

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_		(	SCREAMING_SNAKE_CASE      ,							SCREAMING_SNAKE_CASE    ):
       _UpperCAmelCase   :  List[str]										=				1
       @register_to_config
       def __init__(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int = 1_0_0_0       ,SCREAMING_SNAKE_CASE__		:      Optional[Union[np.ndarray, List[float]]] = None):
        # set `betas`, `alphas`, `timesteps`
        self.set_timesteps(SCREAMING_SNAKE_CASE__)

        # standard deviation of the initial noise distribution
        __lowerCamelCase    :    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.
        __lowerCamelCase    :    int 	=			4

        # running values
        __lowerCamelCase    :    Tuple 	=			[]
       def    lowerCAmelCase					(		self		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      Union[str, torch.device] = None):
        __lowerCamelCase    :    List[str] 	=			num_inference_steps
        __lowerCamelCase    :    int 	=			torch.linspace(1       ,0       ,num_inference_steps + 1)[:-1]
        __lowerCamelCase    :    Dict 	=			torch.cat([steps, torch.tensor([0.0])])

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

        __lowerCamelCase    :    Optional[int] 	=			(1.0 - self.betas**2) ** 0.5

        __lowerCamelCase    :    Union[str, Any] 	=			(torch.atana(self.betas       ,self.alphas) / math.pi * 2)[:-1]
        __lowerCamelCase    :    Tuple 	=			timesteps.to(SCREAMING_SNAKE_CASE__)

        __lowerCamelCase    :    List[str] 	=			[]
       def    lowerCAmelCase					(		self		:      Tuple       ,SCREAMING_SNAKE_CASE__		:      torch.FloatTensor       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      torch.FloatTensor       ,SCREAMING_SNAKE_CASE__		:      bool = True       ,):
        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    :    Tuple 	=			(self.timesteps == timestep).nonzero().item()
        __lowerCamelCase    :    int 	=			timestep_index + 1

        __lowerCamelCase    :    str 	=			sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
        self.ets.append(SCREAMING_SNAKE_CASE__)

        if len(self.ets) == 1:
         __lowerCamelCase    :    List[Any] 	=			self.ets[-1]
        elif len(self.ets) == 2:
         __lowerCamelCase    :    str 	=			(3 * self.ets[-1] - self.ets[-2]) / 2
        elif len(self.ets) == 3:
         __lowerCamelCase    :    Dict 	=			(2_3 * self.ets[-1] - 1_6 * self.ets[-2] + 5 * self.ets[-3]) / 1_2
        else:
         __lowerCamelCase    :    Optional[Any] 	=			(1 / 2_4) * (5_5 * self.ets[-1] - 5_9 * self.ets[-2] + 3_7 * self.ets[-3] - 9 * self.ets[-4])

        __lowerCamelCase    :    Tuple 	=			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    lowerCAmelCase					(		self		:      Tuple       ,SCREAMING_SNAKE_CASE__		:      torch.FloatTensor       ,*SCREAMING_SNAKE_CASE__		:      Any       ,**SCREAMING_SNAKE_CASE__		:      List[str]):
        return sample
       def    lowerCAmelCase					(		self		:      str       ,SCREAMING_SNAKE_CASE__		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      List[Any]):
        __lowerCamelCase    :    Any 	=			self.alphas[timestep_index]
        __lowerCamelCase    :    Dict 	=			self.betas[timestep_index]

        __lowerCamelCase    :    Optional[int] 	=			self.alphas[prev_timestep_index]
        __lowerCamelCase    :    str 	=			self.betas[prev_timestep_index]

        __lowerCamelCase    :    Any 	=			(sample - sigma * ets) / max(SCREAMING_SNAKE_CASE__       ,1E-8)
        __lowerCamelCase    :    Tuple 	=			next_alpha * pred + ets * next_sigma

        return prev_sample


       def __len__(		self		:      Union[str, Any]):
        return self.config.num_train_timesteps







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__      )  ->					bool:
	if len(lowerCamelCase__      ) == 0:
		return False
	__lowerCamelCase    :    List[Any] 	=			len(lowerCamelCase__      ) // 2
	if a_list[midpoint] == item:
		return True
	if item < a_list[midpoint]:
		return binary_search(a_list[:midpoint]     ,			lowerCamelCase__      )
	else:
		return binary_search(a_list[midpoint + 1 :]     ,			lowerCamelCase__      )


if __name__ == "__main__":
					a		=input("""Enter numbers separated by comma:\n""").strip()
					a		=[int(item.strip()) for item in user_input.split(""",""")]
					a		=int(input("""Enter the number to be found in the list:\n""").strip())
					a		="""""" if binary_search(sequence, target) else """not """
					print(F"""{target} was {not_str}found in {sequence}""")




