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

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

import torch

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

@dataclass
class       a		(   __UpperCAmelCase					):
							lowercase_		:						torch.FloatTensor
							lowercase_		:						torch.FloatTensor

class       a		(   __UpperCAmelCase      ,	__UpperCAmelCase					):
							lowercase_		:						int   							=  1







							@register_to_config
							def __init__(						self  :  str      ,				snake_case__  :  Tuple = 2_000      ,				snake_case__  :  Optional[int] = 0.1_5      ,				snake_case__  :  Tuple = 0.0_1      ,				snake_case__  :  Tuple = 1_3_4_8.0      ,				snake_case__  :  Optional[Any] = 1E-5      ,				snake_case__  :  str = 1      ,				):
								"""simple docstring"""







								__lowerCAmelCase         =							sigma_max

								# setable values
								__lowerCAmelCase         =							None

								self.set_sigmas(UpperCAmelCase_      ,				UpperCAmelCase_      ,				UpperCAmelCase_      ,				UpperCAmelCase_ )







							def       UpperCAmelCase__					(						self  :  int      ,				snake_case__  :  str      ,				snake_case__  :  Tuple = None ):
								"""simple docstring"""







								return sample







							def       UpperCAmelCase__					(						self  :  Tuple      ,				snake_case__  :  List[Any]      ,				snake_case__  :  str = None      ,				snake_case__  :  Union[str, Any] = None ):
								"""simple docstring"""







								__lowerCAmelCase         =							sampling_eps if sampling_eps is not None else self.config.sampling_eps

								__lowerCAmelCase         =							torch.linspace(1      ,				UpperCAmelCase_      ,				UpperCAmelCase_      ,				device=UpperCAmelCase_ )







							def       UpperCAmelCase__					(						self  :  Tuple      ,				snake_case__  :  Tuple      ,				snake_case__  :  Tuple = None      ,				snake_case__  :  Optional[Any] = None      ,				snake_case__  :  List[str] = None ):
								"""simple docstring"""







								__lowerCAmelCase         =							sigma_min if sigma_min is not None else self.config.sigma_min
								__lowerCAmelCase         =							sigma_max if sigma_max is not None else self.config.sigma_max
								__lowerCAmelCase         =							sampling_eps if sampling_eps is not None else self.config.sampling_eps
								if self.timesteps is None:
									self.set_timesteps(UpperCAmelCase_      ,				UpperCAmelCase_ )

								__lowerCAmelCase         =							sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
								__lowerCAmelCase         =							torch.exp(torch.linspace(math.log(UpperCAmelCase_ )      ,				math.log(UpperCAmelCase_ )      ,				UpperCAmelCase_ ) )
								__lowerCAmelCase         =							torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps] )







							def       UpperCAmelCase__					(						self  :  Optional[int]      ,				snake_case__  :  Dict      ,				snake_case__  :  Any ):
								"""simple docstring"""







								return torch.where(
								    timesteps == 0      ,				torch.zeros_like(t.to(timesteps.device ) )      ,				self.discrete_sigmas[timesteps - 1].to(timesteps.device )      ,				)







							def       UpperCAmelCase__					(						self  :  Optional[int]      ,				snake_case__  :  Union[str, Any]      ,				snake_case__  :  Union[str, Any]      ,				snake_case__  :  int      ,				snake_case__  :  str = None      ,				snake_case__  :  Optional[int] = True      ,				):
								"""simple docstring"""







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

								__lowerCAmelCase         =							timestep * torch.ones(
								    sample.shape[0]      ,				device=sample.device )  # torch.repeat_interleave(timestep, sample.shape[0])
								__lowerCAmelCase         =							(timestep * (len(self.timesteps ) - 1)).long()

								# mps requires indices to be in the same device, so we use cpu as is the default with cuda
								__lowerCAmelCase         =							timesteps.to(self.discrete_sigmas.device )

								__lowerCAmelCase         =							self.discrete_sigmas[timesteps].to(sample.device )
								__lowerCAmelCase         =							self.get_adjacent_sigma(UpperCAmelCase_      ,				UpperCAmelCase_ ).to(sample.device )
								__lowerCAmelCase         =							torch.zeros_like(UpperCAmelCase_ )
								__lowerCAmelCase         =							(sigma**2 - adjacent_sigma**2) ** 0.5

								# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
								# also equation 47 shows the analog from SDE models to ancestral sampling methods
								__lowerCAmelCase         =							diffusion.flatten()
								while len(diffusion.shape ) < len(sample.shape ):
									__lowerCAmelCase         =							diffusion.unsqueeze(-1 )
								__lowerCAmelCase         =							drift - diffusion**2 * model_output

								#  equation 6: sample noise for the diffusion term of
								__lowerCAmelCase         =							randn_tensor(
								    sample.shape      ,				layout=sample.layout      ,				generator=UpperCAmelCase_      ,				device=sample.device      ,				dtype=sample.dtype )
								__lowerCAmelCase         =							sample - drift  # subtract because `dt` is a small negative timestep
								# TODO is the variable diffusion the correct scaling term for the noise?
								__lowerCAmelCase         =							prev_sample_mean + diffusion * noise  # add impact of diffusion field g

								if not return_dict:
									return (prev_sample, prev_sample_mean)

								return SdeVeOutput(prev_sample=UpperCAmelCase_      ,				prev_sample_mean=UpperCAmelCase_ )







							def       UpperCAmelCase__					(						self  :  Optional[Any]      ,				snake_case__  :  Union[str, Any]      ,				snake_case__  :  Dict      ,				snake_case__  :  List[Any] = None      ,				snake_case__  :  Optional[int] = True      ,				):
								"""simple docstring"""







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

								# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
								# sample noise for correction
								__lowerCAmelCase         =							randn_tensor(sample.shape      ,				layout=sample.layout      ,				generator=UpperCAmelCase_ ).to(sample.device )

								# compute step size from the model_output, the noise, and the snr
								__lowerCAmelCase         =							torch.norm(model_output.reshape(model_output.shape[0]      ,				-1 )      ,				dim=-1 ).mean()
								__lowerCAmelCase         =							torch.norm(noise.reshape(noise.shape[0]      ,				-1 )      ,				dim=-1 ).mean()
								__lowerCAmelCase         =							(self.config.snr * noise_norm / grad_norm) ** 2 * 2
								__lowerCAmelCase         =							step_size * torch.ones(sample.shape[0] ).to(sample.device )
								# self.repeat_scalar(step_size, sample.shape[0])

								# compute corrected sample: model_output term and noise term
								__lowerCAmelCase         =							step_size.flatten()
								while len(step_size.shape ) < len(sample.shape ):
									__lowerCAmelCase         =							step_size.unsqueeze(-1 )
								__lowerCAmelCase         =							sample + step_size * model_output
								__lowerCAmelCase         =							prev_sample_mean + ((step_size * 2) ** 0.5) * noise

								if not return_dict:
									return (prev_sample,)

								return SchedulerOutput(prev_sample=UpperCAmelCase_ )







							def       UpperCAmelCase__					(						self  :  Union[str, Any]      ,				snake_case__  :  Tuple      ,				snake_case__  :  str      ,				snake_case__  :  Union[str, Any]      ,				):
								"""simple docstring"""







								__lowerCAmelCase         =							timesteps.to(original_samples.device )
								__lowerCAmelCase         =							self.discrete_sigmas.to(original_samples.device )[timesteps]
								__lowerCAmelCase         =							(
								    noise * sigmas[:, None, None, None]
								    if noise is not None
								    else torch.randn_like(UpperCAmelCase_ ) * sigmas[:, None, None, None]
								)
								__lowerCAmelCase         =							noise + original_samples
								return noisy_samples







							def __len__(						self  :  str ):
								"""simple docstring"""







								return self.config.num_train_timesteps



from __future__ import annotations

UpperCamelCase_   	=	[True] * 1_0_0_0_0_0_1
UpperCamelCase_   	=	2
while i * i <= 1_0_0_0_0_0_0:
					if seive[i]:
										for j in range(i * i, 1_0_0_0_0_0_1, i):
															UpperCamelCase_   	=	False
					i += 1






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return seive[n]






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return any(digit in "02468" for digit in str(UpperCamelCase  )  )






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 1_0_0_0_0_0_0  ):






	"""simple docstring"""


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






def 		_UpperCAmelCase   (	):






	"""simple docstring"""


	return len(find_circular_primes()  )


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






