# 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    :   CommonSchedulerState
 __lowerCamelCase    :   jnp.ndarray

 # setable values
 __lowerCamelCase    :   jnp.ndarray
 __lowerCamelCase    :   jnp.ndarray
 __lowerCamelCase    :   Optional[int]     =      None
 @classmethod
 def 	UpperCAmelCase__       (  cls		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   )	->							List[str]:
       '''simple docstring'''





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







@dataclass
class 			__snake_case   (     lowerCamelCase__   ):
 __lowerCamelCase    :   DDIMSchedulerState







class 			__snake_case   (     lowerCamelCase__					,   lowerCamelCase__   ):
 __lowerCamelCase    :   Optional[int]     =      [e.name for e in FlaxKarrasDiffusionSchedulers]

 __lowerCamelCase    :   jnp.dtype
 @property
 def 	UpperCAmelCase__       (  self						)	->							Tuple:
       '''simple docstring'''





       return True
 @register_to_config
 def __init__(  self		,   snake_case__ = 1000		,   snake_case__ = 0.0001		,   snake_case__ = 0.02		,   snake_case__ = "linear"		,   snake_case__ = None		,   snake_case__ = True		,   snake_case__ = 0		,   snake_case__ = "epsilon"		,   snake_case__ = jnp.floataa		,   )	->							Dict:
       '''simple docstring'''





       UpperCAmelCase    : Union[str, Any]      =dtype
 def 	UpperCAmelCase__       (  self		,   snake_case__ = None						)	->							DDIMSchedulerState:
       '''simple docstring'''





       if common is None:
             UpperCAmelCase    : List[str]      =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.
       UpperCAmelCase    : Dict      =(
           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
       UpperCAmelCase    : Optional[Any]      =jnp.array(1.0		,   dtype=self.dtype						)

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

       return DDIMSchedulerState.create(
           common=snake_case__		,   final_alpha_cumprod=snake_case__		,   init_noise_sigma=snake_case__		,   timesteps=snake_case__		,   )
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__ = None						)	->							jnp.ndarray:
       '''simple docstring'''





       return sample
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__ = ()						)	->							DDIMSchedulerState:
       '''simple docstring'''





       UpperCAmelCase    : Any      =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
       UpperCAmelCase    : List[str]      =(jnp.arange(0		,   snake_case__						) * step_ratio).round()[::-1] + self.config.steps_offset

       return state.replace(
           num_inference_steps=snake_case__		,   timesteps=snake_case__		,   )
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__						)	->							int:
       '''simple docstring'''





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

       UpperCAmelCase    : str      =(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

       return variance
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__ = 0.0		,   snake_case__ = True		,   )	->							Union[FlaxDDIMSchedulerOutput, Tuple]:
       '''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)
       UpperCAmelCase    : Dict      =timestep - self.config.num_train_timesteps // state.num_inference_steps

       UpperCAmelCase    : Optional[Any]      =state.common.alphas_cumprod
       UpperCAmelCase    : str      =state.final_alpha_cumprod

       # 2. compute alphas, betas
       UpperCAmelCase    : List[Any]      =alphas_cumprod[timestep]
       UpperCAmelCase    : List[str]      =jnp.where(prev_timestep >= 0		,   alphas_cumprod[prev_timestep]		,   snake_case__						)

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

       # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
       UpperCAmelCase    : Union[str, 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
       UpperCAmelCase    : 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=snake_case__		,   state=snake_case__						)
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   )	->							jnp.ndarray:
       '''simple docstring'''





       return add_noise_common(state.common		,   snake_case__		,   snake_case__		,   snake_case__						)
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   )	->							jnp.ndarray:
       '''simple docstring'''





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






 def __len__(  self						)	->							Any:
       '''simple docstring'''





       return self.config.num_train_timesteps

import math





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  list[int]:






      '''simple docstring'''





      if not isinstance(__lowerCAmelCase		,					__lowerCAmelCase						):
            UpperCAmelCase    : Union[str, Any]      =f'''Input value of [number={number}] must be an integer'''
            raise TypeError(__lowerCAmelCase						)
      if number < 1:
            UpperCAmelCase    : Dict      =f'''Input value of [number={number}] must be a positive integer'''
            raise ValueError(__lowerCAmelCase						)
      UpperCAmelCase    : Dict      =[number]
      while number != 1:
            if number % 2 == 0:
                  UpperCAmelCase    : Optional[Any]      =math.floor(math.sqrt(__lowerCAmelCase						)						)
            else:
                  UpperCAmelCase    : List[str]      =math.floor(
                      math.sqrt(__lowerCAmelCase						) * math.sqrt(__lowerCAmelCase						) * math.sqrt(__lowerCAmelCase						)						)
            sequence.append(__lowerCAmelCase						)
      return sequence


if __name__ == "__main__":
     import doctest

     doctest.testmod()
