"""simple docstring"""






from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			):
				UpperCAmelCase__      ,	UpperCAmelCase__             =							coefficient_matrix.shape
				UpperCAmelCase__      ,	UpperCAmelCase__             =							constant_matrix.shape

				if rowsa != colsa:
								UpperCAmelCase__             =							f'''Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'''
								raise ValueError(lowerCamelCase       )

				if colsa != 1:
								UpperCAmelCase__             =							f'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
								raise ValueError(lowerCamelCase       )

				if rowsa != rowsa:
								UpperCAmelCase__             =							(
								    'Coefficient and constant matrices dimensions must be nxn and nx1 but '
								    f'''received {rowsa}x{colsa} and {rowsa}x{colsa}'''
								)
								raise ValueError(lowerCamelCase       )

				if len(lowerCamelCase       ) != rowsa:
								UpperCAmelCase__             =							(
								    'Number of initial values must be equal to number of rows in coefficient '
								    f'''matrix but received {len(lowerCamelCase       )} and {rowsa}'''
								)
								raise ValueError(lowerCamelCase       )

				if iterations <= 0:
								raise ValueError('Iterations must be at least 1'       )

				UpperCAmelCase__             =							np.concatenate(
				    (coefficient_matrix, constant_matrix)					,			axis=1       )

				UpperCAmelCase__      ,	UpperCAmelCase__             =							table.shape

				strictly_diagonally_dominant(lowerCamelCase       )

				# Iterates the whole matrix for given number of times
				for _ in range(lowerCamelCase       ):
								UpperCAmelCase__             =							[]
								for row in range(lowerCamelCase       ):
												UpperCAmelCase__             =							0
												for col in range(lowerCamelCase       ):
																if col == row:
																				UpperCAmelCase__             =							table[row][col]
																elif col == cols - 1:
																				UpperCAmelCase__             =							table[row][col]
																else:
																				temp += (-1) * table[row][col] * init_val[col]
												UpperCAmelCase__             =							(temp + val) / denom
												new_val.append(lowerCamelCase       )
								UpperCAmelCase__             =							new_val

				return [float(lowerCamelCase       ) for i in new_val]



def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__      ,	UpperCAmelCase__             =							table.shape

				UpperCAmelCase__             =							True

				for i in range(0					,			lowerCamelCase       ):
								UpperCAmelCase__             =							0
								for j in range(0					,			cols - 1       ):
												if i == j:
																continue
												else:
																total += table[i][j]

								if table[i][i] <= total:
												raise ValueError('Coefficient matrix is not strictly diagonally dominant'       )

				return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
						import doctest

						doctest.testmod()




"""simple docstring"""






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



def   a_						(					lowerCamelCase       ):
				return np.dot(lowerCamelCase					,			lowerCamelCase       )
class 				snake_case       :




					"""simple docstring"""

					def __init__(				self   :	int    ,*,
					    lowerCamelCase__   :	float = np.inf    ,lowerCamelCase__   :	str = "linear"    ,lowerCamelCase__   :	float = 0.0    ,):
									UpperCAmelCase__             =							regularization
									UpperCAmelCase__             =							gamma
									if kernel == "linear":
													UpperCAmelCase__             =							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__             =							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__             =							f'''Unknown kernel: {kernel}'''
													raise ValueError(lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	List[Any]    ,lowerCamelCase__   :	ndarray    ,lowerCamelCase__   :	ndarray			):
									return np.dot(lowerCamelCase__    ,lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Any    ,lowerCamelCase__   :	ndarray    ,lowerCamelCase__   :	ndarray			):
									return np.exp(-(self.gamma * norm_squared(vectora - vectora			))			)







					def 		__lowerCAmelCase						(				self   :	Tuple    ,lowerCamelCase__   :	list[ndarray]    ,lowerCamelCase__   :	ndarray			):
									UpperCAmelCase__             =							observations
									UpperCAmelCase__             =							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__)      ,	)             =							np.shape(lowerCamelCase__			)

									def to_minimize(lowerCamelCase__   :	ndarray			) -> float:
													UpperCAmelCase__             =							0
													((UpperCAmelCase__)      ,	)             =							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__			)

									UpperCAmelCase__             =							LinearConstraint(lowerCamelCase__    ,0    ,0			)
									UpperCAmelCase__             =							Bounds(0    ,self.regularization			)

									UpperCAmelCase__             =							minimize(
									    lowerCamelCase__    ,np.ones(lowerCamelCase__			)    ,bounds=lowerCamelCase__    ,constraints=[ly_contraint]			).x
									UpperCAmelCase__             =							l_star

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







					def 		__lowerCAmelCase						(				self   :	int    ,lowerCamelCase__   :	ndarray			):
									UpperCAmelCase__             =							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()



