






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

import numpy as np
import torch

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




@dataclass
class     _lowerCAmelCase(	UpperCAmelCase_ ):





       """simple docstring"""







       a    :		torch.FloatTensor
       a    :		torch.FloatTensor
       a    :		Optional[torch.FloatTensor]									=None







class     _lowerCAmelCase(	UpperCAmelCase_							,     UpperCAmelCase_ ):





       """simple docstring"""







       a    :		Tuple									=2





       @register_to_config
       def __init__( self  ,      _lowerCamelCase = 0.0_2  ,      _lowerCamelCase = 1_0_0  ,      _lowerCamelCase = 1.0_0_7  ,      _lowerCamelCase = 8_0  ,      _lowerCamelCase = 0.0_5  ,      _lowerCamelCase = 5_0  ,      ):
         # standard deviation of the initial noise distribution
         UpperCamelCase_: Tuple   				=    sigma_max

         # setable values
         UpperCamelCase_: int   				=    None
         UpperCamelCase_: np.IntTensor   				=    None
         UpperCamelCase_: torch.FloatTensor   				=    None  # sigma(t_i)





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase = None							):
         return sample





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase = None							):
         UpperCamelCase_: Dict   				=    num_inference_steps
         UpperCamelCase_: Dict   				=    np.arange(0  ,      self.num_inference_steps							)[::-1].copy()
         UpperCamelCase_: Dict   				=    torch.from_numpy(_lowerCamelCase							).to(_lowerCamelCase							)
         UpperCamelCase_: Tuple   				=    [
             (
                 self.config.sigma_max**2
                 * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
             )
             for i in self.timesteps
         ]
         UpperCamelCase_: List[str]   				=    torch.tensor(_lowerCamelCase  ,      dtype=torch.floataa  ,      device=_lowerCamelCase							)





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase = None							):
         if self.config.s_min <= sigma <= self.config.s_max:
           UpperCamelCase_: List[Any]   				=    min(self.config.s_churn / self.num_inference_steps  ,      2**0.5 - 1							)
         else:
           UpperCamelCase_: Union[str, Any]   				=    0

         # sample eps ~ N(0, S_noise^2 * I)
         UpperCamelCase_: Any   				=    self.config.s_noise * randn_tensor(sample.shape  ,      generator=_lowerCamelCase							).to(sample.device							)
         UpperCamelCase_: Any   				=    sigma + gamma * sigma
         UpperCamelCase_: List[str]   				=    sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

         return sample_hat, sigma_hat





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase = True  ,      ):
         UpperCamelCase_: Optional[int]   				=    sample_hat + sigma_hat * model_output
         UpperCamelCase_: Dict   				=    (sample_hat - pred_original_sample) / sigma_hat
         UpperCamelCase_: Tuple   				=    sample_hat + (sigma_prev - sigma_hat) * derivative

         if not return_dict:
           return (sample_prev, derivative)

         return KarrasVeOutput(
             prev_sample=_lowerCamelCase  ,      derivative=_lowerCamelCase  ,      pred_original_sample=_lowerCamelCase							)





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase = True  ,      ):
         UpperCamelCase_: Union[str, Any]   				=    sample_prev + sigma_prev * model_output
         UpperCamelCase_: List[str]   				=    (sample_prev - pred_original_sample) / sigma_prev
         UpperCamelCase_: Optional[int]   				=    sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

         if not return_dict:
           return (sample_prev, derivative)

         return KarrasVeOutput(
             prev_sample=_lowerCamelCase  ,      derivative=_lowerCamelCase  ,      pred_original_sample=_lowerCamelCase							)





       def       _a   ( self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase							):
         raise NotImplementedError()











def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  while b:
    UpperCamelCase_				,UpperCamelCase_: int   				=    b, a % b
  return a

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  return a if b == 0 else euclidean_gcd_recursive(UpperCAmelCase__     ,   a % b  )

def   snake_case ()	->    int:
  print(F'''euclidean_gcd(3, 5) = {euclidean_gcd(3     ,   5  )}'''  )
  print(F'''euclidean_gcd(5, 3) = {euclidean_gcd(5     ,   3  )}'''  )
  print(F'''euclidean_gcd(1, 3) = {euclidean_gcd(1     ,   3  )}'''  )
  print(F'''euclidean_gcd(3, 6) = {euclidean_gcd(3     ,   6  )}'''  )
  print(F'''euclidean_gcd(6, 3) = {euclidean_gcd(6     ,   3  )}'''  )

  print(F'''euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3     ,   5  )}'''  )
  print(F'''euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5     ,   3  )}'''  )
  print(F'''euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1     ,   3  )}'''  )
  print(F'''euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3     ,   6  )}'''  )
  print(F'''euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6     ,   3  )}'''  )


if __name__ == "__main__":
   main()