code: 
  
  
  import math
  import warnings
  from dataclasses import dataclass
  from typing import List, Optional, Tuple, Union
  
  import numpy as np
  import torch
  from scipy import integrate
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import BaseOutput
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
  
  
  
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
  class 			a      (      UpperCamelCase_   ):
  		__lowercase													=		42
  		__lowercase													=		None
  
  
  
  
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_=0.9_9_9,	snake_case_="cosine",	)			->							Tuple:
  				if alpha_transform_type == "cosine":
  
  								def alpha_bar_fn(snake_case_	):
  												return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2	) ** 2
  
  				elif alpha_transform_type == "exp":
  
  								def alpha_bar_fn(snake_case_	):
  												return math.exp(t * -1_2.0	)
  
  				else:
  								raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'	)
  
  				A__     :							List[str]   				=[]
  				for i in range(snake_case_	):
  								A__     :							List[Any]   				=i / num_diffusion_timesteps
  								A__     :							str   				=(i + 1) / num_diffusion_timesteps
  								betas.append(min(1 - alpha_bar_fn(snake_case_	) / alpha_bar_fn(snake_case_	),	snake_case_	)	)
  				return torch.tensor(snake_case_,	dtype=torch.floataa	)
  
  
  
  
  class 			a      (      UpperCamelCase_      ,UpperCamelCase_   ):
  		__lowercase													=		[e.name for e in KarrasDiffusionSchedulers]
  		__lowercase													=		1
  
  
  
  
  
  
  		@register_to_config
  		def __init__(  self	,     __UpperCamelCase = 10_00	,     __UpperCamelCase = 0.0001	,     __UpperCamelCase = 0.02	,     __UpperCamelCase = "linear"	,     __UpperCamelCase = None	,     __UpperCamelCase = False	,     __UpperCamelCase = "epsilon"	,     __UpperCamelCase = "linspace"	,     __UpperCamelCase = 0	,     )->			str:
  						'''simple docstring'''
  
  
  						if trained_betas is not None:
  										A__     :							List[Any]   				=torch.tensor(__UpperCamelCase	,     dtype=torch.floataa							)
  						elif beta_schedule == "linear":
  										A__     :							Tuple   				=torch.linspace(__UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	,     dtype=torch.floataa							)
  						elif beta_schedule == "scaled_linear":
  										# this schedule is very specific to the latent diffusion model.
  										A__     :							Any   				=(
  										    torch.linspace(beta_start**0.5	,     beta_end**0.5	,     __UpperCamelCase	,     dtype=torch.floataa							) ** 2
  										)
  						elif beta_schedule == "squaredcos_cap_v2":
  										# Glide cosine schedule
  										A__     :							Any   				=betas_for_alpha_bar(__UpperCamelCase							)
  						else:
  										raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'							)
  
  						A__     :							Any   				=1.0 - self.betas
  						A__     :							Union[str, Any]   				=torch.cumprod(self.alphas	,     dim=0							)
  
  						A__     :							List[Any]   				=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
  						A__     :							Optional[Any]   				=np.concatenate([sigmas[::-1], [0.0]]							).astype(np.floataa							)
  						A__     :							Union[str, Any]   				=torch.from_numpy(__UpperCamelCase							)
  
  						# setable values
  						A__     :							Union[str, Any]   				=None
  						A__     :							str   				=use_karras_sigmas
  						self.set_timesteps(__UpperCamelCase	,     __UpperCamelCase							)
  						A__     :							Dict   				=[]
  						A__     :							Optional[Any]   				=False
  
  
  
  
  
  
  		@property
  		def       lowerCAmelCase_  (  self							)->			Union[str, Any]:
  						'''simple docstring'''
  
  
  						if self.config.timestep_spacing in ["linspace", "trailing"]:
  										return self.sigmas.max()
  
  						return (self.sigmas.max() ** 2 + 1) ** 0.5
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase							)->			torch.FloatTensor:
  						'''simple docstring'''
  
  
  						if isinstance(__UpperCamelCase	,     torch.Tensor							):
  										A__     :							Union[str, Any]   				=timestep.to(self.timesteps.device							)
  						A__     :							str   				=(self.timesteps == timestep).nonzero().item()
  						A__     :							List[str]   				=self.sigmas[step_index]
  						A__     :							Dict   				=sample / ((sigma**2 + 1) ** 0.5)
  						A__     :							List[str]   				=True
  						return sample
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase							)->			Optional[Any]:
  						'''simple docstring'''
  
  
  						def lms_derivative(__UpperCamelCase							):
  										A__     :							int   				=1.0
  										for k in range(__UpperCamelCase							):
  														if current_order == k:
  																		continue
  														prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
  										return prod
  
  						A__     :							List[Any]   				=integrate.quad(__UpperCamelCase	,     self.sigmas[t]	,     self.sigmas[t + 1]	,     epsrel=1E-4							)[0]
  
  						return integrated_coeff
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase = None							)->			Dict:
  						'''simple docstring'''
  
  
  						A__     :							Any   				=num_inference_steps
  
  						# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
  						if self.config.timestep_spacing == "linspace":
  										A__     :							Any   				=np.linspace(0	,     self.config.num_train_timesteps - 1	,     __UpperCamelCase	,     dtype=__UpperCamelCase							)[
  										    ::-1
  										].copy()
  						elif self.config.timestep_spacing == "leading":
  										A__     :							Tuple   				=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__     :							Any   				=(np.arange(0	,     __UpperCamelCase							) * step_ratio).round()[::-1].copy().astype(__UpperCamelCase							)
  										timesteps += self.config.steps_offset
  						elif self.config.timestep_spacing == "trailing":
  										A__     :							Any   				=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__     :							Dict   				=(np.arange(self.config.num_train_timesteps	,     0	,     -step_ratio							)).round().copy().astype(__UpperCamelCase							)
  										timesteps -= 1
  						else:
  										raise ValueError(
  										    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'							)
  
  						A__     :							List[Any]   				=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
  						A__     :							str   				=np.log(__UpperCamelCase							)
  						A__     :							Any   				=np.interp(__UpperCamelCase	,     np.arange(0	,     len(__UpperCamelCase							)							)	,     __UpperCamelCase							)
  
  						if self.use_karras_sigmas:
  										A__     :							List[Any]   				=self._convert_to_karras(in_sigmas=__UpperCamelCase							)
  										A__     :							List[Any]   				=np.array([self._sigma_to_t(__UpperCamelCase	,     __UpperCamelCase							) for sigma in sigmas]							)
  
  						A__     :							Tuple   				=np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
  
  						A__     :							str   				=torch.from_numpy(__UpperCamelCase							).to(device=__UpperCamelCase							)
  						if str(__UpperCamelCase							).startswith('''mps'''							):
  										# mps does not support float64
  										A__     :							Dict   				=torch.from_numpy(__UpperCamelCase							).to(__UpperCamelCase	,     dtype=torch.floataa							)
  						else:
  										A__     :							Union[str, Any]   				=torch.from_numpy(__UpperCamelCase							).to(device=__UpperCamelCase							)
  
  						A__     :							Tuple   				=[]
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase							)->			Optional[int]:
  						'''simple docstring'''
  
  
  						A__     :							Dict   				=np.log(__UpperCamelCase							)
  
  						# get distribution
  						A__     :							Any   				=log_sigma - log_sigmas[:, np.newaxis]
  
  						# get sigmas range
  						A__     :							Any   				=np.cumsum((dists >= 0)	,     axis=0							).argmax(axis=0							).clip(max=log_sigmas.shape[0] - 2							)
  						A__     :							Tuple   				=low_idx + 1
  
  						A__     :							Dict   				=log_sigmas[low_idx]
  						A__     :							List[str]   				=log_sigmas[high_idx]
  
  						# interpolate sigmas
  						A__     :							Union[str, Any]   				=(low - log_sigma) / (low - high)
  						A__     :							List[str]   				=np.clip(__UpperCamelCase	,     0	,     1							)
  
  						# transform interpolation to time range
  						A__     :							str   				=(1 - w) * low_idx + w * high_idx
  						A__     :							Tuple   				=t.reshape(sigma.shape							)
  						return t
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase							)->			torch.FloatTensor:
  						'''simple docstring'''
  
  
  						A__     :							float   				=in_sigmas[-1].item()
  						A__     :							float   				=in_sigmas[0].item()
  
  						A__     :							List[str]   				=7.0  # 7.0 is the value used in the paper
  						A__     :							Union[str, Any]   				=np.linspace(0	,     1	,     self.num_inference_steps							)
  						A__     :							str   				=sigma_min ** (1 / rho)
  						A__     :							Dict   				=sigma_max ** (1 / rho)
  						A__     :							List[Any]   				=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
  						return sigmas
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase = 4	,     __UpperCamelCase = True	,     )->			Union[LMSDiscreteSchedulerOutput, Tuple]:
  						'''simple docstring'''
  
  
  						if not self.is_scale_input_called:
  										warnings.warn(
  										    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
  										    '''See `StableDiffusionPipeline` for a usage example.'''							)
  
  						if isinstance(__UpperCamelCase	,     torch.Tensor							):
  										A__     :							Any   				=timestep.to(self.timesteps.device							)
  						A__     :							Optional[Any]   				=(self.timesteps == timestep).nonzero().item()
  						A__     :							Optional[Any]   				=self.sigmas[step_index]
  
  						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
  						if self.config.prediction_type == "epsilon":
  										A__     :							Optional[Any]   				=sample - sigma * model_output
  						elif self.config.prediction_type == "v_prediction":
  										# * c_out + input * c_skip
  										A__     :							List[Any]   				=model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
  						elif self.config.prediction_type == "sample":
  										A__     :							List[str]   				=model_output
  						else:
  										raise ValueError(
  										    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'							)
  
  						# 2. Convert to an ODE derivative
  						A__     :							Union[str, Any]   				=(sample - pred_original_sample) / sigma
  						self.derivatives.append(__UpperCamelCase							)
  						if len(self.derivatives							) > order:
  										self.derivatives.pop(0							)
  
  						# 3. Compute linear multistep coefficients
  						A__     :							List[str]   				=min(step_index + 1	,     __UpperCamelCase							)
  						A__     :							List[str]   				=[self.get_lms_coefficient(__UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase							) for curr_order in range(__UpperCamelCase							)]
  
  						# 4. Compute previous sample based on the derivatives path
  						A__     :							Optional[int]   				=sample + sum(
  						    coeff * derivative for coeff, derivative in zip(__UpperCamelCase	,     reversed(self.derivatives							)							)							)
  
  						if not return_dict:
  										return (prev_sample,)
  
  						return LMSDiscreteSchedulerOutput(prev_sample=__UpperCamelCase	,     pred_original_sample=__UpperCamelCase							)
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self	,     __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	,     )->			torch.FloatTensor:
  						'''simple docstring'''
  
  
  						A__     :							Optional[int]   				=self.sigmas.to(device=original_samples.device	,     dtype=original_samples.dtype							)
  						if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCamelCase							):
  										# mps does not support float64
  										A__     :							Any   				=self.timesteps.to(original_samples.device	,     dtype=torch.floataa							)
  										A__     :							Optional[Any]   				=timesteps.to(original_samples.device	,     dtype=torch.floataa							)
  						else:
  										A__     :							List[str]   				=self.timesteps.to(original_samples.device							)
  										A__     :							Optional[int]   				=timesteps.to(original_samples.device							)
  
  						A__     :							Union[str, Any]   				=[(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
  						A__     :							Any   				=sigmas[step_indices].flatten()
  						while len(sigma.shape							) < len(original_samples.shape							):
  										A__     :							List[Any]   				=sigma.unsqueeze(-1							)
  
  						A__     :							Any   				=original_samples + noise * sigma
  						return noisy_samples
  
  
  
  
  
  
  		def __len__(  self							)->			str:
  						'''simple docstring'''
  
  
  						return self.config.num_train_timesteps
  
  
  
  
style_context: 
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							Dict:
  				A__     :							Dict   				=len(snake_case_	)
  				for i in range(length - 1	):
  								A__     :							List[Any]   				=False
  								for j in range(length - 1 - i	):
  												if collection[j] > collection[j + 1]:
  																A__     :							Dict   				=True
  																A__				,  A__     :							Union[str, Any]   				=collection[j + 1], collection[j]
  								if not swapped:
  												break  # Stop iteration if the collection is sorted.
  				return collection
  
  
  if __name__ == "__main__":
  						import doctest
  						import time
  
  						doctest.testmod()
  
  						__lowerCamelCase       :       Union[str, Any]				   =			input("Enter numbers separated by a comma:").strip()
  						__lowerCamelCase       :       Optional[int]				   =			[int(item) for item in user_input.split(",")]
  						__lowerCamelCase       :       Optional[int]				   =			time.process_time()
  						print(*bubble_sort(unsorted), sep=",")
  						print(F"Processing time: {(time.process_time() - start)%1E9 + 7}")
  
  
  
  