code: 
  
  # 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
  
  
  
  
  
  
style_context: 
  
  import math
  
  
  
  
  
  
  class     lowerCamelCase_			:
  
  
  
  
  	def __init__(    self	:    Dict				,			__A	:    int				,			__A	:    int				,			__A	:    int				,			__A	:    Any       ):
  		__A   : Union[str, Any]								= x
  		__A   : Union[str, Any]								= y
  		__A   : Optional[int]								= step_size
  		__A   : Dict								= function_to_optimize
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Optional[int]       ):
  		return self.function(self.x				,			self.y       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    int       ):
  		__A   : Dict								= self.step_size
  		return [
  		    SearchProblem(__A				,			__A				,			__A				,			self.function       )
  		    for x, y in (
  		        (self.x - step_size, self.y - step_size),
  		        (self.x - step_size, self.y),
  		        (self.x - step_size, self.y + step_size),
  		        (self.x, self.y - step_size),
  		        (self.x, self.y + step_size),
  		        (self.x + step_size, self.y - step_size),
  		        (self.x + step_size, self.y),
  		        (self.x + step_size, self.y + step_size),
  		    )
  		]
  
  
  
  
  	def __hash__(    self	:    str       ):
  		return hash(str(self       )       )
  
  
  
  
  	def __eq__(    self	:    Union[str, Any]				,			__A	:    Optional[int]       ):
  		if isinstance(__A				,			__A       ):
  			return hash(str(self       )       ) == hash(str(__A       )       )
  		return False
  
  
  
  
  	def __str__(    self	:    List[Any]       ):
  		return F"""x: {self.x} y: {self.y}"""
  
  
  
  
  
  
  def        __SCREAMING_SNAKE_CASE    (      a__						:      Optional[Any] ,a__						:      bool = True ,a__						:      float = math.inf ,a__						:      float = -math.inf ,a__						:      float = math.inf ,a__						:      float = -math.inf ,a__						:      bool = False ,a__						:      int = 10000 ,)				->							SearchProblem:
  	__A   : int								= search_prob
  	__A   : List[str]								= []  # list to store the current score at each iteration
  	__A   : Optional[Any]								= 0
  	__A   : Any								= False
  	__A   : Dict								= set()
  	while not solution_found and iterations < max_iter:
  		visited.add(a__					)
  		iterations += 1
  		__A   : Union[str, Any]								= current_state.score()
  		scores.append(a__					)
  		__A   : List[Any]								= current_state.get_neighbors()
  		__A   : Tuple								= -math.inf
  		__A   : str								= math.inf
  		__A   : Optional[int]								= None  # to hold the next best neighbor
  		for neighbor in neighbors:
  			if neighbor in visited:
  				continue  # do not want to visit the same state again
  			if (
  			    neighbor.x > max_x
  			    or neighbor.x < min_x
  			    or neighbor.y > max_y
  			    or neighbor.y < min_y
  			):
  				continue  # neighbor outside our bounds
  			__A   : int								= neighbor.score() - current_score
  			if find_max:  # finding max
  				# going to direction with greatest ascent
  				if change > max_change and change > 0:
  					__A   : str								= change
  					__A   : Optional[int]								= neighbor
  			else:  # finding min
  				# to direction with greatest descent
  				if change < min_change and change < 0:
  					__A   : List[Any]								= change
  					__A   : List[str]								= neighbor
  		if next_state is not None:
  			# we found at least one neighbor which improved the current state
  			__A   : Tuple								= next_state
  		else:
  			# since we have no neighbor that improves the solution we stop the search
  			__A   : str								= True
  
  	if visualization:
  		from matplotlib import pyplot as plt
  
  		plt.plot(range(a__					) ,a__					)
  		plt.xlabel("""Iterations"""					)
  		plt.ylabel("""Function values"""					)
  		plt.show()
  
  	return current_state
  
  
  if __name__ == "__main__":
  			import doctest
  
  			doctest.testmod()
  			def        __SCREAMING_SNAKE_CASE    (      a__						:      str ,a__						:      Any					)				->							Dict:
  				return (x**2) + (y**2)
  
  			# starting the problem with initial coordinates (3, 4)
  			UpperCAmelCase_       :				Tuple		   =      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  			UpperCAmelCase_       :				Any		   =      hill_climbing(prob, find_max=False)
  			print(
  			    '''The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
  			    f"""{local_min.score()}"""
  			)
  
  			# starting the problem with initial coordinates (12, 47)
  			UpperCAmelCase_       :				List[Any]		   =      SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  			UpperCAmelCase_       :				Any		   =      hill_climbing(
  			    prob, find_max=False, max_x=100, min_x=5, max_y=50, min_y=-5, visualization=True
  			)
  			print(
  			    '''The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '''
  			    f"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
  			)
  			def        __SCREAMING_SNAKE_CASE    (      a__						:      int ,a__						:      List[str]					)				->							Any:
  				return (3 * x**2) - (6 * y)
  
  			UpperCAmelCase_       :				Tuple		   =      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  			UpperCAmelCase_       :				Dict		   =      hill_climbing(prob, find_max=True)
  
  
  
  
  
  
  
  			print(
  			    '''The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
  			    f"""{local_min.score()}"""
  			)
  
  
  
  
  
  