code: 
  
  
  
  
  
  
  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     __a						:
   _lowerCAmelCase : str 				=				4_2
  
   # setable values
   _lowerCAmelCase : Any 				=				4_2
   _lowerCAmelCase : str 				=				4_2
   _lowerCAmelCase : Union[str, Any] 				=				4_2
   _lowerCAmelCase : Union[str, Any] 				=				None
  
   # running values
   _lowerCAmelCase : List[str] 				=				None
  
  
  
  
  
  
  
   @classmethod
   def       __lowercase      (	cls      :     int							,     SCREAMING_SNAKE_CASE      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     Dict							,     SCREAMING_SNAKE_CASE      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     Optional[Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return cls(common=lowerCamelCase__							,     init_noise_sigma=lowerCamelCase__							,     timesteps=lowerCamelCase__							,     sigmas=lowerCamelCase__		)
  
  
  
  
  
  
  
  @dataclass
  class     __a						(					_a ):
   _lowerCAmelCase : Any 				=				4_2
  
  
  
  
  
  
  
  class     __a						(					_a ,     _a ):
   _lowerCAmelCase : Optional[Any] 				=				[e.name for e in FlaxKarrasDiffusionSchedulers]
  
   _lowerCAmelCase : Union[str, Any] 				=				4_2
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Tuple		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return True
  
  
  
  
  
  
  
   @register_to_config
   def __init__(	self      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     Tuple = 10_00							,     SCREAMING_SNAKE_CASE      :     List[str] = 0.0_0_0_1							,     SCREAMING_SNAKE_CASE      :     List[Any] = 0.0_2							,     SCREAMING_SNAKE_CASE      :     Union[str, Any] = "linear"							,     SCREAMING_SNAKE_CASE      :     Dict = None							,     SCREAMING_SNAKE_CASE      :     Any = "epsilon"							,     SCREAMING_SNAKE_CASE      :     Dict = jnp.floataa							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Optional[Any]        = dtype
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     int							,     SCREAMING_SNAKE_CASE      :     Any = None		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        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      :     Any							,     SCREAMING_SNAKE_CASE      :     List[str]							,     SCREAMING_SNAKE_CASE      :     Optional[int]							,     SCREAMING_SNAKE_CASE      :     List[Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        (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      :     str							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     Any							,     SCREAMING_SNAKE_CASE      :     Dict							,     SCREAMING_SNAKE_CASE      :     int		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        def lms_derivative(SCREAMING_SNAKE_CASE      :     Any		):
             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      :     Any							,     SCREAMING_SNAKE_CASE      :     Tuple							,     SCREAMING_SNAKE_CASE      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     Optional[int] = ()		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        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      :     Tuple							,     SCREAMING_SNAKE_CASE      :     str							,     SCREAMING_SNAKE_CASE      :     List[str]							,     SCREAMING_SNAKE_CASE      :     str							,     SCREAMING_SNAKE_CASE      :     Dict							,     SCREAMING_SNAKE_CASE      :     Union[str, Any] = 4							,     SCREAMING_SNAKE_CASE      :     List[str] = True							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        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      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     Optional[Any]							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        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      :     Optional[Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return self.config.num_train_timesteps
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			list[int]:
       if not list_of_ints:
            return []
  
       if min(__lowerCAmelCase    ) < 0:
            raise ValueError("All numbers must be positive"    )
  
       UpperCamelCase__    :     Dict        =						max(len(bin(__lowerCAmelCase    )[2:]    ) for x in list_of_ints    )
       return _msd_radix_sort(__lowerCAmelCase      ,					__lowerCAmelCase    )
  
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase      ,					__lowerCAmelCase    )				->			list[int]:
       if bit_position == 0 or len(__lowerCAmelCase    ) in [0, 1]:
            return list_of_ints
  
       UpperCamelCase__    :     Union[str, Any]        =						[]
       UpperCamelCase__    :     Dict        =						[]
       # Split numbers based on bit at bit_position from the right
       for number in list_of_ints:
            if (number >> (bit_position - 1)) & 1:
                 # number has a one at bit bit_position
                 ones.append(__lowerCAmelCase    )
            else:
                 # number has a zero at bit bit_position
                 zeros.append(__lowerCAmelCase    )
  
      # recursively split both lists further
       UpperCamelCase__    :     str        =						_msd_radix_sort(__lowerCAmelCase      ,					bit_position - 1    )
       UpperCamelCase__    :     Optional[Any]        =						_msd_radix_sort(__lowerCAmelCase      ,					bit_position - 1    )
  
       # recombine lists
       UpperCamelCase__    :     Optional[int]        =						zeros
       res.extend(__lowerCAmelCase    )
  
       return res
  
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			Dict:
       UpperCamelCase__    :     Optional[int]        =						len(__lowerCAmelCase    )
       if not list_of_ints or length == 1:
            return
  
       if min(__lowerCAmelCase    ) < 0:
            raise ValueError("All numbers must be positive"    )
  
       UpperCamelCase__    :     int        =						max(len(bin(__lowerCAmelCase    )[2:]    ) for x in list_of_ints    )
       _msd_radix_sort_inplace(__lowerCAmelCase      ,					__lowerCAmelCase      ,					0      ,					__lowerCAmelCase    )
  
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )				->			List[str]:
       if bit_position == 0 or end_index - begin_index <= 1:
            return
  
       bit_position -= 1
  
       UpperCamelCase__    :     Any        =						begin_index
       UpperCamelCase__    :     List[str]        =						end_index - 1
       while i <= j:
            UpperCamelCase__    :     Tuple        =						False
            if not (list_of_ints[i] >> bit_position) & 1:
                 # found zero at the beginning
                 i += 1
                 UpperCamelCase__    :     Any        =						True
            if (list_of_ints[j] >> bit_position) & 1:
                 # found one at the end
                 j -= 1
                 UpperCamelCase__    :     Dict        =						True
  
            if changed:
                 continue
  
            UpperCamelCase__       ,  UpperCamelCase__    :     Any        =						list_of_ints[j], list_of_ints[i]
            j -= 1
            if j != i:
                 i += 1
  
       _msd_radix_sort_inplace(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )
       _msd_radix_sort_inplace(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()