

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 	__magic_name__				:
     UpperCamelCase_  :CommonSchedulerState
     UpperCamelCase_  :jnp.ndarray

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






     @classmethod
     def   UpperCAmelCase_							(							cls		,	_lowercase		,	_lowercase		,	_lowercase		,	_lowercase		,	)->    Optional[Any]:
         return cls(
             common=UpperCamelCase__		,	final_alpha_cumprod=UpperCamelCase__		,	init_noise_sigma=UpperCamelCase__		,	timesteps=UpperCamelCase__		,	)






@dataclass
class 	__magic_name__				(       _SCREAMING_SNAKE_CASE							):
     UpperCamelCase_  :DDIMSchedulerState






class 	__magic_name__				(       _SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE							):
     UpperCamelCase_  :Union[str, Any]								=			[e.name for e in FlaxKarrasDiffusionSchedulers]

     UpperCamelCase_  :jnp.dtype






     @property
     def   UpperCAmelCase_							(							self  )->    Dict:
         return True






     @register_to_config
     def __init__(							self		,	_lowercase = 1_000		,	_lowercase = 0.0_001		,	_lowercase = 0.02		,	_lowercase = "linear"		,	_lowercase = None		,	_lowercase = True		,	_lowercase = 0		,	_lowercase = "epsilon"		,	_lowercase = jnp.floataa		,	)->    Optional[int]:
         UpperCamelCase_      =	dtype






     def   UpperCAmelCase_							(							self		,	_lowercase = None  )->    Optional[int]:
         if common is None:
             UpperCamelCase_      =	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_      =	(
             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_      =	jnp.array(1.0		,	dtype=self.dtype  )

         UpperCamelCase_      =	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   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase = None  )->    Union[str, Any]:
         return sample






     def   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase = ()  )->    Any:
         UpperCamelCase_      =	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_      =	(jnp.arange(0		,	UpperCamelCase__  ) * step_ratio).round()[::-1] + self.config.steps_offset

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






     def   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase  )->    Union[str, Any]:
         UpperCamelCase_      =	state.common.alphas_cumprod[timestep]
         UpperCamelCase_      =	jnp.where(
             prev_timestep >= 0		,	state.common.alphas_cumprod[prev_timestep]		,	state.final_alpha_cumprod  )
         UpperCamelCase_      =	1 - alpha_prod_t
         UpperCamelCase_      =	1 - alpha_prod_t_prev

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

         return variance






     def   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase		,	_lowercase		,	_lowercase = 0.0		,	_lowercase = True		,	)->    str:
         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_      =	timestep - self.config.num_train_timesteps // state.num_inference_steps

         UpperCamelCase_      =	state.common.alphas_cumprod
         UpperCamelCase_      =	state.final_alpha_cumprod

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

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

         # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         UpperCamelCase_      =	(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_      =	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   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase		,	_lowercase		,	)->    Any:
         return add_noise_common(state.common		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__  )






     def   UpperCAmelCase_							(							self		,	_lowercase		,	_lowercase		,	_lowercase		,	_lowercase		,	)->    Dict:
         return get_velocity_common(state.common		,	UpperCamelCase__		,	UpperCamelCase__		,	UpperCamelCase__  )






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



def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_ )->	str:



    """simple docstring"""






    if power < 0:
        return -1
    base %= mod
    UpperCamelCase_      =	1

    while power > 0:
        if power & 1:
            UpperCamelCase_      =	(result * base) % mod
        UpperCamelCase_      =	power >> 1
        UpperCamelCase_      =	(base * base) % mod

    return result




def  lowerCAmelCase(			)->	Tuple:



    """simple docstring"""






    print(modular_exponential(3 ,	2_0_0 ,	1_3 ) )


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 main()
