code: 
  
  
  import math
  from dataclasses import dataclass
  from typing import List, Optional, Tuple, Union
  
  import numpy as np
  import torch
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import BaseOutput, logging, randn_tensor
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
  
  
  UpperCAmelCase      :						List[Any]    =		logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  
  
  
  
  
  
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
  class 					__lowercase					(       a_     ):
  
  
  
  		"""simple docstring"""
  
  		UpperCamelCase    :				torch.FloatTensor
  		UpperCamelCase    :				Optional[torch.FloatTensor] 					=		None
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	str     ,       lowerCamelCase__		:	Dict=0.9_9_9     ,       lowerCamelCase__		:	Optional[int]="cosine"     ,       ):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			if alpha_transform_type == "cosine":
  
  						def alpha_bar_fn(lowerCamelCase__		:	Tuple			):
  									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(lowerCamelCase__		:	Tuple			):
  									return math.exp(t * -1_2.0			)
  
  			else:
  						raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'			)
  
  			lowerCamelCase								=     []
  			for i in range(lowerCamelCase__			):
  						lowerCamelCase								=     i / num_diffusion_timesteps
  						lowerCamelCase								=     (i + 1) / num_diffusion_timesteps
  						betas.append(min(1 - alpha_bar_fn(lowerCamelCase__			) / alpha_bar_fn(lowerCamelCase__			)     ,       lowerCamelCase__			)			)
  			return torch.tensor(lowerCamelCase__     ,       dtype=torch.floataa			)
  
  
  
  
  
  
  
  class 					__lowercase					(       a_ ,       a_     ):
  
  
  
  		"""simple docstring"""
  
  		UpperCamelCase    :				Tuple 					=		[e.name for e in KarrasDiffusionSchedulers]
  		UpperCamelCase    :				str 					=		1
  
  
  
  
  
  
  
  		@register_to_config
  		def __init__(   self		,			A = 10_00		,			A = 0.0001		,			A = 0.02		,			A = "linear"		,			A = None		,			A = "epsilon"		,			A = "linspace"		,			A = 0		,			)     ->   Union[str, Any]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if trained_betas is not None:
  								lowerCamelCase								=     torch.tensor(A		,			dtype=torch.floataa  )
  					elif beta_schedule == "linear":
  								lowerCamelCase								=     torch.linspace(A		,			A		,			A		,			dtype=torch.floataa  )
  					elif beta_schedule == "scaled_linear":
  								# this schedule is very specific to the latent diffusion model.
  								lowerCamelCase								=     (
  								    torch.linspace(beta_start**0.5		,			beta_end**0.5		,			A		,			dtype=torch.floataa  ) ** 2
  								)
  					elif beta_schedule == "squaredcos_cap_v2":
  								# Glide cosine schedule
  								lowerCamelCase								=     betas_for_alpha_bar(A  )
  					else:
  								raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'  )
  
  					lowerCamelCase								=     1.0 - self.betas
  					lowerCamelCase								=     torch.cumprod(self.alphas		,			dim=0  )
  
  					lowerCamelCase								=     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
  					lowerCamelCase								=     np.concatenate([sigmas[::-1], [0.0]]  ).astype(np.floataa  )
  					lowerCamelCase								=     torch.from_numpy(A  )
  
  					# setable values
  					lowerCamelCase								=     None
  					lowerCamelCase								=     np.linspace(0		,			num_train_timesteps - 1		,			A		,			dtype=A  )[::-1].copy()
  					lowerCamelCase								=     torch.from_numpy(A  )
  					lowerCamelCase								=     False
  
  
  
  
  
  
  
  		@property
  		def 				__A      (   self  )     ->   int:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if self.config.timestep_spacing in ["linspace", "trailing"]:
  								return self.sigmas.max()
  
  					return (self.sigmas.max() ** 2 + 1) ** 0.5
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A  )     ->   torch.FloatTensor:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if isinstance(A		,			torch.Tensor  ):
  								lowerCamelCase								=     timestep.to(self.timesteps.device  )
  					lowerCamelCase								=     (self.timesteps == timestep).nonzero().item()
  					lowerCamelCase								=     self.sigmas[step_index]
  					lowerCamelCase								=     sample / ((sigma**2 + 1) ** 0.5)
  					lowerCamelCase								=     True
  					return sample
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A = None  )     ->   Tuple:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     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":
  								lowerCamelCase								=     np.linspace(0		,			self.config.num_train_timesteps - 1		,			A		,			dtype=A  )[
  								    ::-1
  								].copy()
  					elif self.config.timestep_spacing == "leading":
  								lowerCamelCase								=     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
  								lowerCamelCase								=     (np.arange(0		,			A  ) * step_ratio).round()[::-1].copy().astype(A  )
  								timesteps += self.config.steps_offset
  					elif self.config.timestep_spacing == "trailing":
  								lowerCamelCase								=     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
  								lowerCamelCase								=     (np.arange(self.config.num_train_timesteps		,			0		,			-step_ratio  )).round().copy().astype(A  )
  								timesteps -= 1
  					else:
  								raise ValueError(
  								    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'  )
  
  					lowerCamelCase								=     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
  					lowerCamelCase								=     np.interp(A		,			np.arange(0		,			len(A  )  )		,			A  )
  					lowerCamelCase								=     np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )
  					lowerCamelCase								=     torch.from_numpy(A  ).to(device=A  )
  					if str(A  ).startswith("""mps"""  ):
  								# mps does not support float64
  								lowerCamelCase								=     torch.from_numpy(A  ).to(A		,			dtype=torch.floataa  )
  					else:
  								lowerCamelCase								=     torch.from_numpy(A  ).to(device=A  )
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A		,			A		,			A = None		,			A = True		,			)     ->   Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if (
  					    isinstance(A		,			A  )
  					    or isinstance(A		,			torch.IntTensor  )
  					    or isinstance(A		,			torch.LongTensor  )
  					):
  								raise ValueError(
  								    (
  								        """Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"""
  								        """ `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"""
  								        """ one of the `scheduler.timesteps` as a timestep."""
  								    )		,			)
  
  					if not self.is_scale_input_called:
  								logger.warning(
  								    """The `scale_model_input` function should be called before `step` to ensure correct denoising. """
  								    """See `StableDiffusionPipeline` for a usage example."""  )
  
  					if isinstance(A		,			torch.Tensor  ):
  								lowerCamelCase								=     timestep.to(self.timesteps.device  )
  
  					lowerCamelCase								=     (self.timesteps == timestep).nonzero().item()
  					lowerCamelCase								=     self.sigmas[step_index]
  
  					# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
  					if self.config.prediction_type == "epsilon":
  								lowerCamelCase								=     sample - sigma * model_output
  					elif self.config.prediction_type == "v_prediction":
  								# * c_out + input * c_skip
  								lowerCamelCase								=     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
  					elif self.config.prediction_type == "sample":
  								raise NotImplementedError("""prediction_type not implemented yet: sample"""  )
  					else:
  								raise ValueError(
  								    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'  )
  
  					lowerCamelCase								=     self.sigmas[step_index]
  					lowerCamelCase								=     self.sigmas[step_index + 1]
  					lowerCamelCase								=     (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
  					lowerCamelCase								=     (sigma_to**2 - sigma_up**2) ** 0.5
  
  					# 2. Convert to an ODE derivative
  					lowerCamelCase								=     (sample - pred_original_sample) / sigma
  
  					lowerCamelCase								=     sigma_down - sigma
  
  					lowerCamelCase								=     sample + derivative * dt
  
  					lowerCamelCase								=     model_output.device
  					lowerCamelCase								=     randn_tensor(model_output.shape		,			dtype=model_output.dtype		,			device=A		,			generator=A  )
  
  					lowerCamelCase								=     prev_sample + noise * sigma_up
  
  					if not return_dict:
  								return (prev_sample,)
  
  					return EulerAncestralDiscreteSchedulerOutput(
  					    prev_sample=A		,			pred_original_sample=A  )
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A		,			A		,			)     ->   torch.FloatTensor:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     self.sigmas.to(device=original_samples.device		,			dtype=original_samples.dtype  )
  					if original_samples.device.type == "mps" and torch.is_floating_point(A  ):
  								# mps does not support float64
  								lowerCamelCase								=     self.timesteps.to(original_samples.device		,			dtype=torch.floataa  )
  								lowerCamelCase								=     timesteps.to(original_samples.device		,			dtype=torch.floataa  )
  					else:
  								lowerCamelCase								=     self.timesteps.to(original_samples.device  )
  								lowerCamelCase								=     timesteps.to(original_samples.device  )
  
  					lowerCamelCase								=     [(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
  					lowerCamelCase								=     sigmas[step_indices].flatten()
  					while len(sigma.shape  ) < len(original_samples.shape  ):
  								lowerCamelCase								=     sigma.unsqueeze(-1  )
  
  					lowerCamelCase								=     original_samples + noise * sigma
  					return noisy_samples
  
  
  
  
  
  
  
  		def __len__(   self  )     ->   Union[str, Any]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					return self.config.num_train_timesteps
  
  
style_context: 
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	int = 100     ,       lowerCamelCase__		:	int = 100			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			return max(
  			    sum(int(lowerCamelCase__			) for x in str(base**power			)			)
  			    for base in range(lowerCamelCase__			)
  			    for power in range(lowerCamelCase__			)			)
  
  
  # Tests
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  
  