

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





def  __lowerCamelCase     (			UpperCamelCase__				):







							'''simple docstring'''






							return np.dot(UpperCamelCase__       ,							UpperCamelCase__				)







class 			lowercase    :




				def __init__( self				,       *,
				    snake_case = np.inf				,       snake_case = "linear"				,       snake_case = 0.0				,       ):
											snake_case_          =   regularization
											snake_case_          =   gamma
											if kernel == "linear":
																		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'	)
																		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:
																		snake_case_          =   F'''Unknown kernel: {kernel}'''
																		raise ValueError(snake_case	)




				def    a							( self				,       snake_case				,       snake_case	):
											return np.dot(snake_case				,       snake_case	)




				def    a							( self				,       snake_case				,       snake_case	):
											return np.exp(-(self.gamma * norm_squared(vectora - vectora	))	)




				def    a							( self				,       snake_case				,       snake_case	):
											snake_case_          =   observations
											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

											((snake_case_)    ,   )          =   np.shape(snake_case	)

											def to_minimize(snake_case	) -> float:
																		snake_case_          =   0
																		((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	)

											snake_case_          =   LinearConstraint(snake_case				,       0				,       0	)
											snake_case_          =   Bounds(0				,       self.regularization	)

											snake_case_          =   minimize(
											    snake_case				,       np.ones(snake_case	)				,       bounds=snake_case				,       constraints=[ly_contraint]	).x
											snake_case_          =   l_star

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




				def    a							( self				,       snake_case	):
											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()







def  __lowerCamelCase     (			UpperCamelCase__       ,							UpperCamelCase__				):







							'''simple docstring'''






							return int((input_a, input_a).count(0				) != 0				)





def  __lowerCamelCase     (			):







							'''simple docstring'''






							assert nand_gate(0       ,							0				) == 1
							assert nand_gate(0       ,							1				) == 1
							assert nand_gate(1       ,							0				) == 1
							assert nand_gate(1       ,							1				) == 0


if __name__ == "__main__":
					print(nand_gate(0, 0))
					print(nand_gate(0, 1))
					print(nand_gate(1, 0))
					print(nand_gate(1, 1))




