'''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 	lowerCamelCase_	(snake_case__							, snake_case__    ):
      '''simple docstring'''

      __UpperCamelCase:  Optional[Any]						=						1




      @register_to_config
      def __init__(       self						:				Optional[int]						,					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     :  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.
             _UpperCAmelCase     :  int							      =    4

             # running values
             _UpperCAmelCase     :  Dict							      =    []




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

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

             _UpperCAmelCase     :  List[Any]							      =    (1.0 - self.betas**2) ** 0.5

             _UpperCAmelCase     :  List[str]							      =    (torch.atana(self.betas						,					self.alphas       ) / math.pi * 2)[:-1]
             _UpperCAmelCase     :  Dict							      =    timesteps.to(A       )

             _UpperCAmelCase     :  Dict							      =    []




      def      _A	(       self						:				Optional[int]						,					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     :  Tuple							      =    (self.timesteps == timestep).nonzero().item()
             _UpperCAmelCase     :  Optional[Any]							      =    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     :  str							      =    (3 * self.ets[-1] - self.ets[-2]) / 2
             elif len(self.ets       ) == 3:
                    _UpperCAmelCase     :  Tuple							      =    (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
             else:
                    _UpperCAmelCase     :  Union[str, 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      _A	(       self						:				Union[str, Any]						,					A						:				torch.FloatTensor						,					*A						:				Union[str, Any]						,					**A						:				Dict       ):
             return sample




      def      _A	(       self						:				Optional[Any]						,					A						:				Optional[int]						,					A						:				int						,					A						:				Optional[Any]						,					A						:				List[str]       ):
             _UpperCAmelCase     :  List[str]							      =    self.alphas[timestep_index]
             _UpperCAmelCase     :  List[Any]							      =    self.betas[timestep_index]

             _UpperCAmelCase     :  Optional[Any]							      =    self.alphas[prev_timestep_index]
             _UpperCAmelCase     :  Dict							      =    self.betas[prev_timestep_index]

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

             return prev_sample





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


'''simple docstring'''




def 	UpperCamelCase_							(					_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      str    )    ->    float:


       """simple docstring"""







       def get_matched_characters(_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      str    ) -> str:
              _UpperCAmelCase     :  Tuple							      =    []
              _UpperCAmelCase     :  Dict							      =    min(len(_stra    )			,	len(_stra    )    ) // 2
              for i, l in enumerate(_stra    ):
                     _UpperCAmelCase     :  int							      =    int(max(0			,	i - limit    )    )
                     _UpperCAmelCase     :  Any							      =    int(min(i + limit + 1			,	len(_stra    )    )    )
                     if l in _stra[left:right]:
                            matched.append(_UpperCAmelCase    )
                            _UpperCAmelCase     :  List[Any]							      =    F"""{_stra[0:_stra.index(_UpperCAmelCase    )]} {_stra[_stra.index(_UpperCAmelCase    ) + 1:]}"""

              return "".join(_UpperCAmelCase    )

       # matching characters
       _UpperCAmelCase     :  Union[str, Any]							      =    get_matched_characters(_UpperCAmelCase			,	_UpperCAmelCase    )
       _UpperCAmelCase     :  Tuple							      =    get_matched_characters(_UpperCAmelCase			,	_UpperCAmelCase    )
       _UpperCAmelCase     :  Tuple							      =    len(_UpperCAmelCase    )

       # transposition
       _UpperCAmelCase     :  Optional[Any]							      =    (
           len([(ca, ca) for ca, ca in zip(_UpperCAmelCase			,	_UpperCAmelCase    ) if ca != ca]    ) // 2
       )

       if not match_count:
              _UpperCAmelCase     :  Dict							      =    0.0
       else:
              _UpperCAmelCase     :  Optional[int]							      =    (
                  1
                  / 3
                  * (
                      match_count / len(_UpperCAmelCase    )
                      + match_count / len(_UpperCAmelCase    )
                      + (match_count - transpositions) / match_count
                  )
              )

       # common prefix up to 4 characters
       _UpperCAmelCase     :  str							      =    0
       for ca, ca in zip(stra[:4]			,	stra[:4]    ):
              if ca == ca:
                     prefix_len += 1
              else:
                     break

       return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(jaro_winkler("""hello""", """world"""))

