code: 
  '''simple docstring'''
  
  from typing import List, Optional, Tuple, Union
  
  import torch
  
  from ...utils import randn_tensor
  from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
  
  
  class   a_  (_a    ):
  
  
  
  
         def __init__(     self   ,   snake_case_   ,   snake_case_  ):
           super().__init__()
           self.register_modules(unet=snake_case_   ,   scheduler=snake_case_  )
  
  
  
  
  
  
  
         @torch.no_grad()
         def __call__(     self   ,   snake_case_ = 1   ,   snake_case_ = None   ,   snake_case_ = 1_0_0_0   ,   snake_case_ = "pil"   ,   snake_case_ = True   ,   ):
           # Sample gaussian noise to begin loop
           if isinstance(self.unet.config.sample_size   ,   snake_case_  ):
             _lowerCAmelCase       :  Tuple   				=					(
                 batch_size,
                 self.unet.config.in_channels,
                 self.unet.config.sample_size,
                 self.unet.config.sample_size,
             )
           else:
             _lowerCAmelCase       :  Union[str, Any]   				=					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)
  
           if self.device.type == "mps":
             # randn does not work reproducibly on mps
             _lowerCAmelCase       :  Dict   				=					randn_tensor(snake_case_   ,   generator=snake_case_  )
             _lowerCAmelCase       :  List[Any]   				=					image.to(self.device  )
           else:
             _lowerCAmelCase       :  Tuple   				=					randn_tensor(snake_case_   ,   generator=snake_case_   ,   device=self.device  )
  
           # set step values
           self.scheduler.set_timesteps(snake_case_  )
  
           for t in self.progress_bar(self.scheduler.timesteps  ):
             # 1. predict noise model_output
             _lowerCAmelCase       :  List[Any]   				=					self.unet(snake_case_   ,   snake_case_  ).sample
  
             # 2. compute previous image: x_t -> x_t-1
             _lowerCAmelCase       :  Tuple   				=					self.scheduler.step(snake_case_   ,   snake_case_   ,   snake_case_   ,   generator=snake_case_  ).prev_sample
  
           _lowerCAmelCase       :  Optional[Any]   				=					(image / 2 + 0.5).clamp(0   ,   1  )
           _lowerCAmelCase       :  Optional[int]   				=					image.cpu().permute(0   ,   2   ,   3   ,   1  ).numpy()
           if output_type == "pil":
             _lowerCAmelCase       :  Union[str, Any]   				=					self.numpy_to_pil(snake_case_  )
  
           if not return_dict:
             return (image,)
  
           return ImagePipelineOutput(images=snake_case_  )
  
  
  
  
  
  
style_context: 
  '''simple docstring'''
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int		)    ->						float:
    if common_ratio == 1:
      # Formula for sum if common ratio is 1
      return num_of_terms * first_term
  
    # Formula for finding sum of n terms of a GeometricProgression
    return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)
  
  
  