



"""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       UpperCamelCase  :





     """simple docstring"""






     _lowerCamelCase					: CommonSchedulerState
     _lowerCamelCase					: jnp.ndarray

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





     @classmethod
     def 						A__  (					cls :							List[str]	,      _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       UpperCamelCase  (					a				):





     """simple docstring"""






     _lowerCamelCase					: DDIMSchedulerState


class       UpperCamelCase  (					a      , a				):





     """simple docstring"""






     _lowerCamelCase					: List[str]				   =[e.name for e in FlaxKarrasDiffusionSchedulers]

     _lowerCamelCase					: jnp.dtype





     @property
     def 						A__  (					self :							Optional[Any] ):
          return True





     @register_to_config
     def __init__(					self :							List[Any]	,      _lowerCamelCase :							int = 1_0_0_0	,      _lowerCamelCase :							float = 0.0_001	,      _lowerCamelCase :							float = 0.02	,      _lowerCamelCase :							str = "linear"	,      _lowerCamelCase :							Optional[jnp.ndarray] = None	,      _lowerCamelCase :							bool = True	,      _lowerCamelCase :							int = 0	,      _lowerCamelCase :							str = "epsilon"	,      _lowerCamelCase :							jnp.dtype = jnp.floataa	,      ):
          A__				=   dtype





     def 						A__  (					self :							List[str]	,      _lowerCamelCase :							Optional[CommonSchedulerState] = None ):
          if common is None:
               A__				=   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__				=   (
              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__				=   jnp.array(1.0	,      dtype=self.dtype )

          A__				=   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 						A__  (					self :							str	,      _lowerCamelCase :							DDIMSchedulerState	,      _lowerCamelCase :							jnp.ndarray	,      _lowerCamelCase :							Optional[int] = None ):
          return sample





     def 						A__  (					self :							Optional[int]	,      _lowerCamelCase :							DDIMSchedulerState	,      _lowerCamelCase :							int	,      _lowerCamelCase :							Tuple = () ):
          A__				=   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__				=   (jnp.arange(0	,      _lowerCamelCase ) * step_ratio).round()[::-1] + self.config.steps_offset

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





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

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

          return variance





     def 						A__  (					self :							List[Any]	,      _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)
          A__				=   timestep - self.config.num_train_timesteps // state.num_inference_steps

          A__				=   state.common.alphas_cumprod
          A__				=   state.final_alpha_cumprod

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

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

          # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          A__				=   (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__				=   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 						A__  (					self :							int	,      _lowerCamelCase :							DDIMSchedulerState	,      _lowerCamelCase :							jnp.ndarray	,      _lowerCamelCase :							jnp.ndarray	,      _lowerCamelCase :							jnp.ndarray	,      ):
          return add_noise_common(state.common	,      _lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase )





     def 						A__  (					self :							Tuple	,      _lowerCamelCase :							DDIMSchedulerState	,      _lowerCamelCase :							jnp.ndarray	,      _lowerCamelCase :							jnp.ndarray	,      _lowerCamelCase :							jnp.ndarray	,      ):
          return get_velocity_common(state.common	,      _lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase )





     def __len__(					self :							List[str] ):
          return self.config.num_train_timesteps








"""simple docstring"""







def   a_	(			__a      ):
     if not isinstance(__a		,							__a      ):
          raise TypeError('''recursive_lucas_number accepts only integer arguments.'''      )
     if n_th_number == 0:
          return 2
     if n_th_number == 1:
          return 1

     return recursive_lucas_number(n_th_number - 1      ) + recursive_lucas_number(
         n_th_number - 2      )



def   a_	(			__a      ):
     if not isinstance(__a		,							__a      ):
          raise TypeError('''dynamic_lucas_number accepts only integer arguments.'''      )
     A__	,     A__				=   2, 1
     for _ in range(__a      ):
          A__	,     A__				=   b, a + b
     return a


if __name__ == "__main__":
 from doctest import testmod

 testmod()
 __snake_case	:				Dict  					=			int(input('Enter the number of terms in lucas series:\n').strip())
 print('Using recursive function to calculate lucas series:')
 print(' '.join(str(recursive_lucas_number(i)) for i in range(n)))
 print('\nUsing dynamic function to calculate lucas series:')
 print(' '.join(str(dynamic_lucas_number(i)) for i in range(n)))



