






# 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       snake_case__ (				lowercase_						,     lowercase_):

       '''simple docstring'''
       lowerCamelCase				:					Optional[int]								=			1



       @register_to_config
       def __init__(				self      ,    a__=20_00      ,    a__=0.1      ,    a__=20      ,    a__=1e-3     )			->   Union[str, Any]:






            '''simple docstring'''





            __snake_case      :int 							=    None
            __snake_case      :Optional[Any] 							=    None
            __snake_case      :Any 							=    None



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






            '''simple docstring'''





            __snake_case      :Union[str, Any] 							=    torch.linspace(1      ,    self.config.sampling_eps      ,    a__      ,    device=a__     )



       def        __lowercase    (				self      ,    a__      ,    a__      ,    a__      ,    a__=None     )			->   List[str]:






            '''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
            __snake_case      :Union[str, Any] 							=    (
                -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
            )
            __snake_case      :str 							=    torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff     )     )
            __snake_case      :Optional[Any] 							=    std.flatten()
            while len(std.shape     ) < len(score.shape     ):
                 __snake_case      :Dict 							=    std.unsqueeze(-1     )
            __snake_case      :Dict 							=    -score / std

            # compute
            __snake_case      :List[Any] 							=    -1.0 / len(self.timesteps     )

            __snake_case      :Union[str, Any] 							=    self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
            __snake_case      :Tuple 							=    beta_t.flatten()
            while len(beta_t.shape     ) < len(x.shape     ):
                 __snake_case      :Optional[int] 							=    beta_t.unsqueeze(-1     )
            __snake_case      :Any 							=    -0.5 * beta_t * x

            __snake_case      :str 							=    torch.sqrt(a__     )
            __snake_case      :Optional[Any] 							=    drift - diffusion**2 * score
            __snake_case      :Optional[Any] 							=    x + drift * dt

            # add noise
            __snake_case      :List[Any] 							=    randn_tensor(x.shape      ,    layout=x.layout      ,    generator=a__      ,    device=x.device      ,    dtype=x.dtype     )
            __snake_case      :List[str] 							=    x_mean + diffusion * math.sqrt(-dt     ) * noise

            return x, x_mean



       def __len__(				self     )			->   Optional[Any]:






            '''simple docstring'''





            return self.config.num_train_timesteps










def 	UpperCamelCase	(							snake_case__  : int	):




     '''simple docstring'''






     __snake_case      :List[Any] 							=    0
     while num > 0:
          digit_sum += num % 10
          num //= 10
     return digit_sum






def 	UpperCamelCase	(							snake_case__  : int = 100	):




     '''simple docstring'''






     __snake_case      :Tuple 							=    1
     __snake_case      :Dict 							=    2

     for i in range(2						,max_n + 1	):
          __snake_case      :Optional[int] 							=    pre_numerator
          __snake_case      :List[Any] 							=    2 * i // 3 if i % 3 == 0 else 1
          __snake_case      :Dict 							=    cur_numerator
          __snake_case      :Optional[Any] 							=    e_cont * pre_numerator + temp

     return sum_digits(snake_case__	)


if __name__ == "__main__":
     print(f'''{solution() = }''')


