code: 
  
  
  
  
  
  '''simple docstring'''
  
  
  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 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    None
  		__lowerCAmelCase 				=    None
  		__lowerCAmelCase 				=    None
  
  
  
  
  
  
  
  		@classmethod
  		def        A     (cls						:      int      ):
  			return cls()
  
  
  
  
  
  
  @dataclass
  class 							__UpperCAmelCase  (       A__						):
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    42
  		__lowerCAmelCase 				=    42
  		__lowerCAmelCase 				=    None
  
  
  
  
  
  
  class 							__UpperCAmelCase  (       A__		,					A__						):
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		@property
  		def        A     (self						:      Tuple      ):
  			return True
  
  
  
  
  
  
  
  		@register_to_config
  		def __init__(self						:      Union[str, Any]      ,      _lowerCAmelCase						:      int = 2000      ,      _lowerCAmelCase						:      float = 0.15      ,      _lowerCAmelCase						:      float = 0.01      ,      _lowerCAmelCase						:      float = 1348.0      ,      _lowerCAmelCase						:      float = 1e-5      ,      _lowerCAmelCase						:      int = 1      ,      ):
  			pass
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ):
  			A							  =      ScoreSdeVeSchedulerState.create()
  			return self.set_sigmas(
  			    _lowerCAmelCase      ,      self.config.num_train_timesteps      ,      self.config.sigma_min      ,      self.config.sigma_max      ,      self.config.sampling_eps      ,      )
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      ScoreSdeVeSchedulerState      ,      _lowerCAmelCase						:      int      ,      _lowerCAmelCase						:      Tuple = ()      ,      _lowerCAmelCase						:      float = None      ):
  			A							  =      sampling_eps if sampling_eps is not None else self.config.sampling_eps
  
  			A							  =      jnp.linspace(1      ,      _lowerCAmelCase      ,      _lowerCAmelCase      )
  			return state.replace(timesteps=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      int      ,      _lowerCAmelCase						:      ScoreSdeVeSchedulerState      ,      _lowerCAmelCase						:      int      ,      _lowerCAmelCase						:      float = None      ,      _lowerCAmelCase						:      float = None      ,      _lowerCAmelCase						:      float = None      ,      ):
  			A							  =      sigma_min if sigma_min is not None else self.config.sigma_min
  			A							  =      sigma_max if sigma_max is not None else self.config.sigma_max
  			A							  =      sampling_eps if sampling_eps is not None else self.config.sampling_eps
  			if state.timesteps is None:
  				A							  =      self.set_timesteps(_lowerCAmelCase      ,      _lowerCAmelCase      ,      _lowerCAmelCase      )
  
  			A							  =      jnp.exp(jnp.linspace(jnp.log(_lowerCAmelCase      )      ,      jnp.log(_lowerCAmelCase      )      ,      _lowerCAmelCase      )      )
  			A							  =      jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]      )
  
  			return state.replace(discrete_sigmas=_lowerCAmelCase      ,      sigmas=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      Dict      ,      _lowerCAmelCase						:      Dict      ,      _lowerCAmelCase						:      Union[str, Any]      ):
  			return jnp.where(timesteps == 0      ,      jnp.zeros_like(_lowerCAmelCase      )      ,      state.discrete_sigmas[timesteps - 1]      )
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      ScoreSdeVeSchedulerState      ,      _lowerCAmelCase						:      jnp.ndarray      ,      _lowerCAmelCase						:      int      ,      _lowerCAmelCase						:      jnp.ndarray      ,      _lowerCAmelCase						:      random.KeyArray      ,      _lowerCAmelCase						:      bool = True      ,      ):
  			if state.timesteps is None:
  				raise ValueError(
  				    """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""      )
  
  			A							  =      timestep * jnp.ones(
  			    sample.shape[0]      ,      )
  			A							  =      (timestep * (len(state.timesteps      ) - 1)).long()
  
  			A							  =      state.discrete_sigmas[timesteps]
  			A							  =      self.get_adjacent_sigma(_lowerCAmelCase      ,      _lowerCAmelCase      ,      _lowerCAmelCase      )
  			A							  =      jnp.zeros_like(_lowerCAmelCase      )
  			A							  =      (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
  			A							  =      diffusion.flatten()
  			A							  =      broadcast_to_shape_from_left(_lowerCAmelCase      ,      sample.shape      )
  			A							  =      drift - diffusion**2 * model_output
  
  			#  equation 6: sample noise for the diffusion term of
  			A							  =      random.split(_lowerCAmelCase      ,      num=1      )
  			A							  =      random.normal(key=_lowerCAmelCase      ,      shape=sample.shape      )
  			A							  =      sample - drift  # subtract because `dt` is a small negative timestep
  			# TODO is the variable diffusion the correct scaling term for the noise?
  			A							  =      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=_lowerCAmelCase      ,      prev_sample_mean=_lowerCAmelCase      ,      state=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      Any      ,      _lowerCAmelCase						:      ScoreSdeVeSchedulerState      ,      _lowerCAmelCase						:      jnp.ndarray      ,      _lowerCAmelCase						:      jnp.ndarray      ,      _lowerCAmelCase						:      random.KeyArray      ,      _lowerCAmelCase						:      bool = 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
  			A							  =      random.split(_lowerCAmelCase      ,      num=1      )
  			A							  =      random.normal(key=_lowerCAmelCase      ,      shape=sample.shape      )
  
  			# compute step size from the model_output, the noise, and the snr
  			A							  =      jnp.linalg.norm(_lowerCAmelCase      )
  			A							  =      jnp.linalg.norm(_lowerCAmelCase      )
  			A							  =      (self.config.snr * noise_norm / grad_norm) ** 2 * 2
  			A							  =      step_size * jnp.ones(sample.shape[0]      )
  
  			# compute corrected sample: model_output term and noise term
  			A							  =      step_size.flatten()
  			A							  =      broadcast_to_shape_from_left(_lowerCAmelCase      ,      sample.shape      )
  			A							  =      sample + step_size * model_output
  			A							  =      prev_sample_mean + ((step_size * 2) ** 0.5) * noise
  
  			if not return_dict:
  				return (prev_sample, state)
  
  			return FlaxSdeVeOutput(prev_sample=_lowerCAmelCase      ,      state=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def __len__(self						:      List[Any]      ):
  			return self.config.num_train_timesteps
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  
  _lowerCamelCase				:	List[str]				    =       [[0, 1, 1], [0, 0, 1], [1, 0, 0]]
  
  
  
  class 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(self						:      List[Any]      ,      _lowerCAmelCase						:      List[Any]      ):
  			A							  =      name
  			A							  =      []
  			A							  =      []
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      str      ):
  			self.inbound.append(_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      Any      ):
  			self.outbound.append(_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def __repr__(self						:      Tuple      ):
  			return F"""<node={self.name} inbound={self.inbound} outbound={self.outbound}>"""
  
  
  
  
  
  
  def    __a (     UpperCAmelCase       ,			UpperCAmelCase=3       ,			UpperCAmelCase=0.85    )      ->Tuple:
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	A							  =      {}
  	for node in nodes:
  		A							  =      1
  
  	A							  =      {}
  	for node in nodes:
  		A							  =      len(node.outbound    )
  
  	for i in range(UpperCAmelCase    ):
  		print(f"""======= Iteration {i + 1} ======="""    )
  		for _, node in enumerate(UpperCAmelCase    ):
  			A							  =      (1 - d) + d * sum(
  			    ranks[ib] / outbounds[ib] for ib in node.inbound    )
  		print(UpperCAmelCase    )
  
  
  
  
  def    __a (     )      ->Any:
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	A							  =      list(input("""Enter Names of the Nodes: """    ).split()    )
  
  	A							  =      [Node(UpperCAmelCase    ) for name in names]
  
  	for ri, row in enumerate(UpperCAmelCase    ):
  		for ci, col in enumerate(UpperCAmelCase    ):
  			if col == 1:
  				nodes[ci].add_inbound(names[ri]    )
  				nodes[ri].add_outbound(names[ci]    )
  
  	print("""======= Nodes ======="""    )
  	for node in nodes:
  		print(UpperCAmelCase    )
  
  	page_rank(UpperCAmelCase    )
  
  
  if __name__ == "__main__":
  				main()
  
  