


# 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 						_UpperCAmelCase      (     lowercase		,		lowercase							):
		lowerCamelCase_	:			Any       			=  1






		@register_to_config
		def __init__(						self				:     Optional[Any]   ,  UpperCAmelCase				:     Optional[int]=20_00   ,  UpperCAmelCase				:     List[Any]=0.1   ,  UpperCAmelCase				:     Optional[Any]=20   ,  UpperCAmelCase				:     Dict=1E-3):
				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						None
				SCREAMING_SNAKE_CASE_				:Dict				     =						None
				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						None






		def _snake_case		(						self				:     List[str]   ,  UpperCAmelCase				:     Union[str, Any]   ,  UpperCAmelCase				:     Union[str, torch.device] = None):
				SCREAMING_SNAKE_CASE_				:Any				     =						torch.linspace(1   ,  self.config.sampling_eps   ,  UpperCAmelCase   ,  device=UpperCAmelCase)






		def _snake_case		(						self				:     List[Any]   ,  UpperCAmelCase				:     List[str]   ,  UpperCAmelCase				:     Dict   ,  UpperCAmelCase				:     Tuple   ,  UpperCAmelCase				:     Tuple=None):
				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
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						(
				    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
				)
				SCREAMING_SNAKE_CASE_				:Tuple				     =						torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff))
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						std.flatten()
				while len(std.shape) < len(score.shape):
						SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						std.unsqueeze(-1)
				SCREAMING_SNAKE_CASE_				:Dict				     =						-score / std

				# compute
				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						-1.0 / len(self.timesteps)

				SCREAMING_SNAKE_CASE_				:Optional[int]				     =						self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
				SCREAMING_SNAKE_CASE_				:Tuple				     =						beta_t.flatten()
				while len(beta_t.shape) < len(x.shape):
						SCREAMING_SNAKE_CASE_				:Dict				     =						beta_t.unsqueeze(-1)
				SCREAMING_SNAKE_CASE_				:Dict				     =						-0.5 * beta_t * x

				SCREAMING_SNAKE_CASE_				:Tuple				     =						torch.sqrt(UpperCAmelCase)
				SCREAMING_SNAKE_CASE_				:Dict				     =						drift - diffusion**2 * score
				SCREAMING_SNAKE_CASE_				:Tuple				     =						x + drift * dt

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

				return x, x_mean







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










def     lowercase	(    a     , a     , a     , a ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:int				     =						[False] * len(a )
		SCREAMING_SNAKE_CASE_				:List[Any]				     =						[]
		queue.append(a )
		SCREAMING_SNAKE_CASE_				:int				     =						True

		while queue:
				SCREAMING_SNAKE_CASE_				:int				     =						queue.pop(0 )
				for ind in range(len(graph[u] ) ):
						if visited[ind] is False and graph[u][ind] > 0:
								queue.append(a )
								SCREAMING_SNAKE_CASE_				:Tuple				     =						True
								SCREAMING_SNAKE_CASE_				:Optional[int]				     =						u

		return visited[t]


def     lowercase	(    a     , a     , a ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:Any				     =						[-1] * (len(a ))
		SCREAMING_SNAKE_CASE_				:Tuple				     =						0
		while bfs(a     , a     , a     , a ):
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						float("Inf" )
				SCREAMING_SNAKE_CASE_				:str				     =						sink

				while s != source:
						# Find the minimum value in select path
						SCREAMING_SNAKE_CASE_				:str				     =						min(a     , graph[parent[s]][s] )
						SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						parent[s]

				max_flow += path_flow
				SCREAMING_SNAKE_CASE_				:Dict				     =						sink

				while v != source:
						SCREAMING_SNAKE_CASE_				:int				     =						parent[v]
						graph[u][v] -= path_flow
						graph[v][u] += path_flow
						SCREAMING_SNAKE_CASE_				:Any				     =						parent[v]
		return max_flow


SCREAMING_SNAKE_CASE__     					=			[
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

SCREAMING_SNAKE_CASE__					,    SCREAMING_SNAKE_CASE__     					=			0, 5
print(ford_fulkerson(graph, source, sink))






