._iterate_buckets(a	):
       lowercase__           =  self._buckets[ind]
       if item is None:
         break
       if item is _deleted:
         continue
       if item.key == key:
         return item.val
     raise KeyError(a	)


   def __len__(   self      :    Tuple	)->       int:





     """simple docstring"""







     return self._len


   def __iter__(   self      :    int	)->       Iterator[KEY]:





     """simple docstring"""







     yield from (item.key for item in self._buckets if item)


   def __repr__(   self      :    Union[str, Any]	)->       str:





     """simple docstring"""







     lowercase__           =  ' ,'.join(
         f"""{item.key}: {item.val}""" for item in self._buckets if item	)
     return f"""HashMap({val_string})"""


