'''simple docstring'''

# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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 .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left




@flax.struct.dataclass
class 		SCREAMING_SNAKE_CASE_					:



			"""simple docstring"""






			__magic_name__ :				Optional[jnp.ndarray]   							=       None
			__magic_name__ :				Optional[jnp.ndarray]   							=       None
			__magic_name__ :				Optional[jnp.ndarray]   							=       None



			@classmethod
			def   lowerCamelCase (							cls					):
									return cls()







@dataclass
class 		SCREAMING_SNAKE_CASE_					(_UpperCAmelCase      ):



			"""simple docstring"""






			__magic_name__ :				ScoreSdeVeSchedulerState
			__magic_name__ :				jnp.ndarray
			__magic_name__ :				Optional[jnp.ndarray]   							=       None







class 		SCREAMING_SNAKE_CASE_					(_UpperCAmelCase							,				_UpperCAmelCase      ):



			"""simple docstring"""






			@property
			def   lowerCamelCase (							self					):
									return True



			@register_to_config
			def __init__(							self				,			snake_case_ = 2_000				,			snake_case_ = 0.15				,			snake_case_ = 0.01				,			snake_case_ = 1_348.0				,			snake_case_ = 1e-5				,			snake_case_ = 1				,			):
									pass



			def   lowerCamelCase (							self					):
									snake_case :       Any				=    ScoreSdeVeSchedulerState.create()
									return self.set_sigmas(
									    snake_case_				,			self.config.num_train_timesteps				,			self.config.sigma_min				,			self.config.sigma_max				,			self.config.sampling_eps				,			)



			def   lowerCamelCase (							self				,			snake_case_				,			snake_case_				,			snake_case_ = ()				,			snake_case_ = None					):
									snake_case :       str				=    sampling_eps if sampling_eps is not None else self.config.sampling_eps

									snake_case :       Dict				=    jnp.linspace(1				,			snake_case_				,			snake_case_					)
									return state.replace(timesteps=snake_case_					)



			def   lowerCamelCase (							self				,			snake_case_				,			snake_case_				,			snake_case_ = None				,			snake_case_ = None				,			snake_case_ = None				,			):
									snake_case :       List[str]				=    sigma_min if sigma_min is not None else self.config.sigma_min
									snake_case :       Optional[int]				=    sigma_max if sigma_max is not None else self.config.sigma_max
									snake_case :       Tuple				=    sampling_eps if sampling_eps is not None else self.config.sampling_eps
									if state.timesteps is None:
															snake_case :       Optional[Any]				=    self.set_timesteps(snake_case_				,			snake_case_				,			snake_case_					)

									snake_case :       Optional[Any]				=    jnp.exp(jnp.linspace(jnp.log(snake_case_					)				,			jnp.log(snake_case_					)				,			snake_case_					)					)
									snake_case :       Dict				=    jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]					)

									return state.replace(discrete_sigmas=snake_case_				,			sigmas=snake_case_					)



			def   lowerCamelCase (							self				,			snake_case_				,			snake_case_				,			snake_case_					):
									return jnp.where(timesteps == 0				,			jnp.zeros_like(snake_case_					)				,			state.discrete_sigmas[timesteps - 1]					)



			def   lowerCamelCase (							self				,			snake_case_				,			snake_case_				,			snake_case_				,			snake_case_				,			snake_case_				,			snake_case_ = True				,			):
									if state.timesteps is None:
															raise ValueError(
															    "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"					)

									snake_case :       Tuple				=    timestep * jnp.ones(
									    sample.shape[0]				,			)
									snake_case :       Optional[Any]				=    (timestep * (len(state.timesteps					) - 1)).long()

									snake_case :       Tuple				=    state.discrete_sigmas[timesteps]
									snake_case :       Union[str, Any]				=    self.get_adjacent_sigma(snake_case_				,			snake_case_				,			snake_case_					)
									snake_case :       Optional[Any]				=    jnp.zeros_like(snake_case_					)
									snake_case :       Any				=    (sigma**2 - adjacent_sigma**2) ** 0.5

									# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
									# also equation 47 shows the analog from SDE models to ancestral sampling methods
									snake_case :       List[Any]				=    diffusion.flatten()
									snake_case :       int				=    broadcast_to_shape_from_left(snake_case_				,			sample.shape					)
									snake_case :       List[Any]				=    drift - diffusion**2 * model_output

									#  equation 6: sample noise for the diffusion term of
									snake_case :       Optional[int]				=    random.split(snake_case_				,			num=1					)
									snake_case :       str				=    random.normal(key=snake_case_				,			shape=sample.shape					)
									snake_case :       Tuple				=    sample - drift  # subtract because `dt` is a small negative timestep
									# TODO is the variable diffusion the correct scaling term for the noise?
									snake_case :       List[str]				=    prev_sample_mean + diffusion * noise  # add impact of diffusion field g

									if not return_dict:
															return (prev_sample, prev_sample_mean, state)

									return FlaxSdeVeOutput(prev_sample=snake_case_				,			prev_sample_mean=snake_case_				,			state=snake_case_					)



			def   lowerCamelCase (							self				,			snake_case_				,			snake_case_				,			snake_case_				,			snake_case_				,			snake_case_ = True				,			):
									if state.timesteps is None:
															raise ValueError(
															    "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"					)

									# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
									# sample noise for correction
									snake_case :       Any				=    random.split(snake_case_				,			num=1					)
									snake_case :       str				=    random.normal(key=snake_case_				,			shape=sample.shape					)

									# compute step size from the model_output, the noise, and the snr
									snake_case :       Union[str, Any]				=    jnp.linalg.norm(snake_case_					)
									snake_case :       Optional[int]				=    jnp.linalg.norm(snake_case_					)
									snake_case :       str				=    (self.config.snr * noise_norm / grad_norm) ** 2 * 2
									snake_case :       List[Any]				=    step_size * jnp.ones(sample.shape[0]					)

									# compute corrected sample: model_output term and noise term
									snake_case :       Any				=    step_size.flatten()
									snake_case :       Optional[int]				=    broadcast_to_shape_from_left(snake_case_				,			sample.shape					)
									snake_case :       Dict				=    sample + step_size * model_output
									snake_case :       Optional[Any]				=    prev_sample_mean + ((step_size * 2) ** 0.5) * noise

									if not return_dict:
															return (prev_sample, state)

									return FlaxSdeVeOutput(prev_sample=snake_case_				,			state=snake_case_					)






			def __len__(							self					):
									return self.config.num_train_timesteps






'''simple docstring'''

def        UpperCAmelCase__   (				_lowerCAmelCase    :			int = 400_0000)    ->		int:



						"""simple docstring"""

						snake_case :       List[Any]				=    1
						snake_case :       int				=    2
						snake_case :       List[str]				=    0
						while j <= n:
												if j % 2 == 0:
																		total += j
												snake_case				,					snake_case :       Any				=    j, i + j

						return total


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





