
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   (   SCREAMING_SNAKE_CASE__					,							SCREAMING_SNAKE_CASE__				):







							'''simple docstring'''

							lowerCAmelCase_ 						=						1

							@register_to_config
							def __init__(self  ,  UpperCAmelCase = 1000  ,  UpperCAmelCase = None  )					->       Any:
														self.set_timesteps(a_  )

														# standard deviation of the initial noise distribution
														_snake_case       =  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.
														_snake_case       =  4

														# running values
														_snake_case       =  []

							def 	lowercase							(self  ,  UpperCAmelCase  ,  UpperCAmelCase = None  )					->       str:
														_snake_case       =  num_inference_steps
														_snake_case       =  torch.linspace(1  ,  0  ,  num_inference_steps + 1  )[:-1]
														_snake_case       =  torch.cat([steps, torch.tensor([0.0]  )]  )

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

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

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

														_snake_case       =  []

							def 	lowercase							(self  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase = True  ,  )					->       Tuple:



														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"""  )

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

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

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

														_snake_case       =  self._get_prev_sample(a_  ,  a_  ,  a_  ,  a_  )

														if not return_dict:
																					return (prev_sample,)

														return SchedulerOutput(prev_sample=a_  )

							def 	lowercase							(self  ,  UpperCAmelCase  ,  *UpperCAmelCase  ,  **UpperCAmelCase  )					->       int:
														return sample

							def 	lowercase							(self  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase  )					->       Optional[Any]:
														_snake_case       =  self.alphas[timestep_index]
														_snake_case       =  self.betas[timestep_index]

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

														_snake_case       =  (sample - sigma * ets) / max(a_  ,  1e-8  )
														_snake_case       =  next_alpha * pred + ets * next_sigma

														return prev_sample





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

'''simple docstring'''
def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):

							if not (isinstance(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				) and isinstance(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)):
														raise ValueError("""longest_common_substring() takes two strings for inputs"""				)

							_snake_case       =  len(_SCREAMING_SNAKE_CASE				)
							_snake_case       =  len(_SCREAMING_SNAKE_CASE				)

							_snake_case       =  [[0] * (texta_length + 1) for _ in range(texta_length + 1				)]
							_snake_case       =  0
							_snake_case       =  0

							for i in range(1							, texta_length + 1				):
														for j in range(1							, texta_length + 1				):
																					if texta[i - 1] == texta[j - 1]:
																												_snake_case       =  1 + dp[i - 1][j - 1]
																												if dp[i][j] > ans_length:
																																			_snake_case       =  i
																																			_snake_case       =  dp[i][j]

							return texta[ans_index - ans_length : ans_index]


if __name__ == "__main__":
				import doctest

				doctest.testmod()