"""simple docstring"""






from __future__ import annotations

__lowerCAmelCase    :       str					     =1_0


def 			UpperCAmelCase__       (				lowerCAmelCase__     :list[int]		) ->    list[int]:
      '''simple docstring'''


      lowercase														=	1
      lowercase														=	max(lowerCAmelCase__		)
      while placement <= max_digit:
            # declare and initialize empty buckets
            lowercase														=	[[] for _ in range(lowerCAmelCase__		)]
            # split list_of_ints between the buckets
            for i in list_of_ints:
                  lowercase														=	int((i / placement) % RADIX		)
                  buckets[tmp].append(lowerCAmelCase__		)
            # put each buckets' contents into list_of_ints
            lowercase														=	0
            for b in range(lowerCAmelCase__		):
                  for i in buckets[b]:
                        lowercase														=	i
                        a += 1
        # move to next
            placement *= RADIX
      return list_of_ints


if __name__ == "__main__":
       import doctest

       doctest.testmod()




"""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						(       lowerCAmelCase  ,    lowerCAmelCase	):
      snake_case__			:   Tuple							  =	1

      @register_to_config
      def __init__(						self		,       __lowerCAmelCase = 1000		,       __lowerCAmelCase = None						):







            """simple docstring"""



            self.set_timesteps(__lowerCAmelCase						)

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

            # running values
            lowercase														=	[]

      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase = None						):







            """simple docstring"""



            lowercase														=	num_inference_steps
            lowercase														=	torch.linspace(1		,       0		,       num_inference_steps + 1						)[:-1]
            lowercase														=	torch.cat([steps, torch.tensor([0.0]						)]						)

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

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

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

            lowercase														=	[]

      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase = 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"""						)

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

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

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

            lowercase														=	self._get_prev_sample(__lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase						)

            if not return_dict:
                  return (prev_sample,)

            return SchedulerOutput(prev_sample=__lowerCAmelCase						)

      def 				A__       (						self		,       __lowerCAmelCase		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            return sample

      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase		,       __lowerCAmelCase						):







            """simple docstring"""



            lowercase														=	self.alphas[timestep_index]
            lowercase														=	self.betas[timestep_index]

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

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

            return prev_sample







      def __len__(						self						):







            """simple docstring"""



            return self.config.num_train_timesteps



