


'''simple docstring'''






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin






@dataclass
class    __magic_name__				(						lowerCAmelCase							):
       UpperCAmelCase		 =42
       UpperCAmelCase		 =42
       UpperCAmelCase		 =None






class    __magic_name__				(						lowerCAmelCase   ,lowerCAmelCase							):
       UpperCAmelCase		 =2






       @register_to_config
       def __init__(     self    ,				snake_case = 0.02    ,				snake_case = 1_0_0    ,				snake_case = 1.0_07    ,				snake_case = 8_0    ,				snake_case = 0.05    ,				snake_case = 5_0    ,				)		->    int:




          '''simple docstring'''
          # standard deviation of the initial noise distribution
          _UpperCAmelCase  :  str				       =sigma_max

          # setable values
          _UpperCAmelCase  :  int				       =None
          _UpperCAmelCase  :  np.IntTensor				       =None
          _UpperCAmelCase  :  torch.FloatTensor				       =None  # sigma(t_i)






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case = None)		->    torch.FloatTensor:




          '''simple docstring'''
          return sample






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case = None)		->    Optional[Any]:




          '''simple docstring'''
          _UpperCAmelCase  :  int				       =num_inference_steps
          _UpperCAmelCase  :  Any				       =np.arange(0    ,				self.num_inference_steps)[::-1].copy()
          _UpperCAmelCase  :  Any				       =torch.from_numpy(snake_case).to(snake_case)
          _UpperCAmelCase  :  Optional[Any]				       =[
              (
                  self.config.sigma_max**2
                  * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
              )
              for i in self.timesteps
          ]
          _UpperCAmelCase  :  int				       =torch.tensor(snake_case    ,				dtype=torch.floataa    ,				device=snake_case)






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case    ,				snake_case = None)		->    Tuple[torch.FloatTensor, float]:




          '''simple docstring'''
          if self.config.s_min <= sigma <= self.config.s_max:
             _UpperCAmelCase  :  Optional[int]				       =min(self.config.s_churn / self.num_inference_steps    ,				2**0.5 - 1)
          else:
             _UpperCAmelCase  :  Optional[Any]				       =0

          # sample eps ~ N(0, S_noise^2 * I)
          _UpperCAmelCase  :  List[Any]				       =self.config.s_noise * randn_tensor(sample.shape    ,				generator=snake_case).to(sample.device)
          _UpperCAmelCase  :  Optional[int]				       =sigma + gamma * sigma
          _UpperCAmelCase  :  Optional[Any]				       =sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

          return sample_hat, sigma_hat






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case = True    ,				)		->    Union[KarrasVeOutput, Tuple]:




          '''simple docstring'''
          _UpperCAmelCase  :  int				       =sample_hat + sigma_hat * model_output
          _UpperCAmelCase  :  int				       =(sample_hat - pred_original_sample) / sigma_hat
          _UpperCAmelCase  :  Optional[int]				       =sample_hat + (sigma_prev - sigma_hat) * derivative

          if not return_dict:
             return (sample_prev, derivative)

          return KarrasVeOutput(
              prev_sample=snake_case    ,				derivative=snake_case    ,				pred_original_sample=snake_case)






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case    ,				snake_case = True    ,				)		->    Union[KarrasVeOutput, Tuple]:




          '''simple docstring'''
          _UpperCAmelCase  :  Any				       =sample_prev + sigma_prev * model_output
          _UpperCAmelCase  :  Union[str, Any]				       =(sample_prev - pred_original_sample) / sigma_prev
          _UpperCAmelCase  :  Dict				       =sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

          if not return_dict:
             return (sample_prev, derivative)

          return KarrasVeOutput(
              prev_sample=snake_case    ,				derivative=snake_case    ,				pred_original_sample=snake_case)






       def      lowerCAmelCase						(     self    ,				snake_case    ,				snake_case    ,				snake_case)		->    str:




          '''simple docstring'''
          raise NotImplementedError()





'''simple docstring'''






from __future__ import annotations

from fractions import Fraction





def lowerCamelCase__     (		__lowerCamelCase			:				int			,       __lowerCamelCase			:				int				):







   '''simple docstring'''




   return (
       num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
   )





def lowerCamelCase__     (		__lowerCamelCase			:				int				):







   '''simple docstring'''




   _UpperCAmelCase  :  Optional[int]				       =[]
   _UpperCAmelCase  :  Union[str, Any]				       =1_1
   _UpperCAmelCase  :  Union[str, Any]				       =int('1' + '0' * digit_len				)
   for num in range(__lowerCamelCase			,       __lowerCamelCase				):
      while den <= 9_9:
         if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
            if is_digit_cancelling(__lowerCamelCase			,       __lowerCamelCase				):
               solutions.append(f"{num}/{den}"				)
         den += 1
      num += 1
      _UpperCAmelCase  :  Optional[int]				       =1_0
   return solutions





def lowerCamelCase__     (		__lowerCamelCase			:				int = 2				):







   '''simple docstring'''




   _UpperCAmelCase  :  Any				       =1.0
   for fraction in fraction_list(__lowerCamelCase				):
      _UpperCAmelCase  :  List[str]				       =Fraction(__lowerCamelCase				)
      result *= frac.denominator / frac.numerator
   return int(__lowerCamelCase				)


if __name__ == "__main__":
 print(solution())

