




"""simple docstring"""






class   a__			:





						def __init__(							self      :	List[Any])						->       Dict:




											"""simple docstring"""







											_lowerCAmelCase:Optional[int]									=  0
											_lowerCAmelCase:Optional[Any]									=  0
											_lowerCAmelCase:Dict									=  {}





						def       __UpperCamelCase     (							self      :	List[str]     ,a__      :	int)						->       Tuple:




											"""simple docstring"""







											if vertex not in self.adjacency:
																_lowerCAmelCase:Union[str, Any]									=  {}
																self.num_vertices += 1





						def       __UpperCamelCase     (							self      :	List[str]     ,a__      :	Dict     ,a__      :	List[Any]     ,a__      :	Any)						->       List[Any]:




											"""simple docstring"""







											self.add_vertex(__lowerCamelCase)
											self.add_vertex(__lowerCamelCase)

											if head == tail:
																return

											_lowerCAmelCase:Tuple									=  weight
											_lowerCAmelCase:Optional[Any]									=  weight





						def       __UpperCamelCase     (							self      :	Union[str, Any])						->       Union[str, Any]:




											"""simple docstring"""







											_lowerCAmelCase:Union[str, Any]									=  self.get_edges()
											for edge in edges:
																_lowerCAmelCase:Union[str, Any]									=  edge
																edges.remove((tail, head, weight))
											for i in range(len(__lowerCamelCase)):
																_lowerCAmelCase:Optional[Any]									=  list(edges[i])

											edges.sort(key=lambda a__: e[2])
											for i in range(len(__lowerCamelCase) - 1):
																if edges[i][2] >= edges[i + 1][2]:
																					_lowerCAmelCase:str									=  edges[i][2] + 1
											for edge in edges:
																_lowerCAmelCase:Dict									=  edge
																_lowerCAmelCase:List[str]									=  weight
																_lowerCAmelCase:Union[str, Any]									=  weight





						def __str__(							self      :	Tuple)						->       int:




											"""simple docstring"""







											_lowerCAmelCase:Tuple									=  ""
											for tail in self.adjacency:
																for head in self.adjacency[tail]:
																					_lowerCAmelCase:Dict									=  self.adjacency[head][tail]
																					string += F'{head} -> {tail} == {weight}\n'
											return string.rstrip('''\n''')





						def       __UpperCamelCase     (							self      :	Tuple)						->       Any:




											"""simple docstring"""







											_lowerCAmelCase:Optional[int]									=  []
											for tail in self.adjacency:
																for head in self.adjacency[tail]:
																					output.append((tail, head, self.adjacency[head][tail]))
											return output





						def       __UpperCamelCase     (							self      :	Optional[Any])						->       Union[str, Any]:




											"""simple docstring"""







											return self.adjacency.keys()





						@staticmethod
						def       __UpperCamelCase     (							a__      :	Tuple=None     ,a__      :	Optional[int]=None)						->       Any:




											"""simple docstring"""







											_lowerCAmelCase:int									=  Graph()
											if vertices is None:
																_lowerCAmelCase:int									=  []
											if edges is None:
																_lowerCAmelCase:Any									=  []
											for vertex in vertices:
																g.add_vertex(__lowerCamelCase)
											for edge in edges:
																g.add_edge(*__lowerCamelCase)
											return g




						class   a__			:





												def __init__(							self      :	str)						->       Optional[int]:




																	"""simple docstring"""







																	_lowerCAmelCase:Tuple									=  {}
																	_lowerCAmelCase:Optional[Any]									=  {}





												def __len__(							self      :	Dict)						->       Tuple:




																	"""simple docstring"""







																	return len(self.parent)





												def       __UpperCamelCase     (							self      :	List[Any]     ,a__      :	List[str])						->       Union[str, Any]:




																	"""simple docstring"""







																	if item in self.parent:
																						return self.find(__lowerCamelCase)

																	_lowerCAmelCase:Union[str, Any]									=  item
																	_lowerCAmelCase:List[str]									=  0
																	return item





												def       __UpperCamelCase     (							self      :	int     ,a__      :	List[str])						->       Optional[int]:




																	"""simple docstring"""







																	if item not in self.parent:
																						return self.make_set(__lowerCamelCase)
																	if item != self.parent[item]:
																						_lowerCAmelCase:Any									=  self.find(self.parent[item])
																	return self.parent[item]







												def       __UpperCamelCase     (							self      :	List[Any]     ,a__      :	int     ,a__      :	Dict)						->       int:




																	"""simple docstring"""







																	_lowerCAmelCase:int									=  self.find(__lowerCamelCase)
																	_lowerCAmelCase:int									=  self.find(__lowerCamelCase)

																	if roota == roota:
																						return roota

																	if self.rank[roota] > self.rank[roota]:
																						_lowerCAmelCase:int									=  roota
																						return roota

																	if self.rank[roota] < self.rank[roota]:
																						_lowerCAmelCase:Union[str, Any]									=  roota
																						return roota

																	if self.rank[roota] == self.rank[roota]:
																						self.rank[roota] += 1
																						_lowerCAmelCase:Any									=  roota
																						return roota
																	return None





						@staticmethod
						def       __UpperCamelCase     (							a__      :	Any)						->       str:




											"""simple docstring"""







											_lowerCAmelCase:Any									=  graph.num_vertices

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

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

																										if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																															_lowerCAmelCase:List[Any]									=  [head, tail, weight]
																for vertex in cheap_edge:
																					if cheap_edge[vertex] != -1:
																										_lowerCAmelCase: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])
																															_lowerCAmelCase:int									=  num_components - 1
											_lowerCAmelCase:Union[str, Any]									=  Graph.build(edges=__lowerCamelCase)
											return mst












"""simple docstring"""






# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin




class   a__			(       UpperCamelCase_					,	UpperCamelCase_  ):
						snake_case__             = 1





						@register_to_config
						def __init__(							self      :	Union[str, Any]     ,a__      :	List[str]=2000     ,a__      :	Tuple=0.1     ,a__      :	Union[str, Any]=20     ,a__      :	int=1E-3)						->       Any:




											"""simple docstring"""







											_lowerCAmelCase:Optional[Any]									=  None
											_lowerCAmelCase:List[Any]									=  None
											_lowerCAmelCase:Dict									=  None





						def       __UpperCamelCase     (							self      :	int     ,a__      :	Any     ,a__      :	Union[str, torch.device] = None)						->       List[str]:




											"""simple docstring"""







											_lowerCAmelCase:str									=  torch.linspace(1     ,self.config.sampling_eps     ,a__     ,device=a__)





						def       __UpperCamelCase     (							self      :	Union[str, Any]     ,a__      :	str     ,a__      :	List[Any]     ,a__      :	Union[str, Any]     ,a__      :	Any=None)						->       Tuple:




											"""simple docstring"""







											if self.timesteps is None:
																raise ValueError(
																    '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler''')

											# TODO(Patrick) better comments + non-PyTorch
											# postprocess model score
											_lowerCAmelCase:Union[str, Any]									=  (
											    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
											)
											_lowerCAmelCase:Dict									=  torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff))
											_lowerCAmelCase:Optional[Any]									=  std.flatten()
											while len(std.shape) < len(score.shape):
																_lowerCAmelCase:str									=  std.unsqueeze(-1)
											_lowerCAmelCase:Optional[int]									=  -score / std

											# compute
											_lowerCAmelCase:Optional[Any]									=  -1.0 / len(self.timesteps)

											_lowerCAmelCase:Union[str, Any]									=  self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
											_lowerCAmelCase:Any									=  beta_t.flatten()
											while len(beta_t.shape) < len(x.shape):
																_lowerCAmelCase:List[str]									=  beta_t.unsqueeze(-1)
											_lowerCAmelCase:Tuple									=  -0.5 * beta_t * x

											_lowerCAmelCase:str									=  torch.sqrt(a__)
											_lowerCAmelCase:Union[str, Any]									=  drift - diffusion**2 * score
											_lowerCAmelCase:List[str]									=  x + drift * dt

											# add noise
											_lowerCAmelCase:Any									=  randn_tensor(x.shape     ,layout=x.layout     ,generator=a__     ,device=x.device     ,dtype=x.dtype)
											_lowerCAmelCase:Union[str, Any]									=  x_mean + diffusion * math.sqrt(-dt) * noise

											return x, x_mean







						def __len__(							self      :	int)						->       Tuple:




											"""simple docstring"""







											return self.config.num_train_timesteps






