

"""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      __lowercase			(    __lowerCamelCase	,			__lowerCamelCase					):
  snake_case_				       =       1

  @register_to_config
  def __init__(  self		:			Any					,A		:			int = 1_000					,A		:			Optional[Union[np.ndarray, List[float]]] = None    ):






   '''simple docstring'''
   # set `betas`, `alphas`, `timesteps`
   self.set_timesteps(A    )

   # standard deviation of the initial noise distribution
   UpperCAmelCase__					:  Optional[Any]					   =					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.
   UpperCAmelCase__					:  List[Any]					   =					4

   # running values
   UpperCAmelCase__					:  List[Any]					   =					[]

  def    __lowercase       (  self		:			str					,A		:			int					,A		:			Union[str, torch.device] = None    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Union[str, Any]					   =					num_inference_steps
   UpperCAmelCase__					:  Dict					   =					torch.linspace(1					,0					,num_inference_steps + 1    )[:-1]
   UpperCAmelCase__					:  List[str]					   =					torch.cat([steps, torch.tensor([0.0]    )]    )

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

   UpperCAmelCase__					:  str					   =					(1.0 - self.betas**2) ** 0.5

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

   UpperCAmelCase__					:  Union[str, Any]					   =					[]

  def    __lowercase       (  self		:			Optional[int]					,A		:			torch.FloatTensor					,A		:			int					,A		:			torch.FloatTensor					,A		:			bool = 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"""    )

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

   UpperCAmelCase__					:  int					   =					sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
   self.ets.append(A    )

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

   UpperCAmelCase__					:  Union[str, Any]					   =					self._get_prev_sample(A					,A					,A					,A    )

   if not return_dict:
    return (prev_sample,)

   return SchedulerOutput(prev_sample=A    )

  def    __lowercase       (  self		:			List[str]					,A		:			torch.FloatTensor					,*A		:			Optional[int]					,**A		:			List[Any]    ):






   '''simple docstring'''
   return sample

  def    __lowercase       (  self		:			Union[str, Any]					,A		:			Tuple					,A		:			Union[str, Any]					,A		:			Optional[Any]					,A		:			Dict    ):






   '''simple docstring'''
   UpperCAmelCase__					:  int					   =					self.alphas[timestep_index]
   UpperCAmelCase__					:  Tuple					   =					self.betas[timestep_index]

   UpperCAmelCase__					:  List[str]					   =					self.alphas[prev_timestep_index]
   UpperCAmelCase__					:  List[str]					   =					self.betas[prev_timestep_index]

   UpperCAmelCase__					:  List[str]					   =					(sample - sigma * ets) / max(A					,1e-8    )
   UpperCAmelCase__					:  List[str]					   =					next_alpha * pred + ets * next_sigma

   return prev_sample




  def __len__(  self		:			Optional[int]    ):






   '''simple docstring'''
   return self.config.num_train_timesteps








"""simple docstring"""




def   lowerCAmelCase						(					__UpperCamelCase = 1000      ):
 '''simple docstring'''





 return sum(2 * a * ((a - 1) // 2) for a in range(3							,    n + 1      )      )


if __name__ == "__main__":
      print(solution())





