



'''simple docstring'''





# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

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






class __A    (						A     ,     A		):



 '''simple docstring'''







 __lowerCamelCase					: int    = 1



 @register_to_config
 def __init__(self				,     A=2_000				,     A=0.1				,     A=20				,     A=1E-3 )					->  Optional[Any]:


      """simple docstring"""



      _a											=						None
      _a											=						None
      _a											=						None



 def       a__						(self				,     A				,     A = None )					->  List[Any]:


      """simple docstring"""



      _a											=						torch.linspace(1				,     self.config.sampling_eps				,     A				,     device=A )



 def       a__						(self				,     A				,     A				,     A				,     A=None )					->  Dict:


      """simple docstring"""



      if self.timesteps is None:
           raise ValueError(
               '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler''' )

      # TODO(Patrick) better comments + non-PyTorch
      # postprocess model score
      _a											=						(
          -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
      )
      _a											=						torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff ) )
      _a											=						std.flatten()
      while len(std.shape ) < len(score.shape ):
           _a											=						std.unsqueeze(-1 )
      _a											=						-score / std

      # compute
      _a											=						-1.0 / len(self.timesteps )

      _a											=						self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
      _a											=						beta_t.flatten()
      while len(beta_t.shape ) < len(x.shape ):
           _a											=						beta_t.unsqueeze(-1 )
      _a											=						-0.5 * beta_t * x

      _a											=						torch.sqrt(A )
      _a											=						drift - diffusion**2 * score
      _a											=						x + drift * dt

      # add noise
      _a											=						randn_tensor(x.shape				,     layout=x.layout				,     generator=A				,     device=x.device				,     dtype=x.dtype )
      _a											=						x_mean + diffusion * math.sqrt(-dt ) * noise

      return x, x_mean



 def __len__(self )					->  int:


      """simple docstring"""



      return self.config.num_train_timesteps








'''simple docstring'''





from __future__ import annotations

lowercase_	 =						[True] * 1_000_001
lowercase_	 =						2
while i * i <= 1_000_000:
  if seive[i]:
    for j in range(i * i, 1_000_001, i):
      lowercase_	 =						False
  i += 1




def lowerCAmelCase						(__A):



     """simple docstring"""



     return seive[n]




def lowerCAmelCase						(__A):



     """simple docstring"""



     return any(digit in '''02468''' for digit in str(__A))




def lowerCAmelCase						(__A = 1_000_000):



     """simple docstring"""



     _a											=						[2]  # result already includes the number 2.
     for num in range(3						,			limit + 1						,			2):
          if is_prime(__A) and not contains_an_even_digit(__A):
               _a											=						str(__A)
               _a											=						[int(str_num[j:] + str_num[:j]) for j in range(len(__A))]
               if all(is_prime(__A) for i in list_nums):
                    result.append(__A)
     return result




def lowerCAmelCase						():



     """simple docstring"""



     return len(find_circular_primes())


if __name__ == "__main__":
  print(F"""{len(find_circular_primes()) = }""")



