





"""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      :





 """simple docstring"""


 _lowerCamelCase				 =  42
 _lowerCamelCase				 =  42

 # setable values
 _lowerCamelCase				 =  42
 _lowerCamelCase				 =  42
 _lowerCamelCase				 =  None

 @classmethod
 def       UpperCamelCase__(					cls      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		):



     '''simple docstring'''




     return cls(
         common=__lowerCamelCase      ,		final_alpha_cumprod=__lowerCamelCase      ,		init_noise_sigma=__lowerCamelCase      ,		timesteps=__lowerCamelCase      ,		)






@dataclass
class 	__snake_case      (	SCREAMING_SNAKE_CASE__  ):





 """simple docstring"""


 _lowerCamelCase				 =  42






class 	__snake_case      (	SCREAMING_SNAKE_CASE__							,							SCREAMING_SNAKE_CASE__  ):





 """simple docstring"""


 _lowerCamelCase				 =  [e.name for e in FlaxKarrasDiffusionSchedulers]

 _lowerCamelCase				 =  42

 @property
 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     return True

 @register_to_config
 def __init__(					self      ,		__lowerCamelCase = 1000      ,		__lowerCamelCase = 0.0_0_0_1      ,		__lowerCamelCase = 0.0_2      ,		__lowerCamelCase = "linear"      ,		__lowerCamelCase = None      ,		__lowerCamelCase = True      ,		__lowerCamelCase = 0      ,		__lowerCamelCase = "epsilon"      ,		__lowerCamelCase = jnp.floataa      ,		):



     '''simple docstring'''




     __A					:		Tuple						=  dtype

 def       UpperCamelCase__(					self      ,		__lowerCamelCase = None						):



     '''simple docstring'''




     if common is None:
         __A					:		Any						=  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.
     __A					:		str						=  (
         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
     __A					:		Tuple						=  jnp.array(1.0      ,		dtype=self.dtype						)

     __A					:		Dict						=  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       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase = None						):



     '''simple docstring'''




     return sample

 def       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase = ()						):



     '''simple docstring'''




     __A					:		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
     __A					:		Dict						=  (jnp.arange(0      ,		__lowerCamelCase						) * step_ratio).round()[::-1] + self.config.steps_offset

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

 def       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase						):



     '''simple docstring'''




     __A					:		Dict						=  state.common.alphas_cumprod[timestep]
     __A					:		Union[str, Any]						=  jnp.where(
         prev_timestep >= 0      ,		state.common.alphas_cumprod[prev_timestep]      ,		state.final_alpha_cumprod						)
     __A					:		List[Any]						=  1 - alpha_prod_t
     __A					:		Union[str, Any]						=  1 - alpha_prod_t_prev

     __A					:		Optional[Any]						=  (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

     return variance

 def       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase = 0.0      ,		__lowerCamelCase = 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'''						)

     # 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)
     __A					:		str						=  timestep - self.config.num_train_timesteps // state.num_inference_steps

     __A					:		List[Any]						=  state.common.alphas_cumprod
     __A					:		Dict						=  state.final_alpha_cumprod

     # 2. compute alphas, betas
     __A					:		Tuple						=  alphas_cumprod[timestep]
     __A					:		List[Any]						=  jnp.where(prev_timestep >= 0      ,		alphas_cumprod[prev_timestep]      ,		__lowerCamelCase						)

     __A					:		Tuple						=  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":
         __A					:		List[Any]						=  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         __A					:		Optional[Any]						=  model_output
     elif self.config.prediction_type == "sample":
         __A					:		str						=  model_output
         __A					:		List[Any]						=  (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
     elif self.config.prediction_type == "v_prediction":
         __A					:		str						=  (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
         __A					:		List[str]						=  (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)
     __A					:		List[str]						=  self._get_variance(__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase						)
     __A					:		Optional[Any]						=  eta * variance ** 0.5

     # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
     __A					:		int						=  (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
     __A					:		Optional[Any]						=  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       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		):



     '''simple docstring'''




     return add_noise_common(state.common      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase						)

 def       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		):



     '''simple docstring'''




     return get_velocity_common(state.common      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase						)







 def __len__(					self						):



     '''simple docstring'''




     return self.config.num_train_timesteps











"""simple docstring"""



import decimal







def 	__lowercase  (     )     ->int:



    '''simple docstring'''







    __A					:		List[str]						=  0
    __A					:		Tuple						=  decimal.Context(prec=105		)
    for i in range(2       ,100		):
        __A					:		int						=  decimal.Decimal(snake_case_		)
        __A					:		str						=  number.sqrt(snake_case_		)
        if len(str(snake_case_		)		) > 1:
            answer += int(str(snake_case_		)[0]		)
            __A					:		Optional[Any]						=  str(snake_case_		)[2:101]
            answer += sum(int(snake_case_		) for x in sqrt_number_str		)
    return answer


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       print(f'''{solution() = }''')




