"""simple docstring"""
def 		__a  (      _SCREAMING_SNAKE_CASE = 100						,	_SCREAMING_SNAKE_CASE = 100  )      ->int:
  return max(
      sum(int(_SCREAMING_SNAKE_CASE  ) for x in str(base**power  )  )
      for base in range(_SCREAMING_SNAKE_CASE  )
      for power in range(_SCREAMING_SNAKE_CASE  )  )


# Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()




# 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 			UpperCamelCase_				:




      '''simple docstring'''







      a		:CommonSchedulerState
      a		:jnp.ndarray

      # setable values
      a		:jnp.ndarray
      a		:jnp.ndarray
      a		:Optional[int]						 =      None







      @classmethod
      def lowercase__		( cls					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					):
            return cls(
                common=_UpperCAmelCase					,					final_alpha_cumprod=_UpperCAmelCase					,					init_noise_sigma=_UpperCAmelCase					,					timesteps=_UpperCAmelCase					,					)


@dataclass
class 			UpperCamelCase_				(  A     ):




      '''simple docstring'''







      a		:DDIMSchedulerState


class 			UpperCamelCase_				(  A					,       A     ):




      '''simple docstring'''







      a		:int						 =      [e.name for e in FlaxKarrasDiffusionSchedulers]

      a		:jnp.dtype







      @property
      def lowercase__		( self):
            return True







      @register_to_config
      def __init__( self					,					_UpperCAmelCase = 1_000					,					_UpperCAmelCase = 0.0001					,					_UpperCAmelCase = 0.02					,					_UpperCAmelCase = "linear"					,					_UpperCAmelCase = None					,					_UpperCAmelCase = True					,					_UpperCAmelCase = 0					,					_UpperCAmelCase = "epsilon"					,					_UpperCAmelCase = jnp.floataa					,					):
            lowerCAmelCase_						=      dtype







      def lowercase__		( self					,					_UpperCAmelCase = None):
            if common is None:
                  lowerCAmelCase_						=      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.
            lowerCAmelCase_						=      (
                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
            lowerCAmelCase_						=      jnp.array(1.0					,					dtype=self.dtype)

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

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







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase = None):
            return sample







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase = ()):
            lowerCAmelCase_						=      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
            lowerCAmelCase_						=      (jnp.arange(0					,					_UpperCAmelCase) * step_ratio).round()[::-1] + self.config.steps_offset

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







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase):
            lowerCAmelCase_						=      state.common.alphas_cumprod[timestep]
            lowerCAmelCase_						=      jnp.where(
                prev_timestep >= 0					,					state.common.alphas_cumprod[prev_timestep]					,					state.final_alpha_cumprod)
            lowerCAmelCase_						=      1 - alpha_prod_t
            lowerCAmelCase_						=      1 - alpha_prod_t_prev

            lowerCAmelCase_						=      (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

            return variance







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase = 0.0					,					_UpperCAmelCase = 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)
            lowerCAmelCase_						=      timestep - self.config.num_train_timesteps // state.num_inference_steps

            lowerCAmelCase_						=      state.common.alphas_cumprod
            lowerCAmelCase_						=      state.final_alpha_cumprod

            # 2. compute alphas, betas
            lowerCAmelCase_						=      alphas_cumprod[timestep]
            lowerCAmelCase_						=      jnp.where(prev_timestep >= 0					,					alphas_cumprod[prev_timestep]					,					_UpperCAmelCase)

            lowerCAmelCase_						=      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":
                  lowerCAmelCase_						=      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
                  lowerCAmelCase_						=      model_output
            elif self.config.prediction_type == "sample":
                  lowerCAmelCase_						=      model_output
                  lowerCAmelCase_						=      (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
            elif self.config.prediction_type == "v_prediction":
                  lowerCAmelCase_						=      (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
                  lowerCAmelCase_						=      (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)
            lowerCAmelCase_						=      self._get_variance(_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)
            lowerCAmelCase_						=      eta * variance ** 0.5

            # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
            lowerCAmelCase_						=      (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
            lowerCAmelCase_						=      alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

            if not return_dict:
                  return (prev_sample, state)

            return FlaxDDIMSchedulerOutput(prev_sample=_UpperCAmelCase					,					state=_UpperCAmelCase)







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					):
            return add_noise_common(state.common					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)







      def lowercase__		( self					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase					,					):
            return get_velocity_common(state.common					,					_UpperCAmelCase					,					_UpperCAmelCase					,					_UpperCAmelCase)







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



