
'''simple docstring'''







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
					lowerCAmelCase_       =  None
					lowerCAmelCase_       =  None
					lowerCAmelCase_       =  None






					@classmethod
					def 			_snake_case					(     cls	):


											"""simple docstring"""





											return cls()







@dataclass
class 				lowerCAmelCase__     (						lowerCamelCase_  ):
					lowerCAmelCase_       =  4_2
					lowerCAmelCase_       =  4_2
					lowerCAmelCase_       =  None







class 				lowerCAmelCase__     (						lowerCamelCase_					,		lowerCamelCase_  ):






					@property
					def 			_snake_case					(     self	):


											"""simple docstring"""





											return True






					@register_to_config
					def __init__(     self       ,							__SCREAMING_SNAKE_CASE = 20_00       ,							__SCREAMING_SNAKE_CASE = 0.15       ,							__SCREAMING_SNAKE_CASE = 0.01       ,							__SCREAMING_SNAKE_CASE = 13_48.0       ,							__SCREAMING_SNAKE_CASE = 1E-5       ,							__SCREAMING_SNAKE_CASE = 1       ,							):


											"""simple docstring"""





											pass






					def 			_snake_case					(     self	):


											"""simple docstring"""





											lowercase_			:  List[Any]									= ScoreSdeVeSchedulerState.create()
											return self.set_sigmas(
											    __SCREAMING_SNAKE_CASE       ,							self.config.num_train_timesteps       ,							self.config.sigma_min       ,							self.config.sigma_max       ,							self.config.sampling_eps       ,							)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = ()       ,							__SCREAMING_SNAKE_CASE = None	):


											"""simple docstring"""





											lowercase_			:  int									= sampling_eps if sampling_eps is not None else self.config.sampling_eps

											lowercase_			:  Optional[Any]									= jnp.linspace(1       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)
											return state.replace(timesteps=__SCREAMING_SNAKE_CASE	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = None       ,							__SCREAMING_SNAKE_CASE = None       ,							__SCREAMING_SNAKE_CASE = None       ,							):


											"""simple docstring"""





											lowercase_			:  Tuple									= sigma_min if sigma_min is not None else self.config.sigma_min
											lowercase_			:  int									= sigma_max if sigma_max is not None else self.config.sigma_max
											lowercase_			:  Dict									= sampling_eps if sampling_eps is not None else self.config.sampling_eps
											if state.timesteps is None:
																	lowercase_			:  Optional[Any]									= self.set_timesteps(__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)

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

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






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											return jnp.where(timesteps == 0       ,							jnp.zeros_like(__SCREAMING_SNAKE_CASE	)       ,							state.discrete_sigmas[timesteps - 1]	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = 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'''	)

											lowercase_			:  List[Any]									= timestep * jnp.ones(
											    sample.shape[0]       ,							)
											lowercase_			:  int									= (timestep * (len(state.timesteps	) - 1)).long()

											lowercase_			:  List[Any]									= state.discrete_sigmas[timesteps]
											lowercase_			:  Any									= self.get_adjacent_sigma(__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)
											lowercase_			:  Optional[Any]									= jnp.zeros_like(__SCREAMING_SNAKE_CASE	)
											lowercase_			:  Optional[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
											lowercase_			:  Any									= diffusion.flatten()
											lowercase_			:  List[str]									= broadcast_to_shape_from_left(__SCREAMING_SNAKE_CASE       ,							sample.shape	)
											lowercase_			:  Dict									= drift - diffusion**2 * model_output

											#  equation 6: sample noise for the diffusion term of
											lowercase_			:  Union[str, Any]									= random.split(__SCREAMING_SNAKE_CASE       ,							num=1	)
											lowercase_			:  Any									= random.normal(key=__SCREAMING_SNAKE_CASE       ,							shape=sample.shape	)
											lowercase_			:  Any									= sample - drift  # subtract because `dt` is a small negative timestep
											# TODO is the variable diffusion the correct scaling term for the noise?
											lowercase_			:  Dict									= 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=__SCREAMING_SNAKE_CASE       ,							prev_sample_mean=__SCREAMING_SNAKE_CASE       ,							state=__SCREAMING_SNAKE_CASE	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = 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
											lowercase_			:  int									= random.split(__SCREAMING_SNAKE_CASE       ,							num=1	)
											lowercase_			:  Any									= random.normal(key=__SCREAMING_SNAKE_CASE       ,							shape=sample.shape	)

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

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

											if not return_dict:
																	return (prev_sample, state)

											return FlaxSdeVeOutput(prev_sample=__SCREAMING_SNAKE_CASE       ,							state=__SCREAMING_SNAKE_CASE	)






					def __len__(     self	):


											"""simple docstring"""





											return self.config.num_train_timesteps






'''simple docstring'''







def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				int = 998001							):



						"""simple docstring"""





						lowercase_			:  Dict									= 0
						for i in range(999   ,   99   ,   -1							):  # 3 digit numbers range from 999 down to 100
												for j in range(999   ,   99   ,   -1							):
																		lowercase_			:  int									= str(i * j							)
																		if product_string == product_string[::-1] and i * j < n:
																								lowercase_			:  str									= max(__SCREAMING_SNAKE_CASE   ,   i * j							)
						return answer


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



