

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

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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left



@flax.struct.dataclass
class  __snake_case					:
  # setable values
  __lowerCAmelCase       :		Optional[jnp.ndarray]  	=					None
  __lowerCAmelCase       :		Optional[jnp.ndarray]  	=					None
  __lowerCAmelCase       :		Optional[jnp.ndarray]  	=					None

  @classmethod
  def   lowerCAmelCase__       (   cls):
      return cls()






@dataclass
class  __snake_case					(      lowerCAmelCase__    ):
  __lowerCAmelCase       :		ScoreSdeVeSchedulerState
  __lowerCAmelCase       :		jnp.ndarray
  __lowerCAmelCase       :		Optional[jnp.ndarray]  	=					None






class  __snake_case					(      lowerCAmelCase__       ,	lowerCAmelCase__    ):

  @property
  def   lowerCAmelCase__       (   self):
      return True

  @register_to_config
  def __init__(   self  ,						_A = 2000  ,						_A = 0.1_5  ,						_A = 0.0_1  ,						_A = 1_3_4_8.0  ,						_A = 1E-5  ,						_A = 1  ,						):
      pass

  def   lowerCAmelCase__       (   self):
      SCREAMING_SNAKE_CASE_													=  ScoreSdeVeSchedulerState.create()
      return self.set_sigmas(
          _A  ,						self.config.num_train_timesteps  ,						self.config.sigma_min  ,						self.config.sigma_max  ,						self.config.sampling_eps  ,						)

  def   lowerCAmelCase__       (   self  ,						_A  ,						_A  ,						_A = ()  ,						_A = None):
      SCREAMING_SNAKE_CASE_													=  sampling_eps if sampling_eps is not None else self.config.sampling_eps

      SCREAMING_SNAKE_CASE_													=  jnp.linspace(1  ,						_A  ,						_A)
      return state.replace(timesteps=_A)

  def   lowerCAmelCase__       (   self  ,						_A  ,						_A  ,						_A = None  ,						_A = None  ,						_A = None  ,						):
      SCREAMING_SNAKE_CASE_													=  sigma_min if sigma_min is not None else self.config.sigma_min
      SCREAMING_SNAKE_CASE_													=  sigma_max if sigma_max is not None else self.config.sigma_max
      SCREAMING_SNAKE_CASE_													=  sampling_eps if sampling_eps is not None else self.config.sampling_eps
      if state.timesteps is None:
          SCREAMING_SNAKE_CASE_													=  self.set_timesteps(_A  ,						_A  ,						_A)

      SCREAMING_SNAKE_CASE_													=  jnp.exp(jnp.linspace(jnp.log(_A)  ,						jnp.log(_A)  ,						_A))
      SCREAMING_SNAKE_CASE_													=  jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps])

      return state.replace(discrete_sigmas=_A  ,						sigmas=_A)

  def   lowerCAmelCase__       (   self  ,						_A  ,						_A  ,						_A):
      return jnp.where(timesteps == 0  ,						jnp.zeros_like(_A)  ,						state.discrete_sigmas[timesteps - 1])

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

      SCREAMING_SNAKE_CASE_													=  timestep * jnp.ones(
          sample.shape[0]  ,						)
      SCREAMING_SNAKE_CASE_													=  (timestep * (len(state.timesteps) - 1)).long()

      SCREAMING_SNAKE_CASE_													=  state.discrete_sigmas[timesteps]
      SCREAMING_SNAKE_CASE_													=  self.get_adjacent_sigma(_A  ,						_A  ,						_A)
      SCREAMING_SNAKE_CASE_													=  jnp.zeros_like(_A)
      SCREAMING_SNAKE_CASE_													=  (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
      SCREAMING_SNAKE_CASE_													=  diffusion.flatten()
      SCREAMING_SNAKE_CASE_													=  broadcast_to_shape_from_left(_A  ,						sample.shape)
      SCREAMING_SNAKE_CASE_													=  drift - diffusion**2 * model_output

      #  equation 6: sample noise for the diffusion term of
      SCREAMING_SNAKE_CASE_													=  random.split(_A  ,						num=1)
      SCREAMING_SNAKE_CASE_													=  random.normal(key=_A  ,						shape=sample.shape)
      SCREAMING_SNAKE_CASE_													=  sample - drift  # subtract because `dt` is a small negative timestep
      # TODO is the variable diffusion the correct scaling term for the noise?
      SCREAMING_SNAKE_CASE_													=  prev_sample_mean + diffusion * noise  # add impact of diffusion field g

      if not return_dict:
          return (prev_sample, prev_sample_mean, state)

      return FlaxSdeVeOutput(prev_sample=_A  ,						prev_sample_mean=_A  ,						state=_A)

  def   lowerCAmelCase__       (   self  ,						_A  ,						_A  ,						_A  ,						_A  ,						_A = True  ,						):
      if state.timesteps is None:
          raise ValueError(
              '`state.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
      SCREAMING_SNAKE_CASE_													=  random.split(_A  ,						num=1)
      SCREAMING_SNAKE_CASE_													=  random.normal(key=_A  ,						shape=sample.shape)

      # compute step size from the model_output, the noise, and the snr
      SCREAMING_SNAKE_CASE_													=  jnp.linalg.norm(_A)
      SCREAMING_SNAKE_CASE_													=  jnp.linalg.norm(_A)
      SCREAMING_SNAKE_CASE_													=  (self.config.snr * noise_norm / grad_norm) ** 2 * 2
      SCREAMING_SNAKE_CASE_													=  step_size * jnp.ones(sample.shape[0])

      # compute corrected sample: model_output term and noise term
      SCREAMING_SNAKE_CASE_													=  step_size.flatten()
      SCREAMING_SNAKE_CASE_													=  broadcast_to_shape_from_left(_A  ,						sample.shape)
      SCREAMING_SNAKE_CASE_													=  sample + step_size * model_output
      SCREAMING_SNAKE_CASE_													=  prev_sample_mean + ((step_size * 2) ** 0.5) * noise

      if not return_dict:
          return (prev_sample, state)

      return FlaxSdeVeOutput(prev_sample=_A  ,						state=_A)


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





# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue


def    _UpperCAmelCase    (					_SCREAMING_SNAKE_CASE   :						List[str]    ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_													=  Queue()
    SCREAMING_SNAKE_CASE_													=  [False] * len(_SCREAMING_SNAKE_CASE    )
    SCREAMING_SNAKE_CASE_													=  [-1] * len(_SCREAMING_SNAKE_CASE    )

    def bfs():
        while not queue.empty():
            SCREAMING_SNAKE_CASE_													=  queue.get()
            SCREAMING_SNAKE_CASE_													=  True

            for neighbour in graph[u]:
                if neighbour == u:
                    return False

                if color[neighbour] == -1:
                    SCREAMING_SNAKE_CASE_													=  1 - color[u]
                    queue.put(_SCREAMING_SNAKE_CASE    )

                elif color[neighbour] == color[u]:
                    return False

        return True

    for i in range(len(_SCREAMING_SNAKE_CASE    )    ):
        if not visited[i]:
            queue.put(_SCREAMING_SNAKE_CASE    )
            SCREAMING_SNAKE_CASE_													=  0
            if bfs() is False:
                return False

    return True


if __name__ == "__main__":
       # Adjacency List of graph
       print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))


