






'''simple docstring'''





from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput
class 				lowercase       (							_UpperCAmelCase      ):


    '''simple docstring'''

    def __init__(					self     :     List[str]				,     __lowerCamelCase     :     Tuple				,     __lowerCamelCase     :     Any     )							->							Any:

     '''simple docstring'''




     super().__init__()
     self.register_modules(unet=A_				,     scheduler=A_     )




    @torch.no_grad()
    def __call__(					self     :     Optional[Any]				,     __lowerCamelCase     :     int = 1				,     __lowerCamelCase     :     Optional[torch.Generator] = None				,     __lowerCamelCase     :     int = 50				,     __lowerCamelCase     :     Optional[str] = "pil"				,     __lowerCamelCase     :     bool = True				,     **__lowerCamelCase     :     Optional[Any]				,     )							->							Union[ImagePipelineOutput, Tuple]:

     '''simple docstring'''




     lowerCamelCase__  =     torch.randn(
         (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)				,     generator=A_				,     )
     lowerCamelCase__  =     image.to(self.device     )

     # set step values
     self.scheduler.set_timesteps(A_     )

     for t in self.progress_bar(self.scheduler.timesteps     ):
      # 1. predict noise model_output
      lowerCamelCase__  =     self.unet(A_				,     A_     ).sample

      # 2. predict previous mean of image x_t-1 and add variance depending on eta
      # eta corresponds to η in paper and should be between [0, 1]
      # do x_t -> x_t-1
      lowerCamelCase__  =     self.scheduler.step(A_				,     A_				,     A_     ).prev_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(A_     )

     if not return_dict:
      return (image,), "This is a local test"

     return ImagePipelineOutput(images=A_     ), "This is a local test"













'''simple docstring'''





from decimal import Decimal, getcontext
from math import ceil, factorial






def    lowerCamelCase_     (    lowercase__):

 if not isinstance(lowercase__				,     lowercase__):
  raise TypeError("Undefined for non-integers")
 elif precision < 1:
  raise ValueError("Undefined for non-natural numbers")

 lowerCamelCase__  =     precision
 lowerCamelCase__  =     ceil(precision / 14)
 lowerCamelCase__  =     426880 * Decimal(10005).sqrt()
 lowerCamelCase__  =     1
 lowerCamelCase__  =     13591409
 lowerCamelCase__  =     Decimal(lowercase__)
 for k in range(1				,     lowercase__):
  lowerCamelCase__  =     factorial(6 * k) // (factorial(3 * k) * factorial(lowercase__) ** 3)
  linear_term += 545140134
  exponential_term *= -262537412640768000
  partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
 return str(constant_term / partial_sum)[:-1]


if __name__ == "__main__":
 __A							:							Dict  							=		50
 print(F"""The first {n} digits of pi is: {pi(n)}""")

