






def       snake_case_		(     lowerCAmelCase_       :						int      ):

							if not isinstance(lowerCAmelCase_       ,       lowerCAmelCase_      ):
														__lowercase      :							Tuple				=     F"Input value of [number={number}] must be an integer"
														raise TypeError(lowerCAmelCase_      )

							if number < 1:
														__lowercase      :							Dict				=     F"Input value of [number={number}] must be > 0"
														raise ValueError(lowerCAmelCase_      )

							__lowercase      :							Tuple				=     1

							for i in range(1       ,       lowerCAmelCase_      ):
														current_number *= 4 * i - 2
														current_number //= i + 1

							return current_number


if __name__ == "__main__":
	import doctest

	doctest.testmod()







# 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 		lowerCAmelCase     ( __a      ,       __a			):

					'''simple docstring'''

					_A						:			str									=      1



					@register_to_config
					def __init__(  self				:	Optional[int]		,     __a				:	Tuple=2000		,     __a				:	List[str]=0.1		,     __a				:	str=20		,     __a				:	Optional[int]=1E-3							)			->  int:


												"""simple docstring"""

												__lowercase      :							Tuple				=     None
												__lowercase      :							Union[str, Any]				=     None
												__lowercase      :							int				=     None



					def       lowerCAmelCase				(  self				:	List[Any]		,     __a				:	Any		,     __a				:	Union[str, torch.device] = None							)			->  str:


												"""simple docstring"""

												__lowercase      :							List[str]				=     torch.linspace(1		,     self.config.sampling_eps		,     __a		,     device=__a							)



					def       lowerCAmelCase				(  self				:	Tuple		,     __a				:	List[Any]		,     __a				:	Tuple		,     __a				:	int		,     __a				:	Optional[int]=None							)			->  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
												__lowercase      :							Dict				=     (
												    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
												)
												__lowercase      :							int				=     torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff							)							)
												__lowercase      :							Union[str, Any]				=     std.flatten()
												while len(std.shape							) < len(score.shape							):
																			__lowercase      :							Optional[Any]				=     std.unsqueeze(-1							)
												__lowercase      :							List[Any]				=     -score / std

												# compute
												__lowercase      :							Dict				=     -1.0 / len(self.timesteps							)

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

												__lowercase      :							int				=     torch.sqrt(__a							)
												__lowercase      :							Union[str, Any]				=     drift - diffusion**2 * score
												__lowercase      :							Optional[Any]				=     x + drift * dt

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

												return x, x_mean



					def __len__(  self				:	Tuple							)			->  Optional[int]:


												"""simple docstring"""

												return self.config.num_train_timesteps