






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







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()