






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin

@flax.struct.dataclass
class 		_snake_case	:
			# setable values
			_lowercase		:     Optional[int]        =				None
			_lowercase		:     Optional[jnp.ndarray]        =				None
			_lowercase		:     Optional[jnp.ndarray]        =				None  # sigma(t_i)






			@classmethod
			def  SCREAMING_SNAKE_CASE__     (							cls)   ->							int:
						return cls()



@dataclass
class 		_snake_case	(	A__       ):
			_lowercase		:     jnp.ndarray
			_lowercase		:     jnp.ndarray
			_lowercase		:     KarrasVeSchedulerState



class 		_snake_case	(	A__ ,     A__       ):






			@property
			def  SCREAMING_SNAKE_CASE__     (							self)   ->							Optional[int]:
						return True






			@register_to_config
			def __init__(							self		,       a = 0.02		,       a = 100		,       a = 1.0_07		,       a = 80		,       a = 0.05		,       a = 50		,       )   ->							Optional[int]:
						pass






			def  SCREAMING_SNAKE_CASE__     (							self)   ->							Optional[Any]:
						return KarrasVeSchedulerState.create()






			def  SCREAMING_SNAKE_CASE__     (							self		,       a		,       a		,       a = ())   ->							KarrasVeSchedulerState:
						SCREAMING_SNAKE_CASE							=			jnp.arange(0		,       a)[::-1].copy()
						SCREAMING_SNAKE_CASE							=			[
						    (
						        self.config.sigma_max**2
						        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
						    )
						    for i in timesteps
						]

						return state.replace(
						    num_inference_steps=a		,       schedule=jnp.array(a		,       dtype=jnp.floataa)		,       timesteps=a		,       )






			def  SCREAMING_SNAKE_CASE__     (							self		,       a		,       a		,       a		,       a		,       )   ->							Tuple[jnp.ndarray, float]:
						if self.config.s_min <= sigma <= self.config.s_max:
									SCREAMING_SNAKE_CASE							=			min(self.config.s_churn / state.num_inference_steps		,       2**0.5 - 1)
						else:
									SCREAMING_SNAKE_CASE							=			0

						# sample eps ~ N(0, S_noise^2 * I)
						SCREAMING_SNAKE_CASE							=			random.split(a		,       num=1)
						SCREAMING_SNAKE_CASE							=			self.config.s_noise * random.normal(key=a		,       shape=sample.shape)
						SCREAMING_SNAKE_CASE							=			sigma + gamma * sigma
						SCREAMING_SNAKE_CASE							=			sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

						return sample_hat, sigma_hat






			def  SCREAMING_SNAKE_CASE__     (							self		,       a		,       a		,       a		,       a		,       a		,       a = True		,       )   ->							Union[FlaxKarrasVeOutput, Tuple]:
						SCREAMING_SNAKE_CASE							=			sample_hat + sigma_hat * model_output
						SCREAMING_SNAKE_CASE							=			(sample_hat - pred_original_sample) / sigma_hat
						SCREAMING_SNAKE_CASE							=			sample_hat + (sigma_prev - sigma_hat) * derivative

						if not return_dict:
									return (sample_prev, derivative, state)

						return FlaxKarrasVeOutput(prev_sample=a		,       derivative=a		,       state=a)






			def  SCREAMING_SNAKE_CASE__     (							self		,       a		,       a		,       a		,       a		,       a		,       a		,       a		,       a = True		,       )   ->							Union[FlaxKarrasVeOutput, Tuple]:
						SCREAMING_SNAKE_CASE							=			sample_prev + sigma_prev * model_output
						SCREAMING_SNAKE_CASE							=			(sample_prev - pred_original_sample) / sigma_prev
						SCREAMING_SNAKE_CASE							=			sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

						if not return_dict:
									return (sample_prev, derivative, state)

						return FlaxKarrasVeOutput(prev_sample=a		,       derivative=a		,       state=a)







			def  SCREAMING_SNAKE_CASE__     (							self		,       a		,       a		,       a		,       a)   ->							int:
						raise NotImplementedError()








"""simple docstring"""




def       a_ (	lowercase__ :int = 10**9     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      2

			__lowerCamelCase          =      0
			__lowerCamelCase          =      0
			__lowerCamelCase          =      0
			while perimeter <= max_perimeter:
						perimeters_sum += perimeter

						prev_value += 2 * value
						value += prev_value

						__lowerCamelCase          =      2 * value + 2 if i % 2 == 0 else 2 * value - 2
						i += 1

			return perimeters_sum


if __name__ == "__main__":
					print(f"""{solution() = }""")




