




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'''



    lowerCamelCase_   :			CommonSchedulerState

    # setable values
    lowerCamelCase_   :			jnp.ndarray
    lowerCamelCase_   :			jnp.ndarray
    lowerCamelCase_   :			jnp.ndarray
    lowerCamelCase_   :			Optional[int]			  =   None

    # running values
    lowerCamelCase_   :			Optional[jnp.ndarray]			  =   None







    @classmethod
    def 					_lowercase  (					cls  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   Tuple:
           return cls(common=UpperCamelCase__  ,						init_noise_sigma=UpperCamelCase__  ,						timesteps=UpperCamelCase__  ,						sigmas=UpperCamelCase__  )




@dataclass
class 	UpperCamelCase__			(lowerCAmelCase__  ):

    '''simple docstring'''



    lowerCamelCase_   :			LMSDiscreteSchedulerState




class 	UpperCamelCase__			(lowerCAmelCase__					,       lowerCAmelCase__  ):

    '''simple docstring'''



    lowerCamelCase_   :			Tuple			  =   [e.name for e in FlaxKarrasDiffusionSchedulers]

    lowerCamelCase_   :			jnp.dtype







    @property
    def 					_lowercase  (					self  )  ->   Dict:
           return True







    @register_to_config
    def __init__(					self  ,						UpperCamelCase__ = 1000  ,						UpperCamelCase__ = 0.0001  ,						UpperCamelCase__ = 0.02  ,						UpperCamelCase__ = "linear"  ,						UpperCamelCase__ = None  ,						UpperCamelCase__ = "epsilon"  ,						UpperCamelCase__ = jnp.floataa  ,						)  ->   Optional[int]:
           lowerCamelCase     :   Dict    				=      dtype







    def 					_lowercase  (					self  ,						UpperCamelCase__ = None  )  ->   LMSDiscreteSchedulerState:
           if common is None:
                  lowerCamelCase     :   Optional[int]    				=      CommonSchedulerState.create(self  )

           lowerCamelCase     :   Union[str, Any]    				=      jnp.arange(0  ,						self.config.num_train_timesteps  ).round()[::-1]
           lowerCamelCase     :   Optional[Any]    				=      ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

           # standard deviation of the initial noise distribution
           lowerCamelCase     :   Optional[int]    				=      sigmas.max()

           return LMSDiscreteSchedulerState.create(
               common=UpperCamelCase__  ,						init_noise_sigma=UpperCamelCase__  ,						timesteps=UpperCamelCase__  ,						sigmas=UpperCamelCase__  ,						)







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   jnp.ndarray:
           ((lowerCamelCase)				,   )     :   int    				=      jnp.where(state.timesteps == timestep  ,						size=1  )
           lowerCamelCase     :   int    				=      step_index[0]

           lowerCamelCase     :   List[Any]    				=      state.sigmas[step_index]
           lowerCamelCase     :   Tuple    				=      sample / ((sigma**2 + 1) ** 0.5)
           return sample







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   str:

           def lms_derivative(UpperCamelCase__  ):
                  lowerCamelCase     :   Optional[int]    				=      1.0
                  for k in range(UpperCamelCase__  ):
                         if current_order == k:
                                continue
                         prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
                  return prod

           lowerCamelCase     :   List[str]    				=      integrate.quad(UpperCamelCase__  ,						state.sigmas[t]  ,						state.sigmas[t + 1]  ,						epsrel=1e-4  )[0]

           return integrated_coeff







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__ = ()  )  ->   LMSDiscreteSchedulerState:
           lowerCamelCase     :   Tuple    				=      jnp.linspace(self.config.num_train_timesteps - 1  ,						0  ,						UpperCamelCase__  ,						dtype=self.dtype  )

           lowerCamelCase     :   Optional[int]    				=      jnp.floor(UpperCamelCase__  ).astype(jnp.intaa  )
           lowerCamelCase     :   Optional[int]    				=      jnp.ceil(UpperCamelCase__  ).astype(jnp.intaa  )

           lowerCamelCase     :   Optional[Any]    				=      jnp.mod(UpperCamelCase__  ,						1.0  )

           lowerCamelCase     :   Dict    				=      ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
           lowerCamelCase     :   List[Any]    				=      (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
           lowerCamelCase     :   List[Any]    				=      jnp.concatenate([sigmas, jnp.array([0.0]  ,						dtype=self.dtype  )]  )

           lowerCamelCase     :   Optional[Any]    				=      timesteps.astype(jnp.intaa  )

           # initial running values
           lowerCamelCase     :   int    				=      jnp.zeros((0,) + shape  ,						dtype=self.dtype  )

           return state.replace(
               timesteps=UpperCamelCase__  ,						sigmas=UpperCamelCase__  ,						num_inference_steps=UpperCamelCase__  ,						derivatives=UpperCamelCase__  ,						)







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__ = 4  ,						UpperCamelCase__ = True  ,						)  ->   Union[FlaxLMSSchedulerOutput, Tuple]:
           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"  )

           lowerCamelCase     :   Optional[int]    				=      state.sigmas[timestep]

           # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
           if self.config.prediction_type == "epsilon":
                  lowerCamelCase     :   str    				=      sample - sigma * model_output
           elif self.config.prediction_type == "v_prediction":
                  # * c_out + input * c_skip
                  lowerCamelCase     :   Any    				=      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
           lowerCamelCase     :   Any    				=      (sample - pred_original_sample) / sigma
           lowerCamelCase     :   List[str]    				=      state.replace(derivatives=jnp.append(state.derivatives  ,						UpperCamelCase__  )  )
           if len(state.derivatives  ) > order:
                  lowerCamelCase     :   Union[str, Any]    				=      state.replace(derivatives=jnp.delete(state.derivatives  ,						0  )  )

           # 3. Compute linear multistep coefficients
           lowerCamelCase     :   Union[str, Any]    				=      min(timestep + 1  ,						UpperCamelCase__  )
           lowerCamelCase     :   Dict    				=      [self.get_lms_coefficient(UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ) for curr_order in range(UpperCamelCase__  )]

           # 4. Compute previous sample based on the derivatives path
           lowerCamelCase     :   int    				=      sample + sum(
               coeff * derivative for coeff, derivative in zip(UpperCamelCase__  ,						reversed(state.derivatives  )  )  )

           if not return_dict:
                  return (prev_sample, state)

           return FlaxLMSSchedulerOutput(prev_sample=UpperCamelCase__  ,						state=UpperCamelCase__  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						)  ->   jnp.ndarray:
           lowerCamelCase     :   List[str]    				=      state.sigmas[timesteps].flatten()
           lowerCamelCase     :   Any    				=      broadcast_to_shape_from_left(UpperCamelCase__  ,						noise.shape  )

           lowerCamelCase     :   Any    				=      original_samples + noise * sigma

           return noisy_samples







    def __len__(					self  )  ->   Optional[Any]:
           return self.config.num_train_timesteps












from itertools import compress, repeat
from math import ceil, sqrt

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list[int]:

       if num <= 2:
              return []
       if num == 3:
              return [2]

       # Odd sieve for numbers in range [3, num - 1]
       lowerCamelCase     :   str    				=      bytearray(B"\x01"					) * ((num >> 1) - 1)

       for i in range(3				,int(sqrt(_SCREAMING_SNAKE_CASE					)					) + 1				,2					):
              if sieve[(i >> 1) - 1]:
                     lowerCamelCase     :   Tuple    				=      i**2
                     lowerCamelCase     :   str    				=      repeat(
                         0				,ceil((num - i_squared) / (i << 1)					)					)

       return [2] + list(compress(range(3				,_SCREAMING_SNAKE_CASE				,2					)				,_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






