






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

def      __lowercase					( snake_case ):







				"""simple docstring"""






				return np.dot(snake_case,  snake_case )
class 						lowerCamelCase_				:







				def __init__(						self       ,					*,
				    __lowerCAmelCase = np.inf       ,					__lowerCAmelCase = "linear"       ,					__lowerCAmelCase = 0.0       ,					):
								"""simple docstring"""
								__magic_name__		:str        =      regularization
								__magic_name__		:List[Any]        =      gamma
								if kernel == "linear":
												__magic_name__		: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'''     )
												__magic_name__		:List[str]        =      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:
												__magic_name__		:List[str]        =      F'''Unknown kernel: {kernel}'''
												raise ValueError(__lowerCAmelCase     )







				def 			A	(						self       ,					__lowerCAmelCase       ,					__lowerCAmelCase     ):
								"""simple docstring"""
								return np.dot(__lowerCAmelCase       ,					__lowerCAmelCase     )







				def 			A	(						self       ,					__lowerCAmelCase       ,					__lowerCAmelCase     ):
								"""simple docstring"""
								return np.exp(-(self.gamma * norm_squared(vectora - vectora     ))     )







				def 			A	(						self       ,					__lowerCAmelCase       ,					__lowerCAmelCase     ):
								"""simple docstring"""
								__magic_name__		:Optional[int]        =      observations
								__magic_name__		:str        =      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

								((__magic_name__)     ,				)		:Dict        =      np.shape(__lowerCAmelCase     )

								def to_minimize(__lowerCAmelCase     ) -> float:
												__magic_name__		:Tuple        =      0
												((__magic_name__)     ,				)		:int        =      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     )

								__magic_name__		:Optional[Any]        =      LinearConstraint(__lowerCAmelCase       ,					0       ,					0     )
								__magic_name__		:Union[str, Any]        =      Bounds(0       ,					self.regularization     )

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

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







				def 			A	(						self       ,					__lowerCAmelCase     ):
								"""simple docstring"""
								__magic_name__		:Dict        =      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()














SCREAMING_SNAKE_CASE__      :			str							=		"""Alexander Joslin"""

import operator as op

from .stack import Stack

def      __lowercase					( snake_case ):







				"""simple docstring"""






				__magic_name__		:Optional[int]        =      {'''*''': op.mul, '''/''': op.truediv, '''+''': op.add, '''-''': op.sub}

				__magic_name__		:Stack[int]        =      Stack()
				__magic_name__		:Stack[str]        =      Stack()

				for i in equation:
								if i.isdigit():
												# RULE 1
												operand_stack.push(int(snake_case ) )
								elif i in operators:
												# RULE 2
												operator_stack.push(snake_case )
								elif i == ")":
												# RULE 4
												__magic_name__		:Optional[int]        =      operator_stack.peek()
												operator_stack.pop()
												__magic_name__		:List[str]        =      operand_stack.peek()
												operand_stack.pop()
												__magic_name__		:Optional[Any]        =      operand_stack.peek()
												operand_stack.pop()

												__magic_name__		:Optional[int]        =      operators[opr](snake_case,  snake_case )
												operand_stack.push(snake_case )

    # RULE 5
				return operand_stack.peek()


if __name__ == "__main__":
					SCREAMING_SNAKE_CASE__      :			Any							=		"""(5 + ((4 * 2) * (2 + 3)))"""
					# answer = 45
					print(f"{equation} = {dijkstras_two_stack_algorithm(equation)}")






