


# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput







class  snake_case_     (lowerCamelCase_   ):
					def __init__(   self     :List[str]    ,__snake_case     :Tuple    ,__snake_case     :List[Any]   )      ->					Union[str, Any]:
												super().__init__()
												self.register_modules(unet=__snake_case    ,scheduler=__snake_case   )



					@torch.no_grad()
					def __call__(   self     :str    ,__snake_case     :int = 1    ,__snake_case     :Optional[torch.Generator] = None    ,__snake_case     :int = 50    ,__snake_case     :Optional[str] = "pil"    ,__snake_case     :bool = True    ,**__snake_case     :List[str]    ,)      ->					Union[ImagePipelineOutput, Tuple]:
												a__    =  torch.randn(
												    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)    ,generator=__snake_case    ,)
												a__    =  image.to(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
																			a__    =  self.unet(__snake_case    ,__snake_case   ).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
																			a__    =  self.scheduler.step(__snake_case    ,__snake_case    ,__snake_case   ).prev_sample

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

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

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








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






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

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

							a__    =  precision
							a__    =  ceil(precision / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
						snake_case							: Tuple      =   50
						print(f"""The first {n} digits of pi is: {pi(n)}""")




