code: 
  '''simple docstring'''
  
  from dataclasses import dataclass
  from typing import Optional, Tuple, Union
  
  import flax
  import jax.numpy as jnp
  from scipy import integrate
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from .scheduling_utils_flax import (
      CommonSchedulerState,
      FlaxKarrasDiffusionSchedulers,
      FlaxSchedulerMixin,
      FlaxSchedulerOutput,
      broadcast_to_shape_from_left,
  )
  
  @flax.struct.dataclass
  class 			UpperCAmelCase				:
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		A__  :   Dict          =    42
  
  		# setable values
  		A__  :   Dict          =    42
  		A__  :   Any          =    42
  		A__  :   str          =    42
  		A__  :   Tuple          =    None
  
  		# running values
  		A__  :   Optional[int]          =    None
  		@classmethod
  		def _lowercase  (    cls  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					_snake_case     )				->    List[str]:
  				return cls(common=lowerCamelCase__  ,					init_noise_sigma=lowerCamelCase__  ,					timesteps=lowerCamelCase__  ,					sigmas=lowerCamelCase__     )
  
  
  
  
  
  
  
  @dataclass
  class 			UpperCAmelCase				(					_a ):
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		A__  :   Dict          =    42
  
  
  
  
  
  
  
  class 			UpperCAmelCase				(					_a  ,		_a ):
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		A__  :   List[str]          =    [e.name for e in FlaxKarrasDiffusionSchedulers]
  
  		A__  :   Union[str, Any]          =    42
  		@property
  		def _lowercase  (    self     )				->    int:
  				return True
  		@register_to_config
  		def __init__(    self  ,					_snake_case = 1000  ,					_snake_case = 0.0_001  ,					_snake_case = 0.02  ,					_snake_case = "linear"  ,					_snake_case = None  ,					_snake_case = "epsilon"  ,					_snake_case = jnp.floataa  ,					)				->    str:
  				_UpperCamelCase       : Optional[Any]    =      dtype
  		def _lowercase  (    self  ,					_snake_case = None     )				->    Union[str, Any]:
  				if common is None:
  						_UpperCamelCase       : Union[str, Any]    =      CommonSchedulerState.create(self     )
  
  				_UpperCamelCase       : int    =      jnp.arange(0  ,					self.config.num_train_timesteps     ).round()[::-1]
  				_UpperCamelCase       : Dict    =      ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5
  
  				# standard deviation of the initial noise distribution
  				_UpperCamelCase       : Optional[Any]    =      sigmas.max()
  
  				return LMSDiscreteSchedulerState.create(
  				    common=lowerCamelCase__  ,					init_noise_sigma=lowerCamelCase__  ,					timesteps=lowerCamelCase__  ,					sigmas=lowerCamelCase__  ,					)
  		def _lowercase  (    self  ,					_snake_case  ,					_snake_case  ,					_snake_case     )				->    Dict:
  				(_UpperCamelCase	)       : Optional[Any]    =      jnp.where(state.timesteps == timestep  ,					size=1     )
  				_UpperCamelCase       : Optional[Any]    =      step_index[0]
  
  				_UpperCamelCase       : Dict    =      state.sigmas[step_index]
  				_UpperCamelCase       : Optional[Any]    =      sample / ((sigma**2 + 1) ** 0.5)
  				return sample
  		def _lowercase  (    self  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					_snake_case     )				->    Tuple:
  
  				def lms_derivative(_snake_case     ):
  						_UpperCamelCase       : Optional[Any]    =      1.0
  						for k in range(lowerCamelCase__     ):
  								if current_order == k:
  										continue
  								prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
  						return prod
  
  				_UpperCamelCase       : Tuple    =      integrate.quad(lowerCamelCase__  ,					state.sigmas[t]  ,					state.sigmas[t + 1]  ,					epsrel=1E-4     )[0]
  
  				return integrated_coeff
  		def _lowercase  (    self  ,					_snake_case  ,					_snake_case  ,					_snake_case = ()     )				->    List[str]:
  				_UpperCamelCase       : int    =      jnp.linspace(self.config.num_train_timesteps - 1  ,					0  ,					lowerCamelCase__  ,					dtype=self.dtype     )
  
  				_UpperCamelCase       : Optional[Any]    =      jnp.floor(lowerCamelCase__     ).astype(jnp.intaa     )
  				_UpperCamelCase       : Union[str, Any]    =      jnp.ceil(lowerCamelCase__     ).astype(jnp.intaa     )
  
  				_UpperCamelCase       : List[str]    =      jnp.mod(lowerCamelCase__  ,					1.0     )
  
  				_UpperCamelCase       : Union[str, Any]    =      ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
  				_UpperCamelCase       : Union[str, Any]    =      (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
  				_UpperCamelCase       : Optional[Any]    =      jnp.concatenate([sigmas, jnp.array([0.0]  ,					dtype=self.dtype     )]     )
  
  				_UpperCamelCase       : str    =      timesteps.astype(jnp.intaa     )
  
  				# initial running values
  				_UpperCamelCase       : Dict    =      jnp.zeros((0,) + shape  ,					dtype=self.dtype     )
  
  				return state.replace(
  				    timesteps=lowerCamelCase__  ,					sigmas=lowerCamelCase__  ,					num_inference_steps=lowerCamelCase__  ,					derivatives=lowerCamelCase__  ,					)
  		def _lowercase  (    self  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					_snake_case = 4  ,					_snake_case = True  ,					)				->    List[Any]:
  				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'''     )
  
  				_UpperCamelCase       : Optional[int]    =      state.sigmas[timestep]
  
  				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
  				if self.config.prediction_type == "epsilon":
  						_UpperCamelCase       : Union[str, Any]    =      sample - sigma * model_output
  				elif self.config.prediction_type == "v_prediction":
  						# * c_out + input * c_skip
  						_UpperCamelCase       : Dict    =      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
  				else:
  						raise ValueError(
  						    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''     )
  
  				# 2. Convert to an ODE derivative
  				_UpperCamelCase       : Optional[int]    =      (sample - pred_original_sample) / sigma
  				_UpperCamelCase       : List[Any]    =      state.replace(derivatives=jnp.append(state.derivatives  ,					lowerCamelCase__     )     )
  				if len(state.derivatives     ) > order:
  						_UpperCamelCase       : Tuple    =      state.replace(derivatives=jnp.delete(state.derivatives  ,					0     )     )
  
  				# 3. Compute linear multistep coefficients
  				_UpperCamelCase       : Union[str, Any]    =      min(timestep + 1  ,					lowerCamelCase__     )
  				_UpperCamelCase       : Any    =      [self.get_lms_coefficient(lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__     ) for curr_order in range(lowerCamelCase__     )]
  
  				# 4. Compute previous sample based on the derivatives path
  				_UpperCamelCase       : Optional[int]    =      sample + sum(
  				    coeff * derivative for coeff, derivative in zip(lowerCamelCase__  ,					reversed(state.derivatives     )     )     )
  
  				if not return_dict:
  						return (prev_sample, state)
  
  				return FlaxLMSSchedulerOutput(prev_sample=lowerCamelCase__  ,					state=lowerCamelCase__     )
  		def _lowercase  (    self  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					_snake_case  ,					)				->    List[str]:
  				_UpperCamelCase       : Tuple    =      state.sigmas[timesteps].flatten()
  				_UpperCamelCase       : int    =      broadcast_to_shape_from_left(lowerCamelCase__  ,					noise.shape     )
  
  				_UpperCamelCase       : str    =      original_samples + noise * sigma
  
  				return noisy_samples
  
  
  
  
  		def __len__(    self     )				->    List[Any]:
  				return self.config.num_train_timesteps
  
  
  
  
  
  
style_context: 
  '''simple docstring'''
  
  import unittest
  
  from transformers.image_processing_utils import get_size_dict
  
  class 			UpperCAmelCase				(					unittest.TestCase ):
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		def _lowercase  (    self     )				->    Dict:
  				# Test a dict with the wrong keys raises an error
  				_UpperCamelCase       : List[Any]    =      {'''wrong_key''': 224}
  				with self.assertRaises(_snake_case     ):
  						get_size_dict(_snake_case     )
  
  				_UpperCamelCase       : Dict    =      {'''height''': 224}
  				with self.assertRaises(_snake_case     ):
  						get_size_dict(_snake_case     )
  
  				_UpperCamelCase       : str    =      {'''width''': 224, '''shortest_edge''': 224}
  				with self.assertRaises(_snake_case     ):
  						get_size_dict(_snake_case     )
  
  				# Test a dict with the correct keys is returned as is
  				_UpperCamelCase       : Any    =      {'''height''': 224, '''width''': 224}
  				_UpperCamelCase       : Optional[int]    =      get_size_dict(_snake_case     )
  				self.assertEqual(_snake_case  ,					_snake_case     )
  
  				_UpperCamelCase       : Optional[Any]    =      {'''shortest_edge''': 224}
  				_UpperCamelCase       : int    =      get_size_dict(_snake_case     )
  				self.assertEqual(_snake_case  ,					{'''shortest_edge''': 224}     )
  
  				_UpperCamelCase       : int    =      {'''longest_edge''': 224, '''shortest_edge''': 224}
  				_UpperCamelCase       : Tuple    =      get_size_dict(_snake_case     )
  				self.assertEqual(_snake_case  ,					{'''longest_edge''': 224, '''shortest_edge''': 224}     )
  
  				# Test a single int value which  represents (size, size)
  				_UpperCamelCase       : Any    =      get_size_dict(224     )
  				self.assertEqual(_snake_case  ,					{'''height''': 224, '''width''': 224}     )
  
  				# Test a single int value which represents the shortest edge
  				_UpperCamelCase       : List[Any]    =      get_size_dict(224  ,					default_to_square=_snake_case     )
  				self.assertEqual(_snake_case  ,					{'''shortest_edge''': 224}     )
  
  				# Test a tuple of ints which represents (height, width)
  				_UpperCamelCase       : Any    =      get_size_dict((150, 200)     )
  				self.assertEqual(_snake_case  ,					{'''height''': 150, '''width''': 200}     )
  
  				# Test a tuple of ints which represents (width, height)
  				_UpperCamelCase       : List[str]    =      get_size_dict((150, 200)  ,					height_width_order=_snake_case     )
  				self.assertEqual(_snake_case  ,					{'''height''': 200, '''width''': 150}     )
  
  				# Test an int representing the shortest edge and max_size which represents the longest edge
  				_UpperCamelCase       : Any    =      get_size_dict(224  ,					max_size=256  ,					default_to_square=_snake_case     )
  				self.assertEqual(_snake_case  ,					{'''shortest_edge''': 224, '''longest_edge''': 256}     )
  
  				# Test int with default_to_square=True and max_size fails
  				with self.assertRaises(_snake_case     ):
  						get_size_dict(224  ,					max_size=256  ,					default_to_square=_snake_case     )
  
  
  
  
  
  