code: 
  
  
  import math
  from collections import defaultdict
  from typing import List, Optional, Tuple, Union
  
  import numpy as np
  import torch
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import randn_tensor
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
  
  
  
  def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[Any]    ,		_UpperCamelCase      :				int=0.9_9_9    ,		_UpperCamelCase      :				Union[str, Any]="cosine"    ,		)		->					List[Any]:
  
  
  
  
  
     '''simple docstring'''
  
  
  
  
  
  
  
     if alpha_transform_type == "cosine":
  
        def alpha_bar_fn(_UpperCamelCase      :				Union[str, Any]   ):
           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(_UpperCamelCase      :				Optional[int]   ):
           return math.exp(t * -1_2.0   )
  
     else:
        raise ValueError(F'Unsupported alpha_tranform_type: {alpha_transform_type}'   )
  
     UpperCamelCase__ 						=						[]
     for i in range(UpperCamelCase__   ):
        UpperCamelCase__ 						=						i / num_diffusion_timesteps
        UpperCamelCase__ 						=						(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__):
   _lowerCamelCase :					Optional[Any]    					=					[e.name for e in KarrasDiffusionSchedulers]
   _lowerCamelCase :					Optional[int]    					=					2
  
   @register_to_config
   def __init__( self :	List[str],					a_ :	Optional[Any] = 1000,					a_ :	Optional[int] = 0.00_085,					a_ :	Optional[int] = 0.012,					a_ :	str = "linear",					a_ :	Tuple = None,					a_ :	Optional[int] = "epsilon",					a_ :	str = "linspace",					a_ :	int = 0,					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      if trained_betas is not None:
         UpperCamelCase__ 						=						torch.tensor(__lowerCamelCase,					dtype=torch.floataa					)
      elif beta_schedule == "linear":
         UpperCamelCase__ 						=						torch.linspace(__lowerCamelCase,					__lowerCamelCase,					__lowerCamelCase,					dtype=torch.floataa					)
      elif beta_schedule == "scaled_linear":
         # this schedule is very specific to the latent diffusion model.
         UpperCamelCase__ 						=						(
             torch.linspace(beta_start**0.5,					beta_end**0.5,					__lowerCamelCase,					dtype=torch.floataa					) ** 2
         )
      elif beta_schedule == "squaredcos_cap_v2":
         # Glide cosine schedule
         UpperCamelCase__ 						=						betas_for_alpha_bar(__lowerCamelCase					)
      else:
         raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'					)
  
      UpperCamelCase__ 						=						1.0 - self.betas
      UpperCamelCase__ 						=						torch.cumprod(self.alphas,					dim=0					)
  
      #  set all values
      self.set_timesteps(__lowerCamelCase,					__lowerCamelCase,					__lowerCamelCase					)
  
   def 		lowercase_						( self :	List[str],					a_ :	Dict,					a_ :	List[Any]=None					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      if schedule_timesteps is None:
         UpperCamelCase__ 						=						self.timesteps
  
      UpperCamelCase__ 						=						(schedule_timesteps == timestep).nonzero()
  
      # The sigma index that is taken for the **very** first `step`
      # is always the second index (or the last index if there is only 1)
      # This way we can ensure we don't accidentally skip a sigma in
      # case we start in the middle of the denoising schedule (e.g. for image-to-image)
      if len(self._index_counter					) == 0:
         UpperCamelCase__ 						=						1 if len(__lowerCamelCase					) > 1 else 0
      else:
         UpperCamelCase__ 						=						timestep.cpu().item() if torch.is_tensor(__lowerCamelCase					) else timestep
         UpperCamelCase__ 						=						self._index_counter[timestep_int]
  
      return indices[pos].item()
  
   @property
   def 		lowercase_						( self :	Optional[Any]					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      if self.config.timestep_spacing in ["linspace", "trailing"]:
         return self.sigmas.max()
  
      return (self.sigmas.max() ** 2 + 1) ** 0.5
  
   def 		lowercase_						( self :	Any,					a_ :	Union[str, Any],					a_ :	List[Any],					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						self.index_for_timestep(__lowerCamelCase					)
  
      if self.state_in_first_order:
         UpperCamelCase__ 						=						self.sigmas[step_index]
      else:
         UpperCamelCase__ 						=						self.sigmas_interpol[step_index - 1]
  
      UpperCamelCase__ 						=						sample / ((sigma**2 + 1) ** 0.5)
      return sample
  
   def 		lowercase_						( self :	Optional[int],					a_ :	Tuple,					a_ :	int = None,					a_ :	Tuple = None,					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						num_inference_steps
  
      UpperCamelCase__ 						=						num_train_timesteps or self.config.num_train_timesteps
  
      # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
      if self.config.timestep_spacing == "linspace":
         UpperCamelCase__ 						=						np.linspace(0,					num_train_timesteps - 1,					__lowerCamelCase,					dtype=__lowerCamelCase					)[::-1].copy()
      elif self.config.timestep_spacing == "leading":
         UpperCamelCase__ 						=						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
         UpperCamelCase__ 						=						(np.arange(0,					__lowerCamelCase					) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase					)
         timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
         UpperCamelCase__ 						=						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
         UpperCamelCase__ 						=						(np.arange(__lowerCamelCase,					0,					-step_ratio					)).round().copy().astype(__lowerCamelCase					)
         timesteps -= 1
      else:
         raise ValueError(
             f'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'					)
  
      UpperCamelCase__ 						=						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
      UpperCamelCase__ 						=						torch.from_numpy(np.log(__lowerCamelCase					)					).to(__lowerCamelCase					)
  
      UpperCamelCase__ 						=						np.interp(__lowerCamelCase,					np.arange(0,					len(__lowerCamelCase					)					),					__lowerCamelCase					)
      UpperCamelCase__ 						=						np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
      UpperCamelCase__ 						=						torch.from_numpy(__lowerCamelCase					).to(device=__lowerCamelCase					)
  
      # compute up and down sigmas
      UpperCamelCase__ 						=						sigmas.roll(-1					)
      UpperCamelCase__ 						=						0.0
      UpperCamelCase__ 						=						(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
      UpperCamelCase__ 						=						(sigmas_next**2 - sigmas_up**2) ** 0.5
      UpperCamelCase__ 						=						0.0
  
      # compute interpolated sigmas
      UpperCamelCase__ 						=						sigmas.log().lerp(sigmas_down.log(),					0.5					).exp()
      UpperCamelCase__ 						=						0.0
  
      # set sigmas
      UpperCamelCase__ 						=						torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
      UpperCamelCase__ 						=						torch.cat(
          [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)
      UpperCamelCase__ 						=						torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2					), sigmas_up[-1:]]					)
      UpperCamelCase__ 						=						torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2					), sigmas_down[-1:]]					)
  
      if str(__lowerCamelCase					).startswith("mps"					):
         # mps does not support float64
         UpperCamelCase__ 						=						torch.from_numpy(__lowerCamelCase					).to(__lowerCamelCase,					dtype=torch.floataa					)
      else:
         UpperCamelCase__ 						=						torch.from_numpy(__lowerCamelCase					).to(__lowerCamelCase					)
  
      UpperCamelCase__ 						=						self.sigma_to_t(__lowerCamelCase					).to(__lowerCamelCase,					dtype=timesteps.dtype					)
      UpperCamelCase__ 						=						torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None]),					dim=-1					).flatten()
  
      UpperCamelCase__ 						=						torch.cat([timesteps[:1], interleaved_timesteps]					)
  
      UpperCamelCase__ 						=						None
  
      # for exp beta schedules, such as the one for `pipeline_shap_e.py`
      # we need an index counter
      UpperCamelCase__ 						=						defaultdict(__lowerCamelCase					)
  
   def 		lowercase_						( self :	Optional[int],					a_ :	Dict					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						sigma.log()
  
      # get distribution
      UpperCamelCase__ 						=						log_sigma - self.log_sigmas[:, None]
  
      # get sigmas range
      UpperCamelCase__ 						=						dists.ge(0					).cumsum(dim=0					).argmax(dim=0					).clamp(max=self.log_sigmas.shape[0] - 2					)
      UpperCamelCase__ 						=						low_idx + 1
  
      UpperCamelCase__ 						=						self.log_sigmas[low_idx]
      UpperCamelCase__ 						=						self.log_sigmas[high_idx]
  
      # interpolate sigmas
      UpperCamelCase__ 						=						(low - log_sigma) / (low - high)
      UpperCamelCase__ 						=						w.clamp(0,					1					)
  
      # transform interpolation to time range
      UpperCamelCase__ 						=						(1 - w) * low_idx + w * high_idx
      UpperCamelCase__ 						=						t.view(sigma.shape					)
      return t
  
   @property
   def 		lowercase_						( self :	Union[str, Any]					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      return self.sample is None
  
   def 		lowercase_						( self :	Dict,					a_ :	int,					a_ :	str,					a_ :	int,					a_ :	Tuple = None,					a_ :	Any = True,					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						self.index_for_timestep(__lowerCamelCase					)
  
      # advance index counter by 1
      UpperCamelCase__ 						=						timestep.cpu().item() if torch.is_tensor(__lowerCamelCase					) else timestep
      self._index_counter[timestep_int] += 1
  
      if self.state_in_first_order:
         UpperCamelCase__ 						=						self.sigmas[step_index]
         UpperCamelCase__ 						=						self.sigmas_interpol[step_index]
         UpperCamelCase__ 						=						self.sigmas_up[step_index]
         UpperCamelCase__ 						=						self.sigmas_down[step_index - 1]
      else:
         # 2nd order / KPDM2's method
         UpperCamelCase__ 						=						self.sigmas[step_index - 1]
         UpperCamelCase__ 						=						self.sigmas_interpol[step_index - 1]
         UpperCamelCase__ 						=						self.sigmas_up[step_index - 1]
         UpperCamelCase__ 						=						self.sigmas_down[step_index - 1]
  
      # currently only gamma=0 is supported. This usually works best anyways.
      # We can support gamma in the future but then need to scale the timestep before
      # passing it to the model which requires a change in API
      UpperCamelCase__ 						=						0
      UpperCamelCase__ 						=						sigma * (gamma + 1)  # Note: sigma_hat == sigma for now
  
      UpperCamelCase__ 						=						model_output.device
      UpperCamelCase__ 						=						randn_tensor(model_output.shape,					dtype=model_output.dtype,					device=__lowerCamelCase,					generator=__lowerCamelCase					)
  
      # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
      if self.config.prediction_type == "epsilon":
         UpperCamelCase__ 						=						sigma_hat if self.state_in_first_order else sigma_interpol
         UpperCamelCase__ 						=						sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
         UpperCamelCase__ 						=						sigma_hat if self.state_in_first_order else sigma_interpol
         UpperCamelCase__ 						=						model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
             sample / (sigma_input**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`'					)
  
      if self.state_in_first_order:
         # 2. Convert to an ODE derivative for 1st order
         UpperCamelCase__ 						=						(sample - pred_original_sample) / sigma_hat
         # 3. delta timestep
         UpperCamelCase__ 						=						sigma_interpol - sigma_hat
  
         # store for 2nd order step
         UpperCamelCase__ 						=						sample
         UpperCamelCase__ 						=						dt
         UpperCamelCase__ 						=						sample + derivative * dt
      else:
         # DPM-Solver-2
         # 2. Convert to an ODE derivative for 2nd order
         UpperCamelCase__ 						=						(sample - pred_original_sample) / sigma_interpol
         # 3. delta timestep
         UpperCamelCase__ 						=						sigma_down - sigma_hat
  
         UpperCamelCase__ 						=						self.sample
         UpperCamelCase__ 						=						None
  
         UpperCamelCase__ 						=						sample + derivative * dt
         UpperCamelCase__ 						=						prev_sample + noise * sigma_up
  
      if not return_dict:
         return (prev_sample,)
  
      return SchedulerOutput(prev_sample=__lowerCamelCase					)
  
   def 		lowercase_						( self :	Any,					a_ :	int,					a_ :	Optional[Any],					a_ :	Optional[Any],					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						self.sigmas.to(device=original_samples.device,					dtype=original_samples.dtype					)
      if original_samples.device.type == "mps" and torch.is_floating_point(__lowerCamelCase					):
         # mps does not support float64
         UpperCamelCase__ 						=						self.timesteps.to(original_samples.device,					dtype=torch.floataa					)
         UpperCamelCase__ 						=						timesteps.to(original_samples.device,					dtype=torch.floataa					)
      else:
         UpperCamelCase__ 						=						self.timesteps.to(original_samples.device					)
         UpperCamelCase__ 						=						timesteps.to(original_samples.device					)
  
      UpperCamelCase__ 						=						[self.index_for_timestep(__lowerCamelCase,					__lowerCamelCase					) for t in timesteps]
  
      UpperCamelCase__ 						=						sigmas[step_indices].flatten()
      while len(sigma.shape					) < len(original_samples.shape					):
         UpperCamelCase__ 						=						sigma.unsqueeze(-1					)
  
      UpperCamelCase__ 						=						original_samples + noise * sigma
      return noisy_samples
  
   def __len__( self :	int					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      return self.config.num_train_timesteps
style_context: 
  
  
  '''simple docstring'''
  
  def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				int = 10_00   )		->					int:
  
  
  
  
  
     '''simple docstring'''
  
  
  
  
  
  
  
     return sum(i for i in range(_UpperCamelCase   ) if i % 3 == 0 or i % 5 == 0   )
  
  
  if __name__ == "__main__":
         print(F"""{solution() = }""")