code: 
  
  def        __SCREAMING_SNAKE_CASE    (      a__						:      float					)				->							int:
  	if num < 0:
  		return -1
  	return 1 if num else 0
  def        __SCREAMING_SNAKE_CASE    (      )				->							None:
  	assert signum(5					) == 1
  	assert signum(-5					) == -1
  	assert signum(0					) == 0
  
  
  if __name__ == "__main__":
  			print(signum(12))
  			print(signum(-12))
  			print(signum(0))
  
  
  
  
  
  
style_context: 
  
  # DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
  # and https://github.com/hojonathanho/diffusion
  
  from dataclasses import dataclass
  from typing import Optional, Tuple, Union
  
  import flax
  import jax.numpy as jnp
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from .scheduling_utils_flax import (
      CommonSchedulerState,
      FlaxKarrasDiffusionSchedulers,
      FlaxSchedulerMixin,
      FlaxSchedulerOutput,
      add_noise_common,
      get_velocity_common,
  )
  
  
  
  
  
  
  @flax.struct.dataclass
  class     lowerCamelCase_			:
  	_lowercase		:      CommonSchedulerState
  	_lowercase		:      jnp.ndarray
  
  	# setable values
  	_lowercase		:      jnp.ndarray
  	_lowercase		:      jnp.ndarray
  	_lowercase		:      Optional[int]    				=							None
  
  
  
  
  	@classmethod
  	def 					lowerCAmelCase_					(    cls	:    int				,			__A	:    CommonSchedulerState				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			):
  		return cls(
  		    common=__A				,			final_alpha_cumprod=__A				,			init_noise_sigma=__A				,			timesteps=__A				,			)
  
  
  
  
  
  
  @dataclass
  class     lowerCamelCase_			(  _lowercase  ):
  	_lowercase		:      DDIMSchedulerState
  
  
  
  
  
  
  class     lowerCamelCase_			(  _lowercase	,			_lowercase  ):
  	_lowercase		:      Union[str, Any]    				=							[e.name for e in FlaxKarrasDiffusionSchedulers]
  
  	_lowercase		:      jnp.dtype
  
  
  
  
  	@property
  	def 					lowerCAmelCase_					(    self	:    Tuple       ):
  		return True
  
  
  
  
  	@register_to_config
  	def __init__(    self	:    Any				,			__A	:    int = 1000				,			__A	:    float = 0.0_0_0_1				,			__A	:    float = 0.0_2				,			__A	:    str = "linear"				,			__A	:    Optional[jnp.ndarray] = None				,			__A	:    bool = True				,			__A	:    int = 0				,			__A	:    str = "epsilon"				,			__A	:    jnp.dtype = jnp.floataa				,			):
  		__A   : Optional[int]								= dtype
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Union[str, Any]				,			__A	:    Optional[CommonSchedulerState] = None       ):
  		if common is None:
  			__A   : Any								= CommonSchedulerState.create(self       )
  
  		# At every step in ddim, we are looking into the previous alphas_cumprod
  		# For the final step, there is no previous alphas_cumprod because we are already at 0
  		# `set_alpha_to_one` decides whether we set this parameter simply to one or
  		# whether we use the final alpha of the "non-previous" one.
  		__A   : Tuple								= (
  		    jnp.array(1.0				,			dtype=self.dtype       ) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
  		)
  
  		# standard deviation of the initial noise distribution
  		__A   : List[str]								= jnp.array(1.0				,			dtype=self.dtype       )
  
  		__A   : Any								= jnp.arange(0				,			self.config.num_train_timesteps       ).round()[::-1]
  
  		return DDIMSchedulerState.create(
  		    common=__A				,			final_alpha_cumprod=__A				,			init_noise_sigma=__A				,			timesteps=__A				,			)
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Union[str, Any]				,			__A	:    DDIMSchedulerState				,			__A	:    jnp.ndarray				,			__A	:    Optional[int] = None       ):
  		return sample
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Tuple				,			__A	:    DDIMSchedulerState				,			__A	:    int				,			__A	:    Tuple = ()       ):
  		__A   : Union[str, Any]								= self.config.num_train_timesteps // num_inference_steps
  		# creates integer timesteps by multiplying by ratio
  		# rounding to avoid issues when num_inference_step is power of 3
  		__A   : Optional[Any]								= (jnp.arange(0				,			__A       ) * step_ratio).round()[::-1] + self.config.steps_offset
  
  		return state.replace(
  		    num_inference_steps=__A				,			timesteps=__A				,			)
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Any				,			__A	:    DDIMSchedulerState				,			__A	:    str				,			__A	:    List[Any]       ):
  		__A   : Tuple								= state.common.alphas_cumprod[timestep]
  		__A   : Tuple								= jnp.where(
  		    prev_timestep >= 0				,			state.common.alphas_cumprod[prev_timestep]				,			state.final_alpha_cumprod       )
  		__A   : List[Any]								= 1 - alpha_prod_t
  		__A   : Tuple								= 1 - alpha_prod_t_prev
  
  		__A   : List[Any]								= (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
  
  		return variance
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    List[Any]				,			__A	:    DDIMSchedulerState				,			__A	:    jnp.ndarray				,			__A	:    int				,			__A	:    jnp.ndarray				,			__A	:    float = 0.0				,			__A	:    bool = True				,			):
  		if state.num_inference_steps is None:
  			raise ValueError(
  			    """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""       )
  
  		# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
  		# Ideally, read DDIM paper in-detail understanding
  
  		# Notation (<variable name> -> <name in paper>
  		# - pred_noise_t -> e_theta(x_t, t)
  		# - pred_original_sample -> f_theta(x_t, t) or x_0
  		# - std_dev_t -> sigma_t
  		# - eta -> η
  		# - pred_sample_direction -> "direction pointing to x_t"
  		# - pred_prev_sample -> "x_t-1"
  
  		# 1. get previous step value (=t-1)
  		__A   : Optional[Any]								= timestep - self.config.num_train_timesteps // state.num_inference_steps
  
  		__A   : Optional[int]								= state.common.alphas_cumprod
  		__A   : Optional[int]								= state.final_alpha_cumprod
  
  		# 2. compute alphas, betas
  		__A   : Optional[int]								= alphas_cumprod[timestep]
  		__A   : str								= jnp.where(prev_timestep >= 0				,			alphas_cumprod[prev_timestep]				,			__A       )
  
  		__A   : Any								= 1 - alpha_prod_t
  
  		# 3. compute predicted original sample from predicted noise also called
  		# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  		if self.config.prediction_type == "epsilon":
  			__A   : Any								= (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
  			__A   : List[Any]								= model_output
  		elif self.config.prediction_type == "sample":
  			__A   : Dict								= model_output
  			__A   : Tuple								= (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
  		elif self.config.prediction_type == "v_prediction":
  			__A   : int								= (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
  			__A   : str								= (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
  		else:
  			raise ValueError(
  			    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
  			    """ `v_prediction`"""       )
  
  		# 4. compute variance: "sigma_t(η)" -> see formula (16)
  		# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
  		__A   : Union[str, Any]								= self._get_variance(__A				,			__A				,			__A       )
  		__A   : Any								= eta * variance ** 0.5
  
  		# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  		__A   : Any								= (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon
  
  		# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  		__A   : Optional[int]								= alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction
  
  		if not return_dict:
  			return (prev_sample, state)
  
  		return FlaxDDIMSchedulerOutput(prev_sample=__A				,			state=__A       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    List[str]				,			__A	:    DDIMSchedulerState				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			):
  		return add_noise_common(state.common				,			__A				,			__A				,			__A       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Optional[int]				,			__A	:    DDIMSchedulerState				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			__A	:    jnp.ndarray				,			):
  		return get_velocity_common(state.common				,			__A				,			__A				,			__A       )
  
  
  
  
  	def __len__(    self	:    Union[str, Any]       ):
  		return self.config.num_train_timesteps
  
  
  
  
  
  