'''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 			__lowercase		(						__lowerCamelCase			,							__lowerCamelCase						):







     """simple docstring"""






     SCREAMING_SNAKE_CASE__		   =						1







     @register_to_config
     def __init__(		self     ,			_lowerCamelCase = 1_0_0_0     ,			_lowerCamelCase = None    ):
         # set `betas`, `alphas`, `timesteps`
         self.set_timesteps(UpperCamelCase_    )

         # standard deviation of the initial noise distribution
         __UpperCamelCase	:	Optional[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	:	List[str]		    =  []







     def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			_lowerCamelCase = None    ):
         __UpperCamelCase	:	List[str]		    =  num_inference_steps
         __UpperCamelCase	:	int		    =  torch.linspace(1     ,			0     ,			num_inference_steps + 1    )[:-1]
         __UpperCamelCase	:	List[str]		    =  torch.cat([steps, torch.tensor([0.0]    )]    )

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

         __UpperCamelCase	:	List[str]		    =  (1.0 - self.betas**2) ** 0.5

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

         __UpperCamelCase	:	Dict		    =  []







     def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase = 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	:	Dict		    =  (self.timesteps == timestep).nonzero().item()
         __UpperCamelCase	:	Union[str, Any]		    =  timestep_index + 1

         __UpperCamelCase	:	List[Any]		    =  sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
         self.ets.append(UpperCamelCase_    )

         if len(self.ets    ) == 1:
             __UpperCamelCase	:	Dict		    =  self.ets[-1]
         elif len(self.ets    ) == 2:
             __UpperCamelCase	:	Union[str, Any]		    =  (3 * self.ets[-1] - self.ets[-2]) / 2
         elif len(self.ets    ) == 3:
             __UpperCamelCase	:	Dict		    =  (2_3 * self.ets[-1] - 1_6 * self.ets[-2] + 5 * self.ets[-3]) / 1_2
         else:
             __UpperCamelCase	:	List[Any]		    =  (1 / 2_4) * (5_5 * self.ets[-1] - 5_9 * self.ets[-2] + 3_7 * self.ets[-3] - 9 * self.ets[-4])

         __UpperCamelCase	:	Union[str, Any]		    =  self._get_prev_sample(UpperCamelCase_     ,			UpperCamelCase_     ,			UpperCamelCase_     ,			UpperCamelCase_    )

         if not return_dict:
             return (prev_sample,)

         return SchedulerOutput(prev_sample=UpperCamelCase_    )







     def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			*_lowerCamelCase     ,			**_lowerCamelCase    ):
         return sample







     def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase    ):
         __UpperCamelCase	:	List[str]		    =  self.alphas[timestep_index]
         __UpperCamelCase	:	Optional[Any]		    =  self.betas[timestep_index]

         __UpperCamelCase	:	Dict		    =  self.alphas[prev_timestep_index]
         __UpperCamelCase	:	Optional[int]		    =  self.betas[prev_timestep_index]

         __UpperCamelCase	:	List[Any]		    =  (sample - sigma * ets) / max(UpperCamelCase_     ,			1E-8    )
         __UpperCamelCase	:	Union[str, Any]		    =  next_alpha * pred + ets * next_sigma

         return prev_sample







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




'''simple docstring'''
class 			__lowercase		:







     """simple docstring"""






     def __init__(		self    ):
         __UpperCamelCase	:	Any		    =  0
         __UpperCamelCase	:	Any		    =  0
         __UpperCamelCase	:	Any		    =  {}







     def lowerCAmelCase     (		self     ,			_lowerCamelCase    ):
         if vertex not in self.adjacency:
             __UpperCamelCase	:	Tuple		    =  {}
             self.num_vertices += 1







     def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase    ):
         self.add_vertex(_lowerCamelCase    )
         self.add_vertex(_lowerCamelCase    )

         if head == tail:
             return

         __UpperCamelCase	:	List[Any]		    =  weight
         __UpperCamelCase	:	Optional[int]		    =  weight







     def lowerCAmelCase     (		self    ):
         __UpperCamelCase	:	List[str]		    =  self.get_edges()
         for edge in edges:
             __UpperCamelCase    ,					__UpperCamelCase    ,					__UpperCamelCase	:	Optional[int]		    =  edge
             edges.remove((tail, head, weight)    )
         for i in range(len(_lowerCamelCase    )    ):
             __UpperCamelCase	:	Union[str, Any]		    =  list(edges[i]    )

         edges.sort(key=lambda _lowerCamelCase    : e[2]    )
         for i in range(len(_lowerCamelCase    ) - 1    ):
             if edges[i][2] >= edges[i + 1][2]:
                 __UpperCamelCase	:	Optional[int]		    =  edges[i][2] + 1
         for edge in edges:
             __UpperCamelCase    ,					__UpperCamelCase    ,					__UpperCamelCase	:	Optional[int]		    =  edge
             __UpperCamelCase	:	Tuple		    =  weight
             __UpperCamelCase	:	Optional[Any]		    =  weight







     def __str__(		self    ):
         __UpperCamelCase	:	Optional[Any]		    =  ''
         for tail in self.adjacency:
             for head in self.adjacency[tail]:
                 __UpperCamelCase	:	Tuple		    =  self.adjacency[head][tail]
                 string += f"""{head} -> {tail} == {weight}\n"""
         return string.rstrip('\n'    )







     def lowerCAmelCase     (		self    ):
         __UpperCamelCase	:	Any		    =  []
         for tail in self.adjacency:
             for head in self.adjacency[tail]:
                 output.append((tail, head, self.adjacency[head][tail])    )
         return output







     def lowerCAmelCase     (		self    ):
         return self.adjacency.keys()







     @staticmethod
     def lowerCAmelCase     (		_lowerCamelCase=None     ,			_lowerCamelCase=None    ):
         __UpperCamelCase	:	Tuple		    =  Graph()
         if vertices is None:
             __UpperCamelCase	:	List[Any]		    =  []
         if edges is None:
             __UpperCamelCase	:	Optional[int]		    =  []
         for vertex in vertices:
             g.add_vertex(_lowerCamelCase    )
         for edge in edges:
             g.add_edge(*_lowerCamelCase    )
         return g






     class 			__lowercase		:







          """simple docstring"""






          def __init__(		self    ):
              __UpperCamelCase	:	Union[str, Any]		    =  {}
              __UpperCamelCase	:	int		    =  {}







          def __len__(		self    ):
              return len(self.parent    )







          def lowerCAmelCase     (		self     ,			_lowerCamelCase    ):
              if item in self.parent:
                  return self.find(_lowerCamelCase    )

              __UpperCamelCase	:	Optional[Any]		    =  item
              __UpperCamelCase	:	List[str]		    =  0
              return item







          def lowerCAmelCase     (		self     ,			_lowerCamelCase    ):
              if item not in self.parent:
                  return self.make_set(_lowerCamelCase    )
              if item != self.parent[item]:
                  __UpperCamelCase	:	int		    =  self.find(self.parent[item]    )
              return self.parent[item]







          def lowerCAmelCase     (		self     ,			_lowerCamelCase     ,			_lowerCamelCase    ):
              __UpperCamelCase	:	Tuple		    =  self.find(_lowerCamelCase    )
              __UpperCamelCase	:	Any		    =  self.find(_lowerCamelCase    )

              if roota == roota:
                  return roota

              if self.rank[roota] > self.rank[roota]:
                  __UpperCamelCase	:	Dict		    =  roota
                  return roota

              if self.rank[roota] < self.rank[roota]:
                  __UpperCamelCase	:	Optional[Any]		    =  roota
                  return roota

              if self.rank[roota] == self.rank[roota]:
                  self.rank[roota] += 1
                  __UpperCamelCase	:	Dict		    =  roota
                  return roota
              return None







     @staticmethod
     def lowerCAmelCase     (		_lowerCamelCase    ):
         __UpperCamelCase	:	int		    =  graph.num_vertices

         __UpperCamelCase	:	str		    =  Graph.UnionFind()
         __UpperCamelCase	:	Tuple		    =  []
         while num_components > 1:
             __UpperCamelCase	:	Dict		    =  {}
             for vertex in graph.get_vertices():
                 __UpperCamelCase	:	str		    =  -1

             __UpperCamelCase	:	int		    =  graph.get_edges()
             for edge in edges:
                 __UpperCamelCase    ,					__UpperCamelCase    ,					__UpperCamelCase	:	List[str]		    =  edge
                 edges.remove((tail, head, weight)    )
             for edge in edges:
                 __UpperCamelCase    ,					__UpperCamelCase    ,					__UpperCamelCase	:	Dict		    =  edge
                 __UpperCamelCase	:	List[Any]		    =  union_find.find(_lowerCamelCase    )
                 __UpperCamelCase	:	str		    =  union_find.find(_lowerCamelCase    )
                 if seta != seta:
                     if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
                         __UpperCamelCase	:	str		    =  [head, tail, weight]

                     if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
                         __UpperCamelCase	:	str		    =  [head, tail, weight]
             for vertex in cheap_edge:
                 if cheap_edge[vertex] != -1:
                     __UpperCamelCase    ,					__UpperCamelCase    ,					__UpperCamelCase	:	List[str]		    =  cheap_edge[vertex]
                     if union_find.find(_lowerCamelCase    ) != union_find.find(_lowerCamelCase    ):
                         union_find.union(_lowerCamelCase     ,			_lowerCamelCase    )
                         mst_edges.append(cheap_edge[vertex]    )
                         __UpperCamelCase	:	int		    =  num_components - 1
         __UpperCamelCase	:	Union[str, Any]		    =  Graph.build(edges=_lowerCamelCase    )
         return mst



