





"""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  _SCREAMING_SNAKE_CASE(       UpperCAmelCase__   ,     UpperCAmelCase__  ):
       SCREAMING_SNAKE_CASE_       :				int     						=  1




       @register_to_config
       def __init__(						self		,SCREAMING_SNAKE_CASE__ = 10_00		,SCREAMING_SNAKE_CASE__ = None							)      ->				Tuple:





             """simple docstring"""






             self.set_timesteps(_SCREAMING_SNAKE_CASE							)

             # standard deviation of the initial noise distribution
             __SCREAMING_SNAKE_CASE       :Tuple		    =  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.
             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  4

             # running values
             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  []




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)      ->				Optional[Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Dict		    =  num_inference_steps
             __SCREAMING_SNAKE_CASE       :List[str]		    =  torch.linspace(1		,0		,num_inference_steps + 1							)[:-1]
             __SCREAMING_SNAKE_CASE       :Any		    =  torch.cat([steps, torch.tensor([0.0]							)]							)

             if self.config.trained_betas is not None:
                   __SCREAMING_SNAKE_CASE       :Any		    =  torch.tensor(self.config.trained_betas		,dtype=torch.floataa							)
             else:
                   __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  torch.sin(steps * math.pi / 2							) ** 2

             __SCREAMING_SNAKE_CASE       :List[str]		    =  (1.0 - self.betas**2) ** 0.5

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

             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  []




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = True		,)      ->				Union[SchedulerOutput, Tuple]:





             """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'''							)

             __SCREAMING_SNAKE_CASE       :Dict		    =  (self.timesteps == timestep).nonzero().item()
             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  timestep_index + 1

             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
             self.ets.append(_SCREAMING_SNAKE_CASE							)

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

             __SCREAMING_SNAKE_CASE       :Dict		    =  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    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,*SCREAMING_SNAKE_CASE__		,**SCREAMING_SNAKE_CASE__							)      ->				torch.FloatTensor:





             """simple docstring"""






             return sample




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)      ->				Tuple:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :List[Any]		    =  self.alphas[timestep_index]
             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  self.betas[timestep_index]

             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  self.alphas[prev_timestep_index]
             __SCREAMING_SNAKE_CASE       :Optional[int]		    =  self.betas[prev_timestep_index]

             __SCREAMING_SNAKE_CASE       :str		    =  (sample - sigma * ets) / max(_SCREAMING_SNAKE_CASE		,1E-8							)
             __SCREAMING_SNAKE_CASE       :Dict		    =  next_alpha * pred + ets * next_sigma

             return prev_sample




       def __len__(						self							)      ->				Union[str, Any]:





             """simple docstring"""






             return self.config.num_train_timesteps






"""simple docstring"""
from __future__ import annotations

import math



def 					__lowerCamelCase       (							a_					:		int			,       a_					:		int			,       a_					:		bool			,       a_					:		list[int]			,       a_					:		float							)      ->				int:

      if depth < 0:
            raise ValueError('''Depth cannot be less than 0'''							)

      if len(a_							) == 0:
            raise ValueError('''Scores cannot be empty'''							)

      if depth == height:
            return scores[node_index]

      if is_max:
            return max(
                minimax(depth + 1			,       node_index * 2			,       a_			,       a_			,       a_							)			,       minimax(depth + 1			,       node_index * 2 + 1			,       a_			,       a_			,       a_							)			,       )

      return min(
          minimax(depth + 1			,       node_index * 2			,       a_			,       a_			,       a_							)			,       minimax(depth + 1			,       node_index * 2 + 1			,       a_			,       a_			,       a_							)			,       )



def 					__lowerCamelCase       (							)      ->				None:
      __SCREAMING_SNAKE_CASE       :Dict		    =  [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
      __SCREAMING_SNAKE_CASE       :Optional[int]		    =  math.log(len(a_							)			,       2							)
      print('''Optimal value : '''			,       end=''''''							)
      print(minimax(0			,       0			,       a_			,       a_			,       a_							)							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()