

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


def 					__a				(      SCREAMING_SNAKE_CASE					)					->   Union[str, Any]:






    '''simple docstring'''
    return np.dot(snake_case_				,      snake_case_					)
class     A_      :


    '''simple docstring'''






    def __init__(self   ,					*,
        lowercase__ = np.inf   ,					lowercase__ = "linear"   ,					lowercase__ = 0.0   ,					)   ->					None:
        __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(_a     )


    def    lowerCAmelCase_  (self   ,					lowercase__   ,					lowercase__     )   ->					float:
        return np.dot(_a   ,					_a     )


    def    lowerCAmelCase_  (self   ,					lowercase__   ,					lowercase__     )   ->					float:
        return np.exp(-(self.gamma * norm_squared(vectora - vectora     ))     )


    def    lowerCAmelCase_  (self   ,					lowercase__   ,					lowercase__     )   ->					None:
        __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(_a     )

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

        __UpperCAmelCase     =	LinearConstraint(_a   ,					0   ,					0     )
        __UpperCAmelCase     =	Bounds(0   ,					self.regularization     )

        __UpperCAmelCase     =	minimize(
            _a   ,					np.ones(_a     )   ,					bounds=_a   ,					constraints=[ly_contraint]     ).x
        __UpperCAmelCase     =	l_star

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






    def    lowerCAmelCase_  (self   ,					lowercase__     )   ->					int:
        __UpperCAmelCase     =	sum(
            self.optimum[n]
            * self.classes[n]
            * self.kernel(self.observations[n]   ,					_a     )
            for n in range(len(self.classes     )     )     )
        return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
       import doctest

       doctest.testmod()










# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin







class 						lowercase							(   UpperCamelCase__,UpperCamelCase__		):
     _a							 =						1

     @register_to_config
     def __init__(  self		,     _a=2000		,     _a=0.1		,     _a=20		,     _a=1e-3				)						->							List[Any]:
           _A							:     Dict			=						None
           _A							:     List[Any]			=						None
           _A							:     Dict			=						None

     def 					a__	(  self		,     _a		,     _a = None				)						->							Union[str, Any]:
           _A							:     Union[str, Any]			=						torch.linspace(1		,     self.config.sampling_eps		,     _a		,     device=_a				)

     def 					a__	(  self		,     _a		,     _a		,     _a		,     _a=None				)						->							Dict:
           if self.timesteps is None:
                 raise ValueError(
                     """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""				)

           # TODO(Patrick) better comments + non-PyTorch
           # postprocess model score
           _A							:     Any			=						(
               -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
           )
           _A							:     List[Any]			=						torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff				)				)
           _A							:     List[str]			=						std.flatten()
           while len(std.shape				) < len(score.shape				):
                 _A							:     List[Any]			=						std.unsqueeze(-1				)
           _A							:     int			=						-score / std

           # compute
           _A							:     Tuple			=						-1.0 / len(self.timesteps				)

           _A							:     str			=						self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
           _A							:     List[str]			=						beta_t.flatten()
           while len(beta_t.shape				) < len(x.shape				):
                 _A							:     Union[str, Any]			=						beta_t.unsqueeze(-1				)
           _A							:     Tuple			=						-0.5 * beta_t * x

           _A							:     Tuple			=						torch.sqrt(_a				)
           _A							:     Dict			=						drift - diffusion**2 * score
           _A							:     Dict			=						x + drift * dt

           # add noise
           _A							:     Any			=						randn_tensor(x.shape		,     layout=x.layout		,     generator=_a		,     device=x.device		,     dtype=x.dtype				)
           _A							:     str			=						x_mean + diffusion * math.sqrt(-dt				) * noise

           return x, x_mean



     def __len__(  self				)						->							Optional[Any]:
           return self.config.num_train_timesteps

