'''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        __A      ( UpperCamelCase_		,	UpperCamelCase_	):
    a__       :						str          =  1



    @register_to_config
    def __init__(self    :    Any   ,			__a    :    int = 1000   ,			__a    :    Optional[Union[np.ndarray, List[float]]] = None ):
         # set `betas`, `alphas`, `timesteps`
         self.set_timesteps(A_ )

         # standard deviation of the initial noise distribution
         UpperCAmelCase_           =   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_           =   4

         # running values
         UpperCAmelCase_           =   []



    def 					_lowercase						(self    :    Optional[Any]   ,			__a    :    int   ,			__a    :    Union[str, torch.device] = None ):
         UpperCAmelCase_           =   num_inference_steps
         UpperCAmelCase_           =   torch.linspace(1   ,			0   ,			num_inference_steps + 1 )[:-1]
         UpperCAmelCase_           =   torch.cat([steps, torch.tensor([0.0] )] )

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

         UpperCAmelCase_           =   (1.0 - self.betas**2) ** 0.5

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

         UpperCAmelCase_           =   []



    def 					_lowercase						(self    :    str   ,			__a    :    torch.FloatTensor   ,			__a    :    int   ,			__a    :    torch.FloatTensor   ,			__a    :    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" )

         UpperCAmelCase_           =   (self.timesteps == timestep).nonzero().item()
         UpperCAmelCase_           =   timestep_index + 1

         UpperCAmelCase_           =   sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
         self.ets.append(A_ )

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

         UpperCAmelCase_           =   self._get_prev_sample(A_   ,			A_   ,			A_   ,			A_ )

         if not return_dict:
              return (prev_sample,)

         return SchedulerOutput(prev_sample=A_ )



    def 					_lowercase						(self    :    Dict   ,			__a    :    torch.FloatTensor   ,			*__a    :    Optional[int]   ,			**__a    :    Tuple ):
         return sample



    def 					_lowercase						(self    :    List[str]   ,			__a    :    List[Any]   ,			__a    :    int   ,			__a    :    Any   ,			__a    :    Optional[int] ):
         UpperCAmelCase_           =   self.alphas[timestep_index]
         UpperCAmelCase_           =   self.betas[timestep_index]

         UpperCAmelCase_           =   self.alphas[prev_timestep_index]
         UpperCAmelCase_           =   self.betas[prev_timestep_index]

         UpperCAmelCase_           =   (sample - sigma * ets) / max(A_   ,			1E-8 )
         UpperCAmelCase_           =   next_alpha * pred + ets * next_sigma

         return prev_sample






    def __len__(self    :    int ):
         return self.config.num_train_timesteps









import string


def 			UpperCamelCase(  __UpperCamelCase							:		str ):
		for key in range(len(string.ascii_uppercase ) ):
				lowerCAmelCase_			:     List[Any]									= ''''''
				for symbol in message:
						if symbol in string.ascii_uppercase:
								lowerCAmelCase_			:     Optional[int]									= string.ascii_uppercase.find(__UpperCamelCase )
								lowerCAmelCase_			:     Optional[int]									= num - key
								if num < 0:
										lowerCAmelCase_			:     int									= num + len(string.ascii_uppercase )
								lowerCAmelCase_			:     int									= translated + string.ascii_uppercase[num]
						else:
								lowerCAmelCase_			:     Optional[int]									= translated + symbol
				print(f"""Decryption using Key #{key}: {translated}""" )


def 			UpperCamelCase(  ):
		lowerCAmelCase_			:     Dict									= input('''Encrypted message: ''' )
		lowerCAmelCase_			:     List[str]									= message.upper()
		decrypt(__UpperCamelCase )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





