



"""simple docstring"""
# 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__       ):
  UpperCamelCase	:				torch.FloatTensor
  UpperCamelCase	:				torch.FloatTensor







class 					a	(  UpperCAmelCase__	,      UpperCAmelCase__       ):
  UpperCamelCase	:				Optional[int]     						=					1



  @register_to_config
  def __init__(						self :					Tuple       ,		lowerCAmelCase :					int = 2000       ,		lowerCAmelCase :					float = 0.1_5       ,		lowerCAmelCase :					float = 0.0_1       ,		lowerCAmelCase :					float = 1_3_4_8.0       ,		lowerCAmelCase :					float = 1E-5       ,		lowerCAmelCase :					int = 1       ,		)     ->					Optional[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: int     			=sigma_max

     # setable values
     SCREAMING_SNAKE_CASE_: Any     			=None

     self.set_sigmas(lowerCAmelCase       ,		lowerCAmelCase       ,		lowerCAmelCase       ,		lowerCAmelCase		)



  def 	lowerCamelCase__       (						self :					Any       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					Optional[int] = None		)     ->					torch.FloatTensor:


     '''simple docstring'''




     return sample



  def 	lowerCamelCase__       (						self :					List[str]       ,		lowerCAmelCase :					int       ,		lowerCAmelCase :					float = None       ,		lowerCAmelCase :					Union[str, torch.device] = None		)     ->					str:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Dict     			=sampling_eps if sampling_eps is not None else self.config.sampling_eps

     SCREAMING_SNAKE_CASE_: int     			=torch.linspace(1       ,		lowerCAmelCase       ,		lowerCAmelCase       ,		device=lowerCAmelCase		)



  def 	lowerCamelCase__       (						self :					Any       ,		lowerCAmelCase :					int       ,		lowerCAmelCase :					float = None       ,		lowerCAmelCase :					float = None       ,		lowerCAmelCase :					float = None		)     ->					Optional[int]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Optional[int]     			=sigma_min if sigma_min is not None else self.config.sigma_min
     SCREAMING_SNAKE_CASE_: Any     			=sigma_max if sigma_max is not None else self.config.sigma_max
     SCREAMING_SNAKE_CASE_: Any     			=sampling_eps if sampling_eps is not None else self.config.sampling_eps
     if self.timesteps is None:
        self.set_timesteps(lowerCAmelCase       ,		lowerCAmelCase		)

     SCREAMING_SNAKE_CASE_: Optional[int]     			=sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
     SCREAMING_SNAKE_CASE_: Any     			=torch.exp(torch.linspace(math.log(lowerCAmelCase		)       ,		math.log(lowerCAmelCase		)       ,		lowerCAmelCase		)		)
     SCREAMING_SNAKE_CASE_: List[str]     			=torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]		)



  def 	lowerCamelCase__       (						self :					Dict       ,		lowerCAmelCase :					List[str]       ,		lowerCAmelCase :					str		)     ->					Tuple:


     '''simple docstring'''




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



  def 	lowerCamelCase__       (						self :					List[Any]       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					int       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					Optional[torch.Generator] = None       ,		lowerCAmelCase :					bool = True       ,		)     ->					Union[SdeVeOutput, Tuple]:


     '''simple docstring'''




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

     SCREAMING_SNAKE_CASE_: List[Any]     			=timestep * torch.ones(
         sample.shape[0]       ,		device=sample.device		)  # torch.repeat_interleave(timestep, sample.shape[0])
     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=(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
     SCREAMING_SNAKE_CASE_: Optional[int]     			=timesteps.to(self.discrete_sigmas.device		)

     SCREAMING_SNAKE_CASE_: Optional[int]     			=self.discrete_sigmas[timesteps].to(sample.device		)
     SCREAMING_SNAKE_CASE_: Any     			=self.get_adjacent_sigma(lowerCAmelCase       ,		lowerCAmelCase		).to(sample.device		)
     SCREAMING_SNAKE_CASE_: str     			=torch.zeros_like(lowerCAmelCase		)
     SCREAMING_SNAKE_CASE_: Dict     			=(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
     SCREAMING_SNAKE_CASE_: List[str]     			=diffusion.flatten()
     while len(diffusion.shape		) < len(sample.shape		):
        SCREAMING_SNAKE_CASE_: Optional[Any]     			=diffusion.unsqueeze(-1		)
     SCREAMING_SNAKE_CASE_: Tuple     			=drift - diffusion**2 * model_output

     #  equation 6: sample noise for the diffusion term of
     SCREAMING_SNAKE_CASE_: List[Any]     			=randn_tensor(
         sample.shape       ,		layout=sample.layout       ,		generator=lowerCAmelCase       ,		device=sample.device       ,		dtype=sample.dtype		)
     SCREAMING_SNAKE_CASE_: str     			=sample - drift  # subtract because `dt` is a small negative timestep
     # TODO is the variable diffusion the correct scaling term for the noise?
     SCREAMING_SNAKE_CASE_: Dict     			=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=lowerCAmelCase       ,		prev_sample_mean=lowerCAmelCase		)



  def 	lowerCamelCase__       (						self :					Dict       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					Optional[torch.Generator] = None       ,		lowerCAmelCase :					bool = True       ,		)     ->					Union[SchedulerOutput, Tuple]:


     '''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
     SCREAMING_SNAKE_CASE_: int     			=randn_tensor(sample.shape       ,		layout=sample.layout       ,		generator=lowerCAmelCase		).to(sample.device		)

     # compute step size from the model_output, the noise, and the snr
     SCREAMING_SNAKE_CASE_: str     			=torch.norm(model_output.reshape(model_output.shape[0]       ,		-1		)       ,		dim=-1		).mean()
     SCREAMING_SNAKE_CASE_: Optional[int]     			=torch.norm(noise.reshape(noise.shape[0]       ,		-1		)       ,		dim=-1		).mean()
     SCREAMING_SNAKE_CASE_: Optional[int]     			=(self.config.snr * noise_norm / grad_norm) ** 2 * 2
     SCREAMING_SNAKE_CASE_: Optional[int]     			=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
     SCREAMING_SNAKE_CASE_: List[Any]     			=step_size.flatten()
     while len(step_size.shape		) < len(sample.shape		):
        SCREAMING_SNAKE_CASE_: Optional[Any]     			=step_size.unsqueeze(-1		)
     SCREAMING_SNAKE_CASE_: List[str]     			=sample + step_size * model_output
     SCREAMING_SNAKE_CASE_: Any     			=prev_sample_mean + ((step_size * 2) ** 0.5) * noise

     if not return_dict:
        return (prev_sample,)

     return SchedulerOutput(prev_sample=lowerCAmelCase		)



  def 	lowerCamelCase__       (						self :					List[str]       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					torch.FloatTensor       ,		lowerCAmelCase :					torch.FloatTensor       ,		)     ->					torch.FloatTensor:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=timesteps.to(original_samples.device		)
     SCREAMING_SNAKE_CASE_: Tuple     			=self.discrete_sigmas.to(original_samples.device		)[timesteps]
     SCREAMING_SNAKE_CASE_: str     			=(
         noise * sigmas[:, None, None, None]
         if noise is not None
         else torch.randn_like(lowerCAmelCase		) * sigmas[:, None, None, None]
     )
     SCREAMING_SNAKE_CASE_: Any     			=noise + original_samples
     return noisy_samples





  def __len__(						self :					List[Any]		)     ->					Dict:


     '''simple docstring'''




     return self.config.num_train_timesteps








"""simple docstring"""
def      __magic_name__				(							lowercase = 200_0000 ):
   SCREAMING_SNAKE_CASE_: List[Any]     			=[0 for i in range(n + 1 )]
   SCREAMING_SNAKE_CASE_: Union[str, Any]     			=1
   SCREAMING_SNAKE_CASE_: Optional[Any]     			=1

   for i in range(2							,			int(n**0.5 ) + 1 ):
      if primality_list[i] == 0:
         for j in range(i * i							,			n + 1							,			lowercase ):
            SCREAMING_SNAKE_CASE_: Optional[int]     			=1
   SCREAMING_SNAKE_CASE_: Dict     			=0
   for i in range(lowercase ):
      if primality_list[i] == 0:
         sum_of_primes += i
   return sum_of_primes


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



