



"""simple docstring"""







# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class       UpperCamelCase__			(   SCREAMING_SNAKE_CASE__      ):

			"""simple docstring"""


			A__	:					Dict							  =     4_2
			A__	:					Dict							  =     None



def       _lowerCamelCase				(							UpperCAmelCase_ :       Any,	UpperCAmelCase_ :       List[str]=0.999,	UpperCAmelCase_ :       Tuple="cosine",	)	-> Tuple:






	"""simple docstring"""





	if alpha_transform_type == "cosine":

		def alpha_bar_fn(UpperCAmelCase_ :       int     ):
			return math.cos((t + 0.008) / 1.008 * math.pi / 2     ) ** 2

	elif alpha_transform_type == "exp":

		def alpha_bar_fn(UpperCAmelCase_ :       Optional[int]     ):
			return math.exp(t * -12.0     )

	else:
		raise ValueError(F"""Unsupported alpha_tranform_type: {alpha_transform_type}"""     )

	A__											=					[]
	for i in range(UpperCAmelCase_     ):
		A__											=					i / num_diffusion_timesteps
		A__											=					(i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(UpperCAmelCase_     ) / alpha_bar_fn(UpperCAmelCase_     ),	UpperCAmelCase_     )     )
	return torch.tensor(UpperCAmelCase_,	dtype=torch.floataa     )






class       UpperCamelCase__			(   SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__      ):

			"""simple docstring"""


			A__	:					Any							  =     1


			@register_to_config
			def __init__(      self						,	SCREAMING_SNAKE_CASE__ = 1000						,	SCREAMING_SNAKE_CASE__ = 0.0_0_0_1						,	SCREAMING_SNAKE_CASE__ = 0.0_2						,	SCREAMING_SNAKE_CASE__ = "linear"						,	SCREAMING_SNAKE_CASE__ = None						,	SCREAMING_SNAKE_CASE__ = True						,	SCREAMING_SNAKE_CASE__ = True						,	SCREAMING_SNAKE_CASE__ = 0						,	SCREAMING_SNAKE_CASE__ = "epsilon"						,	SCREAMING_SNAKE_CASE__ = 1.0						,	**SCREAMING_SNAKE_CASE__						,	)      ->	Optional[int]:

				if kwargs.get("set_alpha_to_one"						,	snake_case__		) is not None:
					A__											=					(
					    "The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."
					)
					deprecate("set_alpha_to_one"						,	"1.0.0"						,	snake_case__						,	standard_warn=snake_case__		)
					A__											=					kwargs["set_alpha_to_one"]
				if trained_betas is not None:
					A__											=					torch.tensor(snake_case__						,	dtype=torch.floataa		)
				elif beta_schedule == "linear":
					A__											=					torch.linspace(snake_case__						,	snake_case__						,	snake_case__						,	dtype=torch.floataa		)
				elif beta_schedule == "scaled_linear":
					# this schedule is very specific to the latent diffusion model.
					A__											=					(
					    torch.linspace(beta_start**0.5						,	beta_end**0.5						,	snake_case__						,	dtype=torch.floataa		) ** 2
					)
				elif beta_schedule == "squaredcos_cap_v2":
					# Glide cosine schedule
					A__											=					betas_for_alpha_bar(snake_case__		)
				else:
					raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""		)

				A__											=					1.0 - self.betas
				A__											=					torch.cumprod(self.alphas						,	dim=0		)

				# At every step in inverted ddim, we are looking into the next alphas_cumprod
				# For the final step, there is no next alphas_cumprod, and the index is out of bounds
				# `set_alpha_to_zero` decides whether we set this parameter simply to zero
				# in this case, self.step() just output the predicted noise
				# or whether we use the final alpha of the "non-previous" one.
				A__											=					torch.tensor(0.0		) if set_alpha_to_zero else self.alphas_cumprod[-1]

				# standard deviation of the initial noise distribution
				A__											=					1.0

				# setable values
				A__											=					None
				A__											=					torch.from_numpy(np.arange(0						,	snake_case__		).copy().astype(np.intaa		)		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__ = None		)      ->	Optional[int]:
				return sample


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__ = None		)      ->	Union[str, Any]:

				if num_inference_steps > self.config.num_train_timesteps:
					raise ValueError(
					    f"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
					    f""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
					    f""" maximal {self.config.num_train_timesteps} timesteps."""		)

				A__											=					num_inference_steps
				A__											=					self.config.num_train_timesteps // self.num_inference_steps
				# creates integer timesteps by multiplying by ratio
				# casting to int to avoid issues when num_inference_step is power of 3
				A__											=					(np.arange(0						,	snake_case__		) * step_ratio).round().copy().astype(np.intaa		)
				A__											=					torch.from_numpy(snake_case__		).to(snake_case__		)
				self.timesteps += self.config.steps_offset


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__ = 0.0						,	SCREAMING_SNAKE_CASE__ = False						,	SCREAMING_SNAKE_CASE__ = None						,	SCREAMING_SNAKE_CASE__ = True						,	)      ->	Dict:
				A__											=					timestep + self.config.num_train_timesteps // self.num_inference_steps

				# 2. compute alphas, betas
				# change original implementation to exactly match noise levels for analogous forward process
				A__											=					self.alphas_cumprod[timestep]
				A__											=					(
				    self.alphas_cumprod[prev_timestep]
				    if prev_timestep < self.config.num_train_timesteps
				    else self.final_alpha_cumprod
				)

				A__											=					1 - alpha_prod_t

				# 3. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				if self.config.prediction_type == "epsilon":
					A__											=					(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
					A__											=					model_output
				elif self.config.prediction_type == "sample":
					A__											=					model_output
					A__											=					(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
				elif self.config.prediction_type == "v_prediction":
					A__											=					(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
					A__											=					(alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
				else:
					raise ValueError(
					    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
					    " `v_prediction`"		)

				# 4. Clip or threshold "predicted x_0"
				if self.config.clip_sample:
					A__											=					pred_original_sample.clamp(
					    -self.config.clip_sample_range						,	self.config.clip_sample_range		)

				# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				A__											=					(1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

				# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				A__											=					alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

				if not return_dict:
					return (prev_sample, pred_original_sample)
				return DDIMSchedulerOutput(prev_sample=snake_case__						,	pred_original_sample=snake_case__		)







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










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


def 					_a							(					lowerCAmelCase )->	float:
		return np.dot(lowerCAmelCase    ,						lowerCAmelCase )



class    lowercase_		:



						def __init__(			self	:   int					,							*,
						    snake_case__	:   float = np.inf					,							snake_case__	:   str = "linear"					,							snake_case__	:   float = 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(snake_case__  )



						def 	__a					(			self	:   Tuple					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								return np.dot(snake_case__					,							snake_case__  )



						def 	__a					(			self	:   int					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

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



						def 	__a					(			self	:   int					,							snake_case__	:   list[ndarray]					,							snake_case__	:   ndarray  ):

								"""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(snake_case__  )

								def to_minimize(snake_case__	:   ndarray  ) -> float:
										SCREAMING_SNAKE_CASE_					      =							0
										((SCREAMING_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__  )

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

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






						def 	__a					(			self	:   Any					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_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()