




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 		__A      (			UpperCamelCase__					,						UpperCamelCase__			):
						UpperCamelCase     						=					1

						@register_to_config
						def __init__(		self   :Optional[Any]    , __snake_case   :int = 10_00    , __snake_case   :Optional[Union[np.ndarray, List[float]]] = None ):
										'''simple docstring'''

										self.set_timesteps(__snake_case )

										# standard deviation of the initial noise distribution
										__magic_name__	:	Optional[int]								=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.
										__magic_name__	:	Optional[int]								=4

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

						def     A__						(		self   :Optional[Any]    , __snake_case   :int    , __snake_case   :Union[str, torch.device] = None ):
										'''simple docstring'''

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

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

										__magic_name__	:	Union[str, Any]								=(1.0 - self.betas**2) ** 0.5

										__magic_name__	:	Tuple								=(torch.atana(self.betas    , self.alphas ) / math.pi * 2)[:-1]
										__magic_name__	:	List[Any]								=timesteps.to(__snake_case )

										__magic_name__	:	List[str]								=[]

						def     A__						(		self   :List[Any]    , __snake_case   :torch.FloatTensor    , __snake_case   :int    , __snake_case   :torch.FloatTensor    , __snake_case   :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""" )

										__magic_name__	:	List[Any]								=(self.timesteps == timestep).nonzero().item()
										__magic_name__	:	str								=timestep_index + 1

										__magic_name__	:	Optional[int]								=sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
										self.ets.append(__snake_case )

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

										__magic_name__	:	int								=self._get_prev_sample(__snake_case    , __snake_case    , __snake_case    , __snake_case )

										if not return_dict:
														return (prev_sample,)

										return SchedulerOutput(prev_sample=__snake_case )

						def     A__						(		self   :List[Any]    , __snake_case   :torch.FloatTensor    , *__snake_case   :int    , **__snake_case   :Optional[int] ):
										'''simple docstring'''

										return sample

						def     A__						(		self   :List[str]    , __snake_case   :int    , __snake_case   :List[Any]    , __snake_case   :Optional[int]    , __snake_case   :Any ):
										'''simple docstring'''

										__magic_name__	:	int								=self.alphas[timestep_index]
										__magic_name__	:	Dict								=self.betas[timestep_index]

										__magic_name__	:	Union[str, Any]								=self.alphas[prev_timestep_index]
										__magic_name__	:	Dict								=self.betas[prev_timestep_index]

										__magic_name__	:	List[str]								=(sample - sigma * ets) / max(__snake_case    , 1E-8 )
										__magic_name__	:	Optional[Any]								=next_alpha * pred + ets * next_sigma

										return prev_sample


						def __len__(		self   :List[str] ):
										'''simple docstring'''

										return self.config.num_train_timesteps










from math import pow, sqrt




def 		lowerCAmelCase_   (	*lowerCamelCase   ):
				__magic_name__	:	Tuple								=len(lowerCamelCase   ) > 0 and all(value > 0.0 for value in values   )
				return result




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase   )
				    else ValueError("""Input Error: Molar mass values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(effusion_rate * sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(effusion_rate / sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(molar_mass / pow(effusion_rate_a / effusion_rate_a	,     2   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(pow(effusion_rate_a / effusion_rate_a	,     2   ) / molar_mass	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




