'''simple docstring'''

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     __UpperCAmelCase       ( __a		):
  __A :				torch.FloatTensor
  __A :				torch.FloatTensor
  __A :				Optional[torch.FloatTensor]											= None






class     __UpperCAmelCase       ( __a						,       __a		):
  __A :				Optional[Any]											= 2





  @register_to_config
  def __init__(	self    ,     _lowerCamelCase = 0.02    ,     _lowerCamelCase = 100    ,     _lowerCamelCase = 1.0_07    ,     _lowerCamelCase = 80    ,     _lowerCamelCase = 0.05    ,     _lowerCamelCase = 50    ,     ):
     # standard deviation of the initial noise distribution
     lowerCAmelCase_			=      sigma_max

     # setable values
     lowerCAmelCase_			=      None
     lowerCAmelCase_			=      None
     lowerCAmelCase_			=      None  # sigma(t_i)





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





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase = None ):
     lowerCAmelCase_			=      num_inference_steps
     lowerCAmelCase_			=      np.arange(0    ,     self.num_inference_steps )[::-1].copy()
     lowerCAmelCase_			=      torch.from_numpy(_lowerCamelCase ).to(_lowerCamelCase )
     lowerCAmelCase_			=      [
         (
             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
     ]
     lowerCAmelCase_			=      torch.tensor(_lowerCamelCase    ,     dtype=torch.floataa    ,     device=_lowerCamelCase )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase = None ):
     if self.config.s_min <= sigma <= self.config.s_max:
        lowerCAmelCase_			=      min(self.config.s_churn / self.num_inference_steps    ,     2**0.5 - 1 )
     else:
        lowerCAmelCase_			=      0

     # sample eps ~ N(0, S_noise^2 * I)
     lowerCAmelCase_			=      self.config.s_noise * randn_tensor(sample.shape    ,     generator=_lowerCamelCase ).to(sample.device )
     lowerCAmelCase_			=      sigma + gamma * sigma
     lowerCAmelCase_			=      sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

     return sample_hat, sigma_hat





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase = True    ,     ):
     lowerCAmelCase_			=      sample_hat + sigma_hat * model_output
     lowerCAmelCase_			=      (sample_hat - pred_original_sample) / sigma_hat
     lowerCAmelCase_			=      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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase = True    ,     ):
     lowerCAmelCase_			=      sample_prev + sigma_prev * model_output
     lowerCAmelCase_			=      (sample_prev - pred_original_sample) / sigma_prev
     lowerCAmelCase_			=      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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     raise NotImplementedError()






'''simple docstring'''

from __future__ import annotations



def snake_case_      (					__snake_case  :							list[int | str])			->					None:
   create_state_space_tree(__snake_case	,   []	,   0	,   [0 for i in range(len(__snake_case))])



def snake_case_      (					__snake_case  :							list[int | str]	,   __snake_case  :							list[int | str]	,   __snake_case  :							int	,   __snake_case  :							list[int]	,   )			->					None:

   if index == len(__snake_case):
      print(__snake_case)
      return

   for i in range(len(__snake_case)):
      if not index_used[i]:
         current_sequence.append(sequence[i])
         lowerCAmelCase_			=      True
         create_state_space_tree(__snake_case	,   __snake_case	,   index + 1	,   __snake_case)
         current_sequence.pop()
         lowerCAmelCase_			=      False
A_     :						list[int | str]    							=[3, 1, 2, 4]
generate_all_permutations(sequence)

A_     :						list[int | str]    							=["A", "B", "C"]






generate_all_permutations(sequence_a)





