
'''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		(   UpperCamelCase_    ,   UpperCamelCase_):
					_lowerCAmelCase			     =	1
					@register_to_config
					def __init__(     self,    A = 1000,    A = None      ):

									"""simple docstring"""


									self.set_timesteps(UpperCamelCase__      )

									# standard deviation of the initial noise distribution
									lowerCamelCase					:			str									= 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					:			Tuple									= 4

									# running values
									lowerCamelCase					:			int									= []
					def     UpperCAmelCase_							(     self,    A,    A = None      ):

									"""simple docstring"""


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

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

									lowerCamelCase					:			Dict									= (1.0 - self.betas**2) ** 0.5

									lowerCamelCase					:			Optional[Any]									= (torch.atana(self.betas,    self.alphas      ) / math.pi * 2)[:-1]
									lowerCamelCase					:			List[str]									= timesteps.to(UpperCamelCase__      )

									lowerCamelCase					:			Any									= []
					def     UpperCAmelCase_							(     self,    A,    A,    A,    A = 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					:			Optional[int]									= (self.timesteps == timestep).nonzero().item()
									lowerCamelCase					:			Union[str, Any]									= timestep_index + 1

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

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

									lowerCamelCase					:			Optional[int]									= self._get_prev_sample(UpperCamelCase__,    UpperCamelCase__,    UpperCamelCase__,    UpperCamelCase__      )

									if not return_dict:
													return (prev_sample,)

									return SchedulerOutput(prev_sample=UpperCamelCase__      )
					def     UpperCAmelCase_							(     self,    A,    *A,    **A      ):

									"""simple docstring"""


									return sample
					def     UpperCAmelCase_							(     self,    A,    A,    A,    A      ):

									"""simple docstring"""


									lowerCamelCase					:			Any									= self.alphas[timestep_index]
									lowerCamelCase					:			List[str]									= self.betas[timestep_index]

									lowerCamelCase					:			Union[str, Any]									= self.alphas[prev_timestep_index]
									lowerCamelCase					:			Tuple									= self.betas[prev_timestep_index]

									lowerCamelCase					:			Dict									= (sample - sigma * ets) / max(UpperCamelCase__,    1e-8      )
									lowerCamelCase					:			Optional[Any]									= next_alpha * pred + ets * next_sigma

									return prev_sample




					def __len__(     self      ):

									"""simple docstring"""


									return self.config.num_train_timesteps







'''simple docstring'''






def    UpperCAmelCase							(  UpperCAmelCase__							:							int = 10_00):
				lowerCamelCase					:			Optional[Any]									= 2**power
				lowerCamelCase					:			str									= str(UpperCAmelCase__)
				lowerCamelCase					:			Union[str, Any]									= list(UpperCAmelCase__)
				lowerCamelCase					:			Optional[Any]									= 0

				for i in list_num:
								sum_of_num += int(UpperCAmelCase__)

				return sum_of_num


if __name__ == "__main__":
					A			      =      int(input('Enter the power of 2: ').strip())
					print('2 ^ ', power, ' = ', 2**power)
					A			      =      solution(power)
					print('Sum of the digits is: ', result)
