code: 
  """simple docstring"""
  # 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    _lowerCAmelCase						:
  							# setable values
  							lowercase_     :     Optional[jnp.ndarray]       =							None
  							lowercase_     :     Optional[jnp.ndarray]       =							None
  							lowercase_     :     Optional[jnp.ndarray]       =							None
  
  
  
  							@classmethod
  							def       _a   (      cls   )							->							str:
  								return cls()
  
  
  
  
  
  @dataclass
  class    _lowerCAmelCase						(						lowerCamelCase						):
  							lowercase_     :     ScoreSdeVeSchedulerState
  							lowercase_     :     jnp.ndarray
  							lowercase_     :     Optional[jnp.ndarray]       =							None
  
  
  
  
  
  class    _lowerCAmelCase						(						lowerCamelCase    ,       lowerCamelCase						):
  
  
  
  							@property
  							def       _a   (      self   )							->							Optional[int]:
  								return True
  
  
  
  							@register_to_config
  							def __init__(      self ,						a_ = 2000 ,						a_ = 0.15 ,						a_ = 0.01 ,						a_ = 1348.0 ,						a_ = 1e-5 ,						a_ = 1 ,						)							->							Optional[int]:
  								pass
  
  
  
  							def       _a   (      self   )							->							Dict:
  								_UpperCAmelCase =						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       _a   (      self ,						a_ ,						a_ ,						a_ = () ,						a_ = None   )							->							ScoreSdeVeSchedulerState:
  								_UpperCAmelCase =						sampling_eps if sampling_eps is not None else self.config.sampling_eps
  
  								_UpperCAmelCase =						jnp.linspace(1 ,						a_ ,						a_   )
  								return state.replace(timesteps=a_   )
  
  
  
  							def       _a   (      self ,						a_ ,						a_ ,						a_ = None ,						a_ = None ,						a_ = None ,						)							->							ScoreSdeVeSchedulerState:
  								_UpperCAmelCase =						sigma_min if sigma_min is not None else self.config.sigma_min
  								_UpperCAmelCase =						sigma_max if sigma_max is not None else self.config.sigma_max
  								_UpperCAmelCase =						sampling_eps if sampling_eps is not None else self.config.sampling_eps
  								if state.timesteps is None:
  									_UpperCAmelCase =						self.set_timesteps(a_ ,						a_ ,						a_   )
  
  								_UpperCAmelCase =						jnp.exp(jnp.linspace(jnp.log(a_   ) ,						jnp.log(a_   ) ,						a_   )   )
  								_UpperCAmelCase =						jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]   )
  
  								return state.replace(discrete_sigmas=a_ ,						sigmas=a_   )
  
  
  
  							def       _a   (      self ,						a_ ,						a_ ,						a_   )							->							Any:
  								return jnp.where(timesteps == 0 ,						jnp.zeros_like(a_   ) ,						state.discrete_sigmas[timesteps - 1]   )
  
  
  
  							def       _a   (      self ,						a_ ,						a_ ,						a_ ,						a_ ,						a_ ,						a_ = True ,						)							->							Union[FlaxSdeVeOutput, Tuple]:
  								if state.timesteps is None:
  									raise ValueError(
  									    "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"   )
  
  								_UpperCAmelCase =						timestep * jnp.ones(
  								    sample.shape[0] ,						)
  								_UpperCAmelCase =						(timestep * (len(state.timesteps   ) - 1)).long()
  
  								_UpperCAmelCase =						state.discrete_sigmas[timesteps]
  								_UpperCAmelCase =						self.get_adjacent_sigma(a_ ,						a_ ,						a_   )
  								_UpperCAmelCase =						jnp.zeros_like(a_   )
  								_UpperCAmelCase =						(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
  								_UpperCAmelCase =						diffusion.flatten()
  								_UpperCAmelCase =						broadcast_to_shape_from_left(a_ ,						sample.shape   )
  								_UpperCAmelCase =						drift - diffusion**2 * model_output
  
  								#  equation 6: sample noise for the diffusion term of
  								_UpperCAmelCase =						random.split(a_ ,						num=1   )
  								_UpperCAmelCase =						random.normal(key=a_ ,						shape=sample.shape   )
  								_UpperCAmelCase =						sample - drift  # subtract because `dt` is a small negative timestep
  								# TODO is the variable diffusion the correct scaling term for the noise?
  								_UpperCAmelCase =						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       _a   (      self ,						a_ ,						a_ ,						a_ ,						a_ ,						a_ = True ,						)							->							Union[FlaxSdeVeOutput, Tuple]:
  								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
  								_UpperCAmelCase =						random.split(a_ ,						num=1   )
  								_UpperCAmelCase =						random.normal(key=a_ ,						shape=sample.shape   )
  
  								# compute step size from the model_output, the noise, and the snr
  								_UpperCAmelCase =						jnp.linalg.norm(a_   )
  								_UpperCAmelCase =						jnp.linalg.norm(a_   )
  								_UpperCAmelCase =						(self.config.snr * noise_norm / grad_norm) ** 2 * 2
  								_UpperCAmelCase =						step_size * jnp.ones(sample.shape[0]   )
  
  								# compute corrected sample: model_output term and noise term
  								_UpperCAmelCase =						step_size.flatten()
  								_UpperCAmelCase =						broadcast_to_shape_from_left(a_ ,						sample.shape   )
  								_UpperCAmelCase =						sample + step_size * model_output
  								_UpperCAmelCase =						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   )							->							List[str]:
  								return self.config.num_train_timesteps
  
  
  
  
  
style_context: 
  """simple docstring"""
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
  		raise TypeError("recursive_lucas_number accepts only integer arguments."      )
  	if n_th_number == 0:
  		return 2
  	if n_th_number == 1:
  		return 1
  
  	return recursive_lucas_number(n_th_number - 1      ) + recursive_lucas_number(
  	    n_th_number - 2      )
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
  		raise TypeError("dynamic_lucas_number accepts only integer arguments."      )
  	_UpperCAmelCase ,      _UpperCAmelCase =						2, 1
  	for _ in range(UpperCamelCase__      ):
  		_UpperCAmelCase ,      _UpperCAmelCase =						b, a + b
  	return a
  
  
  if __name__ == "__main__":
  			from doctest import testmod
  
  			testmod()
  			__magic_name__		       =				int(input('''Enter the number of terms in lucas series:\n''').strip())
  			print('''Using recursive function to calculate lucas series:''')
  			print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
  			print('''\nUsing dynamic function to calculate lucas series:''')
  			print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))
  
  
  
  
  