


'''simple docstring'''

import inspect
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput





class      snake_case    (    A_			):





  """simple docstring"""




  def __init__(    self			,  UpperCamelCase			,  UpperCamelCase			,  UpperCamelCase     ):







   """simple docstring"""
   super().__init__()
   self.register_modules(vqvae=_lowerCamelCase			,  unet=_lowerCamelCase			,  scheduler=_lowerCamelCase     )







  @torch.no_grad()
  def __call__(    self			,  UpperCamelCase = 1			,  UpperCamelCase = None			,  UpperCamelCase = 0.0			,  UpperCamelCase = 50			,  UpperCamelCase = "pil"			,  UpperCamelCase = True			,  **UpperCamelCase			,  ):







   """simple docstring"""
   lowerCamelCase_      =  randn_tensor(
       (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)			,  generator=_lowerCamelCase			,  )
   lowerCamelCase_      =  latents.to(self.device     )

   # scale the initial noise by the standard deviation required by the scheduler
   lowerCamelCase_      =  latents * self.scheduler.init_noise_sigma

   self.scheduler.set_timesteps(_lowerCamelCase     )

   # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
   lowerCamelCase_      =  "eta" in set(inspect.signature(self.scheduler.step     ).parameters.keys()     )

   lowerCamelCase_      =  {}
   if accepts_eta:
    lowerCamelCase_      =  eta

   for t in self.progress_bar(self.scheduler.timesteps     ):
    lowerCamelCase_      =  self.scheduler.scale_model_input(_lowerCamelCase			,  _lowerCamelCase     )
    # predict the noise residual
    lowerCamelCase_      =  self.unet(_lowerCamelCase			,  _lowerCamelCase     ).sample
    # compute the previous noisy sample x_t -> x_t-1
    lowerCamelCase_      =  self.scheduler.step(_lowerCamelCase			,  _lowerCamelCase			,  _lowerCamelCase			,  **_lowerCamelCase     ).prev_sample

   # decode the image latents with the VAE
   lowerCamelCase_      =  self.vqvae.decode(_lowerCamelCase     ).sample

   lowerCamelCase_      =  (image / 2 + 0.5).clamp(0			,  1     )
   lowerCamelCase_      =  image.cpu().permute(0			,  2			,  3			,  1     ).numpy()
   if output_type == "pil":
    lowerCamelCase_      =  self.numpy_to_pil(_lowerCamelCase     )

   if not return_dict:
    return (image,)

   return ImagePipelineOutput(images=_lowerCamelCase     )





"""simple docstring"""



from math import pow
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					)     ->					tuple[int, int]:
  if current_sum == needed_sum:
    # If the sum of the powers is equal to needed_sum, then we have a solution.
    solutions_count += 1
    return current_sum, solutions_count

  _snake_case					     =       int(pow(__lowerCamelCase ,					__lowerCamelCase		)		)
  if current_sum + i_to_n <= needed_sum:
    # If the sum of the powers is less than needed_sum, then continue adding powers.
    current_sum += i_to_n
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
    current_sum -= i_to_n
  if i_to_n < needed_sum:
    # If the power of i is less than needed_sum, then try with the next power.
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
  return current_sum, solutions_count
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int		)     ->					int:
  if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
    raise ValueError(
        '''Invalid input\n'''
        '''needed_sum must be between 1 and 1000, power between 2 and 10.'''		)

  return backtrack(__lowerCamelCase ,					__lowerCamelCase ,					1 ,					0 ,					0		)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()



