

'''simple docstring'''



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 			SCREAMING_SNAKE_CASE					:






						'''simple docstring'''






						SCREAMING_SNAKE_CASE__ :				CommonSchedulerState
						SCREAMING_SNAKE_CASE__ :				jnp.ndarray

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




						@classmethod
						def 	__UpperCAmelCase			(					cls :		Tuple     ,					snake_case :		CommonSchedulerState     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					):



										"""simple docstring"""





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



@dataclass
class 			SCREAMING_SNAKE_CASE					(							lowercase_					):






						'''simple docstring'''






						SCREAMING_SNAKE_CASE__ :				DDIMSchedulerState



class 			SCREAMING_SNAKE_CASE					(							lowercase_      ,lowercase_					):






						'''simple docstring'''






						SCREAMING_SNAKE_CASE__ :				Tuple    =				[e.name for e in FlaxKarrasDiffusionSchedulers]

						SCREAMING_SNAKE_CASE__ :				jnp.dtype




						@property
						def 	__UpperCAmelCase			(					self :		Tuple   ):



										"""simple docstring"""





										return True




						@register_to_config
						def __init__(					self :		Optional[int]     ,					snake_case :		int = 1000     ,					snake_case :		float = 0.0001     ,					snake_case :		float = 0.02     ,					snake_case :		str = "linear"     ,					snake_case :		Optional[jnp.ndarray] = None     ,					snake_case :		bool = True     ,					snake_case :		int = 0     ,					snake_case :		str = "epsilon"     ,					snake_case :		jnp.dtype = jnp.floataa     ,					):



										"""simple docstring"""





										_snake_case : Any												=		dtype




						def 	__UpperCAmelCase			(					self :		List[str]     ,					snake_case :		Optional[CommonSchedulerState] = None   ):



										"""simple docstring"""





										if common is None:
														_snake_case : 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.
										_snake_case : Any												=		(
										    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
										_snake_case : List[Any]												=		jnp.array(1.0     ,					dtype=self.dtype   )

										_snake_case : Union[str, 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 :		Any     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		jnp.ndarray     ,					snake_case :		Optional[int] = None   ):



										"""simple docstring"""





										return sample




						def 	__UpperCAmelCase			(					self :		Tuple     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		int     ,					snake_case :		Tuple = ()   ):



										"""simple docstring"""





										_snake_case : Dict												=		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
										_snake_case : Dict												=		(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 :		int     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		Optional[Any]     ,					snake_case :		List[Any]   ):



										"""simple docstring"""





										_snake_case : Tuple												=		state.common.alphas_cumprod[timestep]
										_snake_case : Optional[int]												=		jnp.where(
										    prev_timestep >= 0     ,					state.common.alphas_cumprod[prev_timestep]     ,					state.final_alpha_cumprod   )
										_snake_case : Tuple												=		1 - alpha_prod_t
										_snake_case : str												=		1 - alpha_prod_t_prev

										_snake_case : List[str]												=		(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

										return variance




						def 	__UpperCAmelCase			(					self :		Optional[Any]     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		jnp.ndarray     ,					snake_case :		int     ,					snake_case :		jnp.ndarray     ,					snake_case :		float = 0.0     ,					snake_case :		bool = 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)
										_snake_case : List[str]												=		timestep - self.config.num_train_timesteps // state.num_inference_steps

										_snake_case : Optional[int]												=		state.common.alphas_cumprod
										_snake_case : int												=		state.final_alpha_cumprod

										# 2. compute alphas, betas
										_snake_case : str												=		alphas_cumprod[timestep]
										_snake_case : Dict												=		jnp.where(prev_timestep >= 0     ,					alphas_cumprod[prev_timestep]     ,					snake_case   )

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

										# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
										_snake_case : 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
										_snake_case : 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 :		List[str]     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					):



										"""simple docstring"""





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




						def 	__UpperCAmelCase			(					self :		Tuple     ,					snake_case :		DDIMSchedulerState     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					snake_case :		jnp.ndarray     ,					):



										"""simple docstring"""





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




						def __len__(					self :		List[str]   ):



										"""simple docstring"""





										return self.config.num_train_timesteps






'''simple docstring'''



def   lowerCamelCase__       (      a__			,      a__)		->    int:



    """simple docstring"""







    _snake_case : Tuple												=		0
    for ele in arr:
        total_sum += product_sum(a__			,      depth + 1) if isinstance(a__			,      a__) else ele
    return total_sum * depth

def   lowerCamelCase__       (      a__)		->    int:



    """simple docstring"""







    return product_sum(a__			,      1)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



