




# 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 	__lowerCAmelCase			:
							# setable values
							UpperCamelCase__        =						None
							UpperCamelCase__        =						None
							UpperCamelCase__        =						None
							@classmethod
							def    lowerCamelCase__							(		cls		:Optional[Any]       ):







												'''simple docstring'''







												return cls()







@dataclass
class 	__lowerCAmelCase			(			A__				):
							UpperCamelCase__        =						42
							UpperCamelCase__        =						42
							UpperCamelCase__        =						None







class 	__lowerCAmelCase			(			A__   , A__				):
							@property
							def    lowerCamelCase__							(		self		:Dict       ):







												'''simple docstring'''







												return True
							@register_to_config
							def __init__(		self		:List[Any]	,   __magic_name__		:int = 2000	,   __magic_name__		:float = 0.15	,   __magic_name__		:float = 0.01	,   __magic_name__		:float = 1348.0	,   __magic_name__		:float = 1E-5	,   __magic_name__		:int = 1	,   ):







												'''simple docstring'''







												pass
							def    lowerCamelCase__							(		self		:Union[str, Any]       ):







												'''simple docstring'''







												a		       =							ScoreSdeVeSchedulerState.create()
												return self.set_sigmas(
												    __magic_name__	,   self.config.num_train_timesteps	,   self.config.sigma_min	,   self.config.sigma_max	,   self.config.sampling_eps	,   )
							def    lowerCamelCase__							(		self		:Optional[Any]	,   __magic_name__		:ScoreSdeVeSchedulerState	,   __magic_name__		:int	,   __magic_name__		:Tuple = ()	,   __magic_name__		:float = None       ):







												'''simple docstring'''







												a		       =							sampling_eps if sampling_eps is not None else self.config.sampling_eps

												a		       =							jnp.linspace(1	,   __magic_name__	,   __magic_name__       )
												return state.replace(timesteps=__magic_name__       )
							def    lowerCamelCase__							(		self		:List[Any]	,   __magic_name__		:ScoreSdeVeSchedulerState	,   __magic_name__		:int	,   __magic_name__		:float = None	,   __magic_name__		:float = None	,   __magic_name__		:float = None	,   ):







												'''simple docstring'''







												a		       =							sigma_min if sigma_min is not None else self.config.sigma_min
												a		       =							sigma_max if sigma_max is not None else self.config.sigma_max
												a		       =							sampling_eps if sampling_eps is not None else self.config.sampling_eps
												if state.timesteps is None:
																	a		       =							self.set_timesteps(__magic_name__	,   __magic_name__	,   __magic_name__       )

												a		       =							jnp.exp(jnp.linspace(jnp.log(__magic_name__       )	,   jnp.log(__magic_name__       )	,   __magic_name__       )       )
												a		       =							jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]       )

												return state.replace(discrete_sigmas=__magic_name__	,   sigmas=__magic_name__       )
							def    lowerCamelCase__							(		self		:Tuple	,   __magic_name__		:Optional[int]	,   __magic_name__		:Union[str, Any]	,   __magic_name__		:Any       ):







												'''simple docstring'''







												return jnp.where(timesteps == 0	,   jnp.zeros_like(__magic_name__       )	,   state.discrete_sigmas[timesteps - 1]       )
							def    lowerCamelCase__							(		self		:str	,   __magic_name__		:ScoreSdeVeSchedulerState	,   __magic_name__		:jnp.ndarray	,   __magic_name__		:int	,   __magic_name__		:jnp.ndarray	,   __magic_name__		:random.KeyArray	,   __magic_name__		:bool = True	,   ):







												'''simple docstring'''







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

												a		       =							timestep * jnp.ones(
												    sample.shape[0]	,   )
												a		       =							(timestep * (len(state.timesteps       ) - 1)).long()

												a		       =							state.discrete_sigmas[timesteps]
												a		       =							self.get_adjacent_sigma(__magic_name__	,   __magic_name__	,   __magic_name__       )
												a		       =							jnp.zeros_like(__magic_name__       )
												a		       =							(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
												a		       =							diffusion.flatten()
												a		       =							broadcast_to_shape_from_left(__magic_name__	,   sample.shape       )
												a		       =							drift - diffusion**2 * model_output

												#  equation 6: sample noise for the diffusion term of
												a		       =							random.split(__magic_name__	,   num=1       )
												a		       =							random.normal(key=__magic_name__	,   shape=sample.shape       )
												a		       =							sample - drift  # subtract because `dt` is a small negative timestep
												# TODO is the variable diffusion the correct scaling term for the noise?
												a		       =							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=__magic_name__	,   prev_sample_mean=__magic_name__	,   state=__magic_name__       )
							def    lowerCamelCase__							(		self		:Tuple	,   __magic_name__		:ScoreSdeVeSchedulerState	,   __magic_name__		:jnp.ndarray	,   __magic_name__		:jnp.ndarray	,   __magic_name__		:random.KeyArray	,   __magic_name__		:bool = True	,   ):







												'''simple docstring'''







												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
												a		       =							random.split(__magic_name__	,   num=1       )
												a		       =							random.normal(key=__magic_name__	,   shape=sample.shape       )

												# compute step size from the model_output, the noise, and the snr
												a		       =							jnp.linalg.norm(__magic_name__       )
												a		       =							jnp.linalg.norm(__magic_name__       )
												a		       =							(self.config.snr * noise_norm / grad_norm) ** 2 * 2
												a		       =							step_size * jnp.ones(sample.shape[0]       )

												# compute corrected sample: model_output term and noise term
												a		       =							step_size.flatten()
												a		       =							broadcast_to_shape_from_left(__magic_name__	,   sample.shape       )
												a		       =							sample + step_size * model_output
												a		       =							prev_sample_mean + ((step_size * 2) ** 0.5) * noise

												if not return_dict:
																	return (prev_sample, state)

												return FlaxSdeVeOutput(prev_sample=__magic_name__	,   state=__magic_name__       )





							def __len__(		self		:Dict       ):







												'''simple docstring'''







												return self.config.num_train_timesteps







from itertools import combinations, product





def 	__A	(			__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)   -> bool:
	if xa == ya == 0 or xa == ya == 0:
		return False
	a		       =							xa * xa + ya * ya
	a		       =							xa * xa + ya * ya
	a		       =							(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
	return (
	    a_square + b_square == c_square
	    or a_square + c_square == b_square
	    or b_square + c_square == a_square
	)





def 	__A	(			__lowerCamelCase = 50					)   -> int:
	return sum(
	    1
	    for pta, pta in combinations(product(range(limit + 1					)							,    repeat=2					)							,    2					)
	    if is_right(*__lowerCamelCase							,    *__lowerCamelCase					)					)


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

