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 							UpperCAmelCase_     :
       __lowerCamelCase										=     42
  
       # setable values
       __lowerCamelCase										=     42
       __lowerCamelCase										=     42
       __lowerCamelCase										=     42
       __lowerCamelCase										=     None
  
       # running values
       __lowerCamelCase										=     None
  
  
  
  
       @classmethod
       def      __UpperCAmelCase     (							cls  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            return cls(common=_lowerCAmelCase  ,	init_noise_sigma=_lowerCAmelCase  ,	timesteps=_lowerCAmelCase  ,	sigmas=_lowerCAmelCase		)
  
  
  
  
  
  
  
  @dataclass
  class 							UpperCAmelCase_     (		__lowerCamelCase		):
       __lowerCamelCase										=     42
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     (		__lowerCamelCase       ,			__lowerCamelCase		):
       __lowerCamelCase										=     [e.name for e in FlaxKarrasDiffusionSchedulers]
  
       __lowerCamelCase										=     42
  
  
  
  
       @property
       def      __UpperCAmelCase     (							self		):
            return True
  
  
  
  
       @register_to_config
       def __init__(							self  ,	_lowerCAmelCase = 1000  ,	_lowerCAmelCase = 0.0_0_0_1  ,	_lowerCAmelCase = 0.0_2  ,	_lowerCAmelCase = "linear"  ,	_lowerCAmelCase = None  ,	_lowerCAmelCase = "epsilon"  ,	_lowerCAmelCase = jnp.floataa  ,	):
            UpperCAmelCase__			:     Optional[Any]										= dtype
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase = None		):
            if common is None:
                 UpperCAmelCase__			:     Optional[int]										= CommonSchedulerState.create(self		)
  
            UpperCAmelCase__			:     Any										= jnp.arange(0  ,	self.config.num_train_timesteps		).round()[::-1]
            UpperCAmelCase__			:     Optional[int]										= ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5
  
            # standard deviation of the initial noise distribution
            UpperCAmelCase__			:     List[str]										= sigmas.max()
  
            return LMSDiscreteSchedulerState.create(
                common=_lowerCAmelCase  ,	init_noise_sigma=_lowerCAmelCase  ,	timesteps=_lowerCAmelCase  ,	sigmas=_lowerCAmelCase  ,	)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            (UpperCAmelCase__		)			:     Optional[int]										= jnp.where(state.timesteps == timestep  ,	size=1		)
            UpperCAmelCase__			:     Tuple										= step_index[0]
  
            UpperCAmelCase__			:     List[str]										= state.sigmas[step_index]
            UpperCAmelCase__			:     Optional[Any]										= sample / ((sigma**2 + 1) ** 0.5)
            return sample
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
  
            def lms_derivative(_lowerCAmelCase		):
                 UpperCAmelCase__			:     List[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__			:     Optional[Any]										= integrate.quad(_lowerCAmelCase  ,	state.sigmas[t]  ,	state.sigmas[t + 1]  ,	epsrel=1e-4		)[0]
  
            return integrated_coeff
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase = ()		):
            UpperCAmelCase__			:     List[Any]										= jnp.linspace(self.config.num_train_timesteps - 1  ,	0  ,	_lowerCAmelCase  ,	dtype=self.dtype		)
  
            UpperCAmelCase__			:     Tuple										= jnp.floor(_lowerCAmelCase		).astype(jnp.intaa		)
            UpperCAmelCase__			:     Optional[Any]										= jnp.ceil(_lowerCAmelCase		).astype(jnp.intaa		)
  
            UpperCAmelCase__			:     List[Any]										= jnp.mod(_lowerCAmelCase  ,	1.0		)
  
            UpperCAmelCase__			:     int										= ((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__			:     str										= jnp.concatenate([sigmas, jnp.array([0.0]  ,	dtype=self.dtype		)]		)
  
            UpperCAmelCase__			:     str										= timesteps.astype(jnp.intaa		)
  
            # initial running values
            UpperCAmelCase__			:     Tuple										= jnp.zeros((0,) + shape  ,	dtype=self.dtype		)
  
            return state.replace(
                timesteps=_lowerCAmelCase  ,	sigmas=_lowerCAmelCase  ,	num_inference_steps=_lowerCAmelCase  ,	derivatives=_lowerCAmelCase  ,	)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase = 4  ,	_lowerCAmelCase = 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"""		)
  
            UpperCAmelCase__			:     Union[str, Any]										= state.sigmas[timestep]
  
            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            if self.config.prediction_type == "epsilon":
                 UpperCAmelCase__			:     Optional[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__			:     Dict										= (sample - pred_original_sample) / sigma
            UpperCAmelCase__			:     Union[str, Any]										= state.replace(derivatives=jnp.append(state.derivatives  ,	_lowerCAmelCase		)		)
            if len(state.derivatives		) > order:
                 UpperCAmelCase__			:     Optional[int]										= state.replace(derivatives=jnp.delete(state.derivatives  ,	0		)		)
  
            # 3. Compute linear multistep coefficients
            UpperCAmelCase__			:     Union[str, Any]										= min(timestep + 1  ,	_lowerCAmelCase		)
            UpperCAmelCase__			:     List[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__			:     Dict										= 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      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	):
            UpperCAmelCase__			:     int										= state.sigmas[timesteps].flatten()
            UpperCAmelCase__			:     Dict										= broadcast_to_shape_from_left(_lowerCAmelCase  ,	noise.shape		)
  
            UpperCAmelCase__			:     Any										= original_samples + noise * sigma
  
            return noisy_samples
  
  
  
  
       def __len__(							self		):
            return self.config.num_train_timesteps
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
  
  
  
  
       def __init__(							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     List[Any]										= value
            UpperCAmelCase__			:     Node | None										= None
            UpperCAmelCase__			:     Node | None										= None
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
       __lowerCamelCase										=     42
  
  
  
  
       def __init__(							self		):
            UpperCAmelCase__			:     Any										= 0
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            if node is None:
                 return
  
            if path_sum == self.target:
                 self.paths += 1
  
            if node.left:
                 self.depth_first_search(node.left  ,	path_sum + node.left.value		)
            if node.right:
                 self.depth_first_search(node.right  ,	path_sum + node.right.value		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase = None		):
            if node is None:
                 return 0
            if target is not None:
                 UpperCAmelCase__			:     List[Any]										= target
  
            self.depth_first_search(_lowerCAmelCase  ,	node.value		)
            self.path_sum(node.left		)
            self.path_sum(node.right		)
  
            return self.paths
  
  
  if __name__ == "__main__":
        import doctest
  
        doctest.testmod()
  
  
  
  
  
  
  