

'''simple docstring'''



import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput



class 				_snake_case					(   a_     , a_			):
  SCREAMING_SNAKE_CASE			:       List[str]				=     1

  @register_to_config
  def __init__(				self      , _SCREAMING_SNAKE_CASE = 10_00      , _SCREAMING_SNAKE_CASE = None	):





      '''simple docstring'''

      self.set_timesteps(_SCREAMING_SNAKE_CASE	)

      # standard deviation of the initial noise distribution
      lowerCAmelCase 						=							1.0

      # For now we only support F-PNDM, i.e. the runge-kutta method
      # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
      # mainly at formula (9), (12), (13) and the Algorithm 2.
      lowerCAmelCase 						=							4

      # running values
      lowerCAmelCase 						=							[]

  def   _SCREAMING_SNAKE_CASE				(				self      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE = None	):





      '''simple docstring'''

      lowerCAmelCase 						=							num_inference_steps
      lowerCAmelCase 						=							torch.linspace(1      , 0      , num_inference_steps + 1	)[:-1]
      lowerCAmelCase 						=							torch.cat([steps, torch.tensor([0.0]	)]	)

      if self.config.trained_betas is not None:
          lowerCAmelCase 						=							torch.tensor(self.config.trained_betas      , dtype=torch.floataa	)
      else:
          lowerCAmelCase 						=							torch.sin(steps * math.pi / 2	) ** 2

      lowerCAmelCase 						=							(1.0 - self.betas**2) ** 0.5

      lowerCAmelCase 						=							(torch.atana(self.betas      , self.alphas	) / math.pi * 2)[:-1]
      lowerCAmelCase 						=							timesteps.to(_SCREAMING_SNAKE_CASE	)

      lowerCAmelCase 						=							[]

  def   _SCREAMING_SNAKE_CASE				(				self      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE = True      , ):





      '''simple docstring'''

      if self.num_inference_steps is None:
          raise ValueError(
              'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'	)

      lowerCAmelCase 						=							(self.timesteps == timestep).nonzero().item()
      lowerCAmelCase 						=							timestep_index + 1

      lowerCAmelCase 						=							sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
      self.ets.append(_SCREAMING_SNAKE_CASE	)

      if len(self.ets	) == 1:
          lowerCAmelCase 						=							self.ets[-1]
      elif len(self.ets	) == 2:
          lowerCAmelCase 						=							(3 * self.ets[-1] - self.ets[-2]) / 2
      elif len(self.ets	) == 3:
          lowerCAmelCase 						=							(23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
      else:
          lowerCAmelCase 						=							(1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

      lowerCAmelCase 						=							self._get_prev_sample(_SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE	)

      if not return_dict:
          return (prev_sample,)

      return SchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE	)

  def   _SCREAMING_SNAKE_CASE				(				self      , _SCREAMING_SNAKE_CASE      , *_SCREAMING_SNAKE_CASE      , **_SCREAMING_SNAKE_CASE	):





      '''simple docstring'''

      return sample

  def   _SCREAMING_SNAKE_CASE				(				self      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE      , _SCREAMING_SNAKE_CASE	):





      '''simple docstring'''

      lowerCAmelCase 						=							self.alphas[timestep_index]
      lowerCAmelCase 						=							self.betas[timestep_index]

      lowerCAmelCase 						=							self.alphas[prev_timestep_index]
      lowerCAmelCase 						=							self.betas[prev_timestep_index]

      lowerCAmelCase 						=							(sample - sigma * ets) / max(_SCREAMING_SNAKE_CASE      , 1e-8	)
      lowerCAmelCase 						=							next_alpha * pred + ets * next_sigma

      return prev_sample


  def __len__(				self	):





      '''simple docstring'''

      return self.config.num_train_timesteps








'''simple docstring'''



import operator


def       snake_case   (	snake_case      : list					,		snake_case      : bool = False					,		snake_case      : list | None = None			) ->  list:


    """simple docstring"""


    lowerCAmelCase 						=							operator.lt if reverse else operator.gt
    lowerCAmelCase 						=							solution or []

    if not arr:
        return solution

    lowerCAmelCase 						=							[arr.pop(0			)]
    for i, item in enumerate(snake_case			):
        if _operator(snake_case					,		sublist[-1]			):
            sublist.append(snake_case			)
            arr.pop(snake_case			)

    #  merging sublist into solution list
    if not solution:
        solution.extend(snake_case			)
    else:
        while sublist:
            lowerCAmelCase 						=							sublist.pop(0			)
            for i, xx in enumerate(snake_case			):
                if not _operator(snake_case					,		snake_case			):
                    solution.insert(snake_case					,		snake_case			)
                    break
            else:
                solution.append(snake_case			)

    strand_sort(snake_case					,		snake_case					,		snake_case			)
    return solution


if __name__ == "__main__":
     assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
     assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]





