

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

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

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



@dataclass
class 						_A     (				snake_case				):





  '''simple docstring'''



  __lowerCamelCase			:      torch.FloatTensor
  __lowerCamelCase			:      torch.FloatTensor







class 						_A     (				snake_case						,    snake_case				):





  '''simple docstring'''



  __lowerCamelCase			:      List[str]					=   1





  @register_to_config
  def __init__(  self   ,SCREAMING_SNAKE_CASE_ = 2000   ,SCREAMING_SNAKE_CASE_ = 0.15   ,SCREAMING_SNAKE_CASE_ = 0.01   ,SCREAMING_SNAKE_CASE_ = 13_48.0   ,SCREAMING_SNAKE_CASE_ = 1E-5   ,SCREAMING_SNAKE_CASE_ = 1   ,):

      '''simple docstring'''
      # standard deviation of the initial noise distribution
      snake_case							:		Union[str, Any]        =		sigma_max

      # setable values
      snake_case							:		Any        =		None

      self.set_sigmas(SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_    )





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_ = None    ):

      '''simple docstring'''
      return sample





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_ = None   ,SCREAMING_SNAKE_CASE_ = None    ):

      '''simple docstring'''
      snake_case							:		Any        =		sampling_eps if sampling_eps is not None else self.config.sampling_eps

      snake_case							:		str        =		torch.linspace(1   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,device=SCREAMING_SNAKE_CASE_    )





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_ = None   ,SCREAMING_SNAKE_CASE_ = None   ,SCREAMING_SNAKE_CASE_ = None    ):

      '''simple docstring'''
      snake_case							:		List[Any]        =		sigma_min if sigma_min is not None else self.config.sigma_min
      snake_case							:		str        =		sigma_max if sigma_max is not None else self.config.sigma_max
      snake_case							:		Any        =		sampling_eps if sampling_eps is not None else self.config.sampling_eps
      if self.timesteps is None:
          self.set_timesteps(SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_    )

      snake_case							:		str        =		sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
      snake_case							:		List[Any]        =		torch.exp(torch.linspace(math.log(SCREAMING_SNAKE_CASE_    )   ,math.log(SCREAMING_SNAKE_CASE_    )   ,SCREAMING_SNAKE_CASE_    )    )
      snake_case							:		Optional[Any]        =		torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]    )





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_    ):

      '''simple docstring'''
      return torch.where(
          timesteps == 0   ,torch.zeros_like(t.to(timesteps.device    )    )   ,self.discrete_sigmas[timesteps - 1].to(timesteps.device    )   ,)





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_ = None   ,SCREAMING_SNAKE_CASE_ = True   ,):

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

      snake_case							:		Optional[Any]        =		timestep * torch.ones(
          sample.shape[0]   ,device=sample.device    )  # torch.repeat_interleave(timestep, sample.shape[0])
      snake_case							:		List[str]        =		(timestep * (len(self.timesteps    ) - 1)).long()

      # mps requires indices to be in the same device, so we use cpu as is the default with cuda
      snake_case							:		Dict        =		timesteps.to(self.discrete_sigmas.device    )

      snake_case							:		Any        =		self.discrete_sigmas[timesteps].to(sample.device    )
      snake_case							:		str        =		self.get_adjacent_sigma(SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_    ).to(sample.device    )
      snake_case							:		Tuple        =		torch.zeros_like(SCREAMING_SNAKE_CASE_    )
      snake_case							:		Optional[Any]        =		(sigma**2 - adjacent_sigma**2) ** 0.5

      # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
      # also equation 47 shows the analog from SDE models to ancestral sampling methods
      snake_case							:		Tuple        =		diffusion.flatten()
      while len(diffusion.shape    ) < len(sample.shape    ):
          snake_case							:		Dict        =		diffusion.unsqueeze(-1    )
      snake_case							:		List[Any]        =		drift - diffusion**2 * model_output

      #  equation 6: sample noise for the diffusion term of
      snake_case							:		Tuple        =		randn_tensor(
          sample.shape   ,layout=sample.layout   ,generator=SCREAMING_SNAKE_CASE_   ,device=sample.device   ,dtype=sample.dtype    )
      snake_case							:		Tuple        =		sample - drift  # subtract because `dt` is a small negative timestep
      # TODO is the variable diffusion the correct scaling term for the noise?
      snake_case							:		List[str]        =		prev_sample_mean + diffusion * noise  # add impact of diffusion field g

      if not return_dict:
          return (prev_sample, prev_sample_mean)

      return SdeVeOutput(prev_sample=SCREAMING_SNAKE_CASE_   ,prev_sample_mean=SCREAMING_SNAKE_CASE_    )





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_ = None   ,SCREAMING_SNAKE_CASE_ = True   ,):

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

      # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
      # sample noise for correction
      snake_case							:		Dict        =		randn_tensor(sample.shape   ,layout=sample.layout   ,generator=SCREAMING_SNAKE_CASE_    ).to(sample.device    )

      # compute step size from the model_output, the noise, and the snr
      snake_case							:		List[str]        =		torch.norm(model_output.reshape(model_output.shape[0]   ,-1    )   ,dim=-1    ).mean()
      snake_case							:		List[Any]        =		torch.norm(noise.reshape(noise.shape[0]   ,-1    )   ,dim=-1    ).mean()
      snake_case							:		str        =		(self.config.snr * noise_norm / grad_norm) ** 2 * 2
      snake_case							:		int        =		step_size * torch.ones(sample.shape[0]    ).to(sample.device    )
      # self.repeat_scalar(step_size, sample.shape[0])

      # compute corrected sample: model_output term and noise term
      snake_case							:		Optional[int]        =		step_size.flatten()
      while len(step_size.shape    ) < len(sample.shape    ):
          snake_case							:		Union[str, Any]        =		step_size.unsqueeze(-1    )
      snake_case							:		Optional[Any]        =		sample + step_size * model_output
      snake_case							:		Any        =		prev_sample_mean + ((step_size * 2) ** 0.5) * noise

      if not return_dict:
          return (prev_sample,)

      return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_    )





  def    snake_case_       (  self   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,SCREAMING_SNAKE_CASE_   ,):

      '''simple docstring'''
      # Make sure sigmas and timesteps have the same device and dtype as original_samples
      snake_case							:		Optional[Any]        =		timesteps.to(original_samples.device    )
      snake_case							:		Any        =		self.discrete_sigmas.to(original_samples.device    )[timesteps]
      snake_case							:		Tuple        =		(
          noise * sigmas[:, None, None, None]
          if noise is not None
          else torch.randn_like(SCREAMING_SNAKE_CASE_    ) * sigmas[:, None, None, None]
      )
      snake_case							:		Optional[Any]        =		noise + original_samples
      return noisy_samples





  def __len__(  self    ):

      '''simple docstring'''
      return self.config.num_train_timesteps









"""simple docstring"""

class 							lowercase_			:



 '''simple docstring'''

 def __init__(					self			:			List[Any]       ,				_UpperCAmelCase			:			Optional[Any]       ,				_UpperCAmelCase			:			int       ,				_UpperCAmelCase			:			int						):
       _A     =  None
       _A     =  None
       _A     =  graph

       self._normalize_graph(_UpperCAmelCase       ,				_UpperCAmelCase						)
       _A     =  len(_UpperCAmelCase						)
       _A     =  None

 def      lowerCAmelCase_				(					self			:			Optional[Any]       ,				_UpperCAmelCase			:			Union[str, Any]       ,				_UpperCAmelCase			:			Dict						):
       if sources is int:
             _A     =  [sources]
       if sinks is int:
             _A     =  [sinks]

       if len(_UpperCAmelCase						) == 0 or len(_UpperCAmelCase						) == 0:
             return

       _A     =  sources[0]
       _A     =  sinks[0]

       # make fake vertex if there are more
       # than one source or sink
       if len(_UpperCAmelCase						) > 1 or len(_UpperCAmelCase						) > 1:
             _A     =  0
             for i in sources:
                   max_input_flow += sum(self.graph[i]						)

             _A     =  len(self.graph						) + 1
             for room in self.graph:
                   room.insert(0       ,				0						)
             self.graph.insert(0       ,				[0] * size						)
             for i in sources:
                   _A     =  max_input_flow
             _A     =  0

             _A     =  len(self.graph						) + 1
             for room in self.graph:
                   room.append(0						)
             self.graph.append([0] * size						)
             for i in sinks:
                   _A     =  max_input_flow
             _A     =  size - 1

 def      lowerCAmelCase_				(					self			:			Optional[Any]						):
       if self.maximum_flow_algorithm is None:
             raise Exception('You need to set maximum flow algorithm before.'						)
       if self.source_index is None or self.sink_index is None:
             return 0

       self.maximum_flow_algorithm.execute()
       return self.maximum_flow_algorithm.getMaximumFlow()



 def      lowerCAmelCase_				(					self			:			List[str]       ,				_UpperCAmelCase			:			Union[str, Any]						):
       _A     =  algorithm(self						)





class 							lowercase_			:



 '''simple docstring'''

 def __init__(					self			:			List[Any]       ,				_UpperCAmelCase			:			Union[str, Any]						):
       _A     =  flow_network
       _A     =  flow_network.verticesCount
       _A     =  flow_network.sourceIndex
       _A     =  flow_network.sinkIndex
       # it's just a reference, so you shouldn't change
       # it in your algorithms, use deep copy before doing that
       _A     =  flow_network.graph
       _A     =  False

 def      lowerCAmelCase_				(					self			:			Optional[Any]						):
       if not self.executed:
             self._algorithm()
             _A     =  True



 def      lowerCAmelCase_				(					self			:			int						):
       pass





class 							lowercase_			(	__lowerCAmelCase				):



 '''simple docstring'''

 def __init__(					self			:			int       ,				_UpperCAmelCase			:			Any						):
       super().__init__(_UpperCAmelCase						)
       # use this to save your result
       _A     =  -1



 def      lowerCAmelCase_				(					self			:			Optional[Any]						):
       if not self.executed:
             raise Exception('You should execute algorithm before using its result!'						)

       return self.maximum_flow





class 							lowercase_			(	__lowerCAmelCase				):



 '''simple docstring'''

 def __init__(					self			:			Dict       ,				_UpperCAmelCase			:			List[Any]						):
       super().__init__(_UpperCAmelCase						)

       _A     =  [[0] * self.verticies_count for i in range(self.verticies_count						)]

       _A     =  [0] * self.verticies_count
       _A     =  [0] * self.verticies_count

 def      lowerCAmelCase_				(					self			:			Dict						):
       _A     =  self.verticies_count

       # push some substance to graph
       for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]						):
             self.preflow[self.source_index][nextvertex_index] += bandwidth
             self.preflow[nextvertex_index][self.source_index] -= bandwidth
             self.excesses[nextvertex_index] += bandwidth

       # Relabel-to-front selection rule
       _A     =  [
           i
           for i in range(self.verticies_count						)
           if i != self.source_index and i != self.sink_index
       ]

       # move through list
       _A     =  0
       while i < len(_UpperCAmelCase						):
             _A     =  vertices_list[i]
             _A     =  self.heights[vertex_index]
             self.process_vertex(_UpperCAmelCase						)
             if self.heights[vertex_index] > previous_height:
                   # if it was relabeled, swap elements
                   # and start from 0 index
                   vertices_list.insert(0       ,				vertices_list.pop(_UpperCAmelCase						)						)
                   _A     =  0
             else:
                   i += 1

       _A     =  sum(self.preflow[self.source_index]						)

 def      lowerCAmelCase_				(					self			:			int       ,				_UpperCAmelCase			:			Any						):
       while self.excesses[vertex_index] > 0:
             for neighbour_index in range(self.verticies_count						):
                   # if it's neighbour and current vertex is higher
                   if (
                       self.graph[vertex_index][neighbour_index]
                       - self.preflow[vertex_index][neighbour_index]
                       > 0
                       and self.heights[vertex_index] > self.heights[neighbour_index]
                   ):
                         self.push(_UpperCAmelCase       ,				_UpperCAmelCase						)

             self.relabel(_UpperCAmelCase						)

 def      lowerCAmelCase_				(					self			:			Dict       ,				_UpperCAmelCase			:			Tuple       ,				_UpperCAmelCase			:			Tuple						):
       _A     =  min(
           self.excesses[from_index]       ,				self.graph[from_index][to_index] - self.preflow[from_index][to_index]       ,				)
       self.preflow[from_index][to_index] += preflow_delta
       self.preflow[to_index][from_index] -= preflow_delta
       self.excesses[from_index] -= preflow_delta
       self.excesses[to_index] += preflow_delta



 def      lowerCAmelCase_				(					self			:			Union[str, Any]       ,				_UpperCAmelCase			:			int						):
       _A     =  None
       for to_index in range(self.verticies_count						):
             if (
                 self.graph[vertex_index][to_index]
                 - self.preflow[vertex_index][to_index]
                 > 0
             ) and (min_height is None or self.heights[to_index] < min_height):
                   _A     =  self.heights[to_index]

       if min_height is not None:
             _A     =  min_height + 1


if __name__ == "__main__":
       a							      =     [0]
       a							      =     [3]
       # graph = [
       #     [0, 0, 4, 6, 0, 0],
       #     [0, 0, 5, 2, 0, 0],
       #     [0, 0, 0, 0, 4, 4],
       #     [0, 0, 0, 0, 6, 6],
       #     [0, 0, 0, 0, 0, 0],
       #     [0, 0, 0, 0, 0, 0],
       # ]
       a							      =     [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

       # prepare our network
       a							      =     FlowNetwork(graph, entrances, exits)
       # set algorithm
       flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
       # and calculate
       a							      =     flow_network.find_maximum_flow()

       print(F'''maximum flow is {maximum_flow}''')

