






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin






@flax.struct.dataclass
class 		lowercase_					:






      '''simple docstring'''




      __snake_case       =  None
      __snake_case       =  None
      __snake_case       =  None  # sigma(t_i)







      @classmethod
      def       __lowerCAmelCase					(      cls      :						Optional[int]  )    ->Optional[int]:




       """simple docstring"""


       return cls()






@dataclass
class 		lowercase_					(	lowercase   ):






      '''simple docstring'''




      __snake_case       =  42
      __snake_case       =  42
      __snake_case       =  42






class 		lowercase_					(	lowercase ,  lowercase   ):






      '''simple docstring'''




      @property
      def       __lowerCAmelCase					(      self      :						List[Any]  )    ->Any:




       """simple docstring"""


       return True







      @register_to_config
      def __init__(      self      :						Optional[int] ,					__UpperCAmelCase      :						float = 0.02 ,					__UpperCAmelCase      :						float = 100 ,					__UpperCAmelCase      :						float = 1.007 ,					__UpperCAmelCase      :						float = 80 ,					__UpperCAmelCase      :						float = 0.05 ,					__UpperCAmelCase      :						float = 50 ,					)    ->int:




       """simple docstring"""


       pass







      def       __lowerCAmelCase					(      self      :						List[Any]  )    ->str:




       """simple docstring"""


       return KarrasVeSchedulerState.create()







      def       __lowerCAmelCase					(      self      :						List[str] ,					__UpperCAmelCase      :						KarrasVeSchedulerState ,					__UpperCAmelCase      :						int ,					__UpperCAmelCase      :						Tuple = ()  )    ->KarrasVeSchedulerState:




       """simple docstring"""


       a		  =      jnp.arange(0 ,					__UpperCAmelCase  )[::-1].copy()
       a		  =      [
           (
               self.config.sigma_max**2
               * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
           )
           for i in timesteps
       ]

       return state.replace(
           num_inference_steps=__UpperCAmelCase ,					schedule=jnp.array(__UpperCAmelCase ,					dtype=jnp.floataa  ) ,					timesteps=__UpperCAmelCase ,					)







      def       __lowerCAmelCase					(      self      :						Optional[int] ,					__UpperCAmelCase      :						KarrasVeSchedulerState ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						float ,					__UpperCAmelCase      :						random.KeyArray ,					)    ->Tuple[jnp.ndarray, float]:




       """simple docstring"""


       if self.config.s_min <= sigma <= self.config.s_max:
        a		  =      min(self.config.s_churn / state.num_inference_steps ,					2**0.5 - 1  )
       else:
        a		  =      0

       # sample eps ~ N(0, S_noise^2 * I)
       a		  =      random.split(__UpperCAmelCase ,					num=1  )
       a		  =      self.config.s_noise * random.normal(key=__UpperCAmelCase ,					shape=sample.shape  )
       a		  =      sigma + gamma * sigma
       a		  =      sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

       return sample_hat, sigma_hat







      def       __lowerCAmelCase					(      self      :						Dict ,					__UpperCAmelCase      :						KarrasVeSchedulerState ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						float ,					__UpperCAmelCase      :						float ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						bool = True ,					)    ->Union[FlaxKarrasVeOutput, Tuple]:




       """simple docstring"""


       a		  =      sample_hat + sigma_hat * model_output
       a		  =      (sample_hat - pred_original_sample) / sigma_hat
       a		  =      sample_hat + (sigma_prev - sigma_hat) * derivative

       if not return_dict:
        return (sample_prev, derivative, state)

       return FlaxKarrasVeOutput(prev_sample=__UpperCAmelCase ,					derivative=__UpperCAmelCase ,					state=__UpperCAmelCase  )







      def       __lowerCAmelCase					(      self      :						Optional[Any] ,					__UpperCAmelCase      :						KarrasVeSchedulerState ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						float ,					__UpperCAmelCase      :						float ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						jnp.ndarray ,					__UpperCAmelCase      :						bool = True ,					)    ->Union[FlaxKarrasVeOutput, Tuple]:




       """simple docstring"""


       a		  =      sample_prev + sigma_prev * model_output
       a		  =      (sample_prev - pred_original_sample) / sigma_prev
       a		  =      sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

       if not return_dict:
        return (sample_prev, derivative, state)

       return FlaxKarrasVeOutput(prev_sample=__UpperCAmelCase ,					derivative=__UpperCAmelCase ,					state=__UpperCAmelCase  )







      def       __lowerCAmelCase					(      self      :						Union[str, Any] ,					__UpperCAmelCase      :						KarrasVeSchedulerState ,					__UpperCAmelCase      :						str ,					__UpperCAmelCase      :						List[str] ,					__UpperCAmelCase      :						int  )    ->Union[str, Any]:




       """simple docstring"""


       raise NotImplementedError()



'''simple docstring'''

from math import pow
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     ):
 if current_sum == needed_sum:
  # If the sum of the powers is equal to needed_sum, then we have a solution.
  solutions_count += 1
  return current_sum, solutions_count

 lowercase__				:    Optional[Any]  =					int(pow(UpperCAmelCase		,     UpperCAmelCase     )     )
 if current_sum + i_to_n <= needed_sum:
  # If the sum of the powers is less than needed_sum, then continue adding powers.
  current_sum += i_to_n
  lowercase__ ,							lowercase__				:    Dict  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
  current_sum -= i_to_n
 if i_to_n < needed_sum:
  # If the power of i is less than needed_sum, then try with the next power.
  lowercase__ ,							lowercase__				:    str  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
 return current_sum, solutions_count
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
  raise ValueError(
      '''Invalid input\n'''
      '''needed_sum must be between 1 and 1000, power between 2 and 10.'''     )

 return backtrack(UpperCAmelCase		,     UpperCAmelCase		,     1		,     0		,     0     )[1]  # Return the solutions_count


if __name__ == "__main__":
  import doctest

  doctest.testmod()

