





'''simple docstring'''




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 			SCREAMING_SNAKE_CASE   :
     # setable values
     lowerCAmelCase		      =	None
     lowerCAmelCase		      =	None
     lowerCAmelCase		      =	None  # sigma(t_i)


     @classmethod
     def 							SCREAMING_SNAKE_CASE  (						cls):

          '''simple docstring'''






          return cls()




@dataclass
class 			SCREAMING_SNAKE_CASE   (a__							):
     lowerCAmelCase		      =	42
     lowerCAmelCase		      =	42
     lowerCAmelCase		      =	42




class 			SCREAMING_SNAKE_CASE   (a__ ,		a__							):


     @property
     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return True


     @register_to_config
     def __init__(						self						,     _UpperCAmelCase = 0.02						,     _UpperCAmelCase = 100						,     _UpperCAmelCase = 1.007						,     _UpperCAmelCase = 80						,     _UpperCAmelCase = 0.05						,     _UpperCAmelCase = 50						,     ):

          '''simple docstring'''






          pass


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return KarrasVeSchedulerState.create()


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase = ()):

          '''simple docstring'''






          __A						:			str								=	jnp.arange(0						,     _UpperCAmelCase)[::-1].copy()
          __A						:			Optional[int]								=	[
              (
                  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 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     ):

          '''simple docstring'''






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

          # sample eps ~ N(0, S_noise^2 * I)
          __A						:			Dict								=	random.split(_UpperCAmelCase						,     num=1)
          __A						:			List[Any]								=	self.config.s_noise * random.normal(key=_UpperCAmelCase						,     shape=sample.shape)
          __A						:			Dict								=	sigma + gamma * sigma
          __A						:			Optional[int]								=	sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

          return sample_hat, sigma_hat


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase = True						,     ):

          '''simple docstring'''






          __A						:			List[str]								=	sample_hat + sigma_hat * model_output
          __A						:			Optional[int]								=	(sample_hat - pred_original_sample) / sigma_hat
          __A						:			Dict								=	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 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase = True						,     ):

          '''simple docstring'''






          __A						:			List[Any]								=	sample_prev + sigma_prev * model_output
          __A						:			int								=	(sample_prev - pred_original_sample) / sigma_prev
          __A						:			Optional[int]								=	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 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase						,     _UpperCAmelCase):

          '''simple docstring'''






          raise NotImplementedError()






'''simple docstring'''




import itertools
import math






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					bool:

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5			,							int(math.sqrt(__snake_case      ) + 1      )			,							6      ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 	_lowerCAmelCase      (  )					->					List[Any]:
     __A						:			Optional[Any]								=	2
     while True:
          if is_prime(__snake_case      ):
               yield num
          num += 1






def 	_lowerCAmelCase      (  __snake_case  :			int = 1_00_01      )					->					int:
     return next(itertools.islice(prime_generator()			,							nth - 1			,							__snake_case      )      )


if __name__ == "__main__":
  print(f"""{solution() = }""")