





"""simple docstring"""





# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

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

import flax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)





@flax.struct.dataclass
class 			snake_case		:
      lowerCamelCase__						= 42
      lowerCamelCase__						= 42

      # setable values
      lowerCamelCase__						= 42
      lowerCamelCase__						= 42
      lowerCamelCase__						= None

      @classmethod
      def 						SCREAMING_SNAKE_CASE_			(			cls   :Tuple						,							_lowerCamelCase   :CommonSchedulerState						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							):
       return cls(
           common=_lowerCamelCase						,							final_alpha_cumprod=_lowerCamelCase						,							init_noise_sigma=_lowerCamelCase						,							timesteps=_lowerCamelCase						,							)







@dataclass
class 			snake_case		(   __UpperCAmelCase   ):
      lowerCamelCase__						= 42







class 			snake_case		(   __UpperCAmelCase ,     __UpperCAmelCase   ):
      lowerCamelCase__						= [e.name for e in FlaxKarrasDiffusionSchedulers]

      lowerCamelCase__						= 42

      @property
      def 						SCREAMING_SNAKE_CASE_			(			self   :int						):
       return True

      @register_to_config
      def __init__(			self   :List[Any]						,							_lowerCamelCase   :int = 1_0_0_0						,							_lowerCamelCase   :float = 0.0_0_0_1						,							_lowerCamelCase   :float = 0.0_2						,							_lowerCamelCase   :str = "linear"						,							_lowerCamelCase   :Optional[jnp.ndarray] = None						,							_lowerCamelCase   :bool = True						,							_lowerCamelCase   :int = 0						,							_lowerCamelCase   :str = "epsilon"						,							_lowerCamelCase   :jnp.dtype = jnp.floataa						,							):
       __SCREAMING_SNAKE_CASE :			Dict												=       dtype

      def 						SCREAMING_SNAKE_CASE_			(			self   :List[str]						,							_lowerCamelCase   :Optional[CommonSchedulerState] = None						):
       if common is None:
        __SCREAMING_SNAKE_CASE :			int												=       CommonSchedulerState.create(self						)

       # At every step in ddim, we are looking into the previous alphas_cumprod
       # For the final step, there is no previous alphas_cumprod because we are already at 0
       # `set_alpha_to_one` decides whether we set this parameter simply to one or
       # whether we use the final alpha of the "non-previous" one.
       __SCREAMING_SNAKE_CASE :			int												=       (
           jnp.array(1.0						,							dtype=self.dtype						) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
       )

       # standard deviation of the initial noise distribution
       __SCREAMING_SNAKE_CASE :			int												=       jnp.array(1.0						,							dtype=self.dtype						)

       __SCREAMING_SNAKE_CASE :			Optional[Any]												=       jnp.arange(0						,							self.config.num_train_timesteps						).round()[::-1]

       return DDIMSchedulerState.create(
           common=_lowerCamelCase						,							final_alpha_cumprod=_lowerCamelCase						,							init_noise_sigma=_lowerCamelCase						,							timesteps=_lowerCamelCase						,							)

      def 						SCREAMING_SNAKE_CASE_			(			self   :Union[str, Any]						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :Optional[int] = None						):
       return sample

      def 						SCREAMING_SNAKE_CASE_			(			self   :Optional[int]						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :int						,							_lowerCamelCase   :Tuple = ()						):
       __SCREAMING_SNAKE_CASE :			int												=       self.config.num_train_timesteps // num_inference_steps
       # creates integer timesteps by multiplying by ratio
       # rounding to avoid issues when num_inference_step is power of 3
       __SCREAMING_SNAKE_CASE :			List[Any]												=       (jnp.arange(0						,							_lowerCamelCase						) * step_ratio).round()[::-1] + self.config.steps_offset

       return state.replace(
           num_inference_steps=_lowerCamelCase						,							timesteps=_lowerCamelCase						,							)

      def 						SCREAMING_SNAKE_CASE_			(			self   :Tuple						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :Tuple						,							_lowerCamelCase   :int						):
       __SCREAMING_SNAKE_CASE :			int												=       state.common.alphas_cumprod[timestep]
       __SCREAMING_SNAKE_CASE :			int												=       jnp.where(
           prev_timestep >= 0						,							state.common.alphas_cumprod[prev_timestep]						,							state.final_alpha_cumprod						)
       __SCREAMING_SNAKE_CASE :			Any												=       1 - alpha_prod_t
       __SCREAMING_SNAKE_CASE :			Any												=       1 - alpha_prod_t_prev

       __SCREAMING_SNAKE_CASE :			Union[str, Any]												=       (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

       return variance

      def 						SCREAMING_SNAKE_CASE_			(			self   :str						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :int						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :float = 0.0						,							_lowerCamelCase   :bool = 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'''						)

       # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
       # Ideally, read DDIM paper in-detail understanding

       # Notation (<variable name> -> <name in paper>
       # - pred_noise_t -> e_theta(x_t, t)
       # - pred_original_sample -> f_theta(x_t, t) or x_0
       # - std_dev_t -> sigma_t
       # - eta -> η
       # - pred_sample_direction -> "direction pointing to x_t"
       # - pred_prev_sample -> "x_t-1"

       # 1. get previous step value (=t-1)
       __SCREAMING_SNAKE_CASE :			Any												=       timestep - self.config.num_train_timesteps // state.num_inference_steps

       __SCREAMING_SNAKE_CASE :			int												=       state.common.alphas_cumprod
       __SCREAMING_SNAKE_CASE :			List[str]												=       state.final_alpha_cumprod

       # 2. compute alphas, betas
       __SCREAMING_SNAKE_CASE :			Dict												=       alphas_cumprod[timestep]
       __SCREAMING_SNAKE_CASE :			Tuple												=       jnp.where(prev_timestep >= 0						,							alphas_cumprod[prev_timestep]						,							_lowerCamelCase						)

       __SCREAMING_SNAKE_CASE :			int												=       1 - alpha_prod_t

       # 3. compute predicted original sample from predicted noise also called
       # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
       if self.config.prediction_type == "epsilon":
        __SCREAMING_SNAKE_CASE :			int												=       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
        __SCREAMING_SNAKE_CASE :			Dict												=       model_output
       elif self.config.prediction_type == "sample":
        __SCREAMING_SNAKE_CASE :			List[Any]												=       model_output
        __SCREAMING_SNAKE_CASE :			Union[str, Any]												=       (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
       elif self.config.prediction_type == "v_prediction":
        __SCREAMING_SNAKE_CASE :			Any												=       (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
        __SCREAMING_SNAKE_CASE :			List[Any]												=       (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
       else:
        raise ValueError(
            f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'''
            ''' `v_prediction`'''						)

       # 4. compute variance: "sigma_t(η)" -> see formula (16)
       # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
       __SCREAMING_SNAKE_CASE :			str												=       self._get_variance(_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE :			Optional[Any]												=       eta * variance ** 0.5

       # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
       __SCREAMING_SNAKE_CASE :			Any												=       (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

       # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
       __SCREAMING_SNAKE_CASE :			int												=       alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

       if not return_dict:
        return (prev_sample, state)

       return FlaxDDIMSchedulerOutput(prev_sample=_lowerCamelCase						,							state=_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_			(			self   :Dict						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							):
       return add_noise_common(state.common						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_			(			self   :List[str]						,							_lowerCamelCase   :DDIMSchedulerState						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							_lowerCamelCase   :jnp.ndarray						,							):
       return get_velocity_common(state.common						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)



      def __len__(			self   :Tuple						):
       return self.config.num_train_timesteps








"""simple docstring"""





import math




def 		lowerCAmelCase_	(  lowercase_   :							int		):

 '''simple docstring'''






 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(lowercase_		) + 1		) ,      6		):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True




def 		lowerCAmelCase_	(  lowercase_   :							int = 6008_5147_5143		):

 '''simple docstring'''






 try:
  __SCREAMING_SNAKE_CASE :			Any												=       int(lowercase_		)
 except (TypeError, ValueError):
  raise TypeError('''Parameter n must be int or castable to int.'''		)
 if n <= 0:
  raise ValueError('''Parameter n must be greater than or equal to one.'''		)
 __SCREAMING_SNAKE_CASE :			List[str]												=       0
 if is_prime(lowercase_		):
  return n
 while n % 2 == 0:
  n //= 2
 if is_prime(lowercase_		):
  return n
 for i in range(3 ,      int(math.sqrt(lowercase_		)		) + 1 ,      2		):
  if n % i == 0:
   if is_prime(n // i		):
    __SCREAMING_SNAKE_CASE :			Optional[int]												=       n // i
    break
   elif is_prime(lowercase_		):
    __SCREAMING_SNAKE_CASE :			Any												=       i
 return max_number


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

