
"""simple docstring"""




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



def 							_lowerCamelCase			(			__a     ):
		return np.dot(__a,				__a     )





class 			snake_case  :

							def __init__(self							,							*,
							    SCREAMING_SNAKE_CASE_ = np.inf							,							SCREAMING_SNAKE_CASE_ = "linear"							,							SCREAMING_SNAKE_CASE_ = 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(SCREAMING_SNAKE_CASE_     )

							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									return np.dot(SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     )

							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







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

							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     ):

									"""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(SCREAMING_SNAKE_CASE_     )

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

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

									SCREAMING_SNAKE_CASE_    			=			minimize(
									    SCREAMING_SNAKE_CASE_							,							np.ones(SCREAMING_SNAKE_CASE_     )							,							bounds=SCREAMING_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(SCREAMING_SNAKE_CASE_     ):
											for j in range(SCREAMING_SNAKE_CASE_     ):
													s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
													    observations[i]							,							observations[j]     )
									SCREAMING_SNAKE_CASE_    			=			s / n







							def _lowercase       (self							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			sum(
									    self.optimum[n]
									    * self.classes[n]
									    * self.kernel(self.observations[n]							,							SCREAMING_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()

"""simple docstring"""




import doctest
from collections import deque

import numpy as np





class 			snake_case  :

							def __init__(self     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			[2, 1, 2, -1]
									SCREAMING_SNAKE_CASE_    			=			[1, 2, 3, 4]







							def _lowercase       (self     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			len(self.first_signal     )
									SCREAMING_SNAKE_CASE_    			=			len(self.second_signal     )

									SCREAMING_SNAKE_CASE_    			=			max(SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     )

									# create a zero matrix of max_length x max_length
									SCREAMING_SNAKE_CASE_    			=			[[0] * max_length for i in range(SCREAMING_SNAKE_CASE_     )]

									# fills the smaller signal with zeros to make both signals of same length
									if length_first_signal < length_second_signal:
											self.first_signal += [0] * (max_length - length_first_signal)
									elif length_first_signal > length_second_signal:
											self.second_signal += [0] * (max_length - length_second_signal)
									for i in range(SCREAMING_SNAKE_CASE_     ):
											SCREAMING_SNAKE_CASE_    			=			deque(self.second_signal     )
											rotated_signal.rotate(SCREAMING_SNAKE_CASE_     )
											for j, item in enumerate(SCREAMING_SNAKE_CASE_     ):
													matrix[i][j] += item

        # multiply the matrix with the first signal
									SCREAMING_SNAKE_CASE_    			=			np.matmul(np.transpose(SCREAMING_SNAKE_CASE_     )							,							np.transpose(self.first_signal     )     )

									# rounding-off to two decimal places
									return [round(SCREAMING_SNAKE_CASE_							,							2     ) for i in final_signal]


if __name__ == "__main__":
						doctest.testmod()