from __future__ import annotations

import math




def       lowerCAmelCase_     (		lowercase:							int		):







 '''simple docstring'''

 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5  ,					int(math.sqrt(lowercase		) + 1		)  ,					6		):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True




def       lowerCAmelCase_     (		lowercase:							int		):







 '''simple docstring'''
 _UpperCamelCase:     Optional[Any]							= str(lowercase		)
 _UpperCamelCase:     Tuple							= [n]
 for i in range(1  ,					len(lowercase		)		):
  list_nums.append(int(str_num[i:]		)		)
  list_nums.append(int(str_num[:-i]		)		)
 return list_nums




def       lowerCAmelCase_     (		lowercase:							int		):







 '''simple docstring'''
 if len(str(lowercase		)		) > 3:
  if not is_prime(int(str(lowercase		)[-3:]		)		) or not is_prime(int(str(lowercase		)[:3]		)		):
   return False
 return True




def       lowerCAmelCase_     (		lowercase:							int = 11		):







 '''simple docstring'''
 _UpperCamelCase:     list[int]							= []
 _UpperCamelCase:     Union[str, Any]							= 13
 while len(lowercase		) != count:
  if validate(lowercase		):
   _UpperCamelCase:     Union[str, Any]							= list_truncated_nums(lowercase		)
   if all(is_prime(lowercase		) for i in list_nums		):
    list_truncated_primes.append(lowercase		)
  num += 2
 return list_truncated_primes




def       lowerCAmelCase_     (		):







 '''simple docstring'''
 return sum(compute_truncated_primes(11		)		)


if __name__ == "__main__":
  print(f"""{sum(compute_truncated_primes(1_1)) = }""")
import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize




def       lowerCAmelCase_     (		lowercase:							ndarray		)    ->				float:







 '''simple docstring'''
 return np.dot(lowercase  ,					lowercase		)




class  __magic_name__  :





   """simple docstring"""




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



    """simple docstring"""



    _UpperCamelCase:     int							= regularization
    _UpperCamelCase:     Optional[int]							= gamma
    if kernel == "linear":
     _UpperCamelCase:     Optional[Any]							= 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'''							)
     _UpperCamelCase:     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:
     _UpperCamelCase:     Optional[int]							= f"""Unknown kernel: {kernel}"""
     raise ValueError(_lowercase							)



   def   lowerCAmelCase						(	self					:  Union[str, Any]		,  _lowercase					:  ndarray		,  _lowercase					:  ndarray							):



    """simple docstring"""



    return np.dot(_lowercase		,  _lowercase							)



   def   lowerCAmelCase						(	self					:  str		,  _lowercase					:  ndarray		,  _lowercase					:  ndarray							):



    """simple docstring"""



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



   def   lowerCAmelCase						(	self					:  str		,  _lowercase					:  list[ndarray]		,  _lowercase					:  ndarray							):



    """simple docstring"""



    _UpperCamelCase:     List[str]							= observations
    _UpperCamelCase:     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

    ((_UpperCamelCase)	,							):     Any							= np.shape(_lowercase							)

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

    _UpperCamelCase:     Optional[Any]							= LinearConstraint(_lowercase		,  0		,  0							)
    _UpperCamelCase:     Optional[int]							= Bounds(0		,  self.regularization							)

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

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



   def   lowerCAmelCase						(	self					:  Optional[Any]		,  _lowercase					:  ndarray							):



    """simple docstring"""



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


if __name__ == "__main__":
  import doctest

  doctest.testmod()