

from typing import List, Optional, Tuple, Union

import torch

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



class   __lowercase				( UpperCAmelCase_	):




			"""simple docstring"""







			_UpperCAmelCase   :							UNetaDModel
			_UpperCAmelCase   :							KarrasVeScheduler



			def __init__( self  :     Union[str, Any]   ,						lowerCAmelCase__  :     UNetaDModel   ,						lowerCAmelCase__  :     KarrasVeScheduler):
									super().__init__()
									self.register_modules(unet=lowerCAmelCase__   ,						scheduler=lowerCAmelCase__)




			@torch.no_grad()
			def __call__( self  :     Union[str, Any]   ,						lowerCAmelCase__  :     int = 1   ,						lowerCAmelCase__  :     int = 50   ,						lowerCAmelCase__  :     Optional[Union[torch.Generator, List[torch.Generator]]] = None   ,						lowerCAmelCase__  :     Optional[str] = "pil"   ,						lowerCAmelCase__  :     bool = True   ,						**lowerCAmelCase__  :     Optional[int]   ,						):
									SCREAMING_SNAKE_CASE_: List[Any]  		=       self.unet.config.sample_size
									SCREAMING_SNAKE_CASE_: str  		=       (batch_size, 3, img_size, img_size)

									SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       self.unet

									# sample x_0 ~ N(0, sigma_0^2 * I)
									SCREAMING_SNAKE_CASE_: str  		=       randn_tensor(lowerCAmelCase__   ,						generator=lowerCAmelCase__   ,						device=self.device) * self.scheduler.init_noise_sigma

									self.scheduler.set_timesteps(lowerCAmelCase__)

									for t in self.progress_bar(self.scheduler.timesteps):
															# here sigma_t == t_i from the paper
															SCREAMING_SNAKE_CASE_: List[str]  		=       self.scheduler.schedule[t]
															SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       self.scheduler.schedule[t - 1] if t > 0 else 0

															# 1. Select temporarily increased noise level sigma_hat
															# 2. Add new noise to move from sample_i to sample_hat
															SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: Any  		=       self.scheduler.add_noise_to_input(lowerCAmelCase__   ,						lowerCAmelCase__   ,						generator=lowerCAmelCase__)

															# 3. Predict the noise residual given the noise magnitude `sigma_hat`
															# The model inputs and output are adjusted by following eq. (213) in [1].
															SCREAMING_SNAKE_CASE_: Optional[Any]  		=       (sigma_hat / 2) * model((sample_hat + 1) / 2   ,						sigma_hat / 2).sample

															# 4. Evaluate dx/dt at sigma_hat
															# 5. Take Euler step from sigma to sigma_prev
															SCREAMING_SNAKE_CASE_: Any  		=       self.scheduler.step(lowerCAmelCase__   ,						lowerCAmelCase__   ,						lowerCAmelCase__   ,						lowerCAmelCase__)

															if sigma_prev != 0:
																					# 6. Apply 2nd order correction
																					# The model inputs and output are adjusted by following eq. (213) in [1].
																					SCREAMING_SNAKE_CASE_: Any  		=       (sigma_prev / 2) * model((step_output.prev_sample + 1) / 2   ,						sigma_prev / 2).sample
																					SCREAMING_SNAKE_CASE_: List[str]  		=       self.scheduler.step_correct(
																					    lowerCAmelCase__   ,						lowerCAmelCase__   ,						lowerCAmelCase__   ,						lowerCAmelCase__   ,						step_output.prev_sample   ,						step_output["derivative"]   ,						)
															SCREAMING_SNAKE_CASE_: Tuple  		=       step_output.prev_sample

									SCREAMING_SNAKE_CASE_: Optional[int]  		=       (sample / 2 + 0.5).clamp(0   ,						1)
									SCREAMING_SNAKE_CASE_: Optional[Any]  		=       sample.cpu().permute(0   ,						2   ,						3   ,						1).numpy()
									if output_type == "pil":
															SCREAMING_SNAKE_CASE_: List[str]  		=       self.numpy_to_pil(lowerCAmelCase__)

									if not return_dict:
															return (image,)

									return ImagePipelineOutput(images=lowerCAmelCase__)








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


def       A       (					lowercase )   ->  str:
		'''simple docstring'''

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

		UpperCamelCase		=     precision
		UpperCamelCase		=     ceil(precision / 14 )
		UpperCamelCase		=     426_880 * Decimal(10_005 ).sqrt()
		UpperCamelCase		=     1
		UpperCamelCase		=     13_591_409
		UpperCamelCase		=     Decimal(lowercase )
		for k in range(1    ,       lowercase ):
				UpperCamelCase		=     factorial(6 * k ) // (factorial(3 * k ) * factorial(lowercase ) ** 3)
				linear_term += 545_140_134
				exponential_term *= -262_537_412_640_768_000
				partial_sum += Decimal(multinomial_term * linear_term ) / exponential_term
		return str(constant_term / partial_sum )[:-1]


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