# 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 			__snake_case  :
					# setable values
					__lowerCamelCase	 =       None
					__lowerCamelCase	 =       None
					__lowerCamelCase	 =       None




					@classmethod
					def       __a      (       cls		)					->  List[str]:



									'''simple docstring'''







									return cls()





@dataclass
class 			__snake_case  (      _lowerCamelCase     ):
					__lowerCamelCase	 =       42
					__lowerCamelCase	 =       42
					__lowerCamelCase	 =       None





class 			__snake_case  (      _lowerCamelCase   ,_lowerCamelCase     ):




					@property
					def       __a      (       self		)					->  Optional[Any]:



									'''simple docstring'''







									return True




					@register_to_config
					def __init__(       self   ,	__UpperCamelCase = 2000   ,	__UpperCamelCase = 0.1_5   ,	__UpperCamelCase = 0.0_1   ,	__UpperCamelCase = 1_3_4_8.0   ,	__UpperCamelCase = 1E-5   ,	__UpperCamelCase = 1   ,	)					->  Optional[Any]:



									'''simple docstring'''







									pass




					def       __a      (       self		)					->  Any:



									'''simple docstring'''







									snake_case__ :     Any 							=				ScoreSdeVeSchedulerState.create()
									return self.set_sigmas(
									    __UpperCamelCase   ,	self.config.num_train_timesteps   ,	self.config.sigma_min   ,	self.config.sigma_max   ,	self.config.sampling_eps   ,	)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase = ()   ,	__UpperCamelCase = None		)					->  ScoreSdeVeSchedulerState:



									'''simple docstring'''







									snake_case__ :     Union[str, Any] 							=				sampling_eps if sampling_eps is not None else self.config.sampling_eps

									snake_case__ :     str 							=				jnp.linspace(1   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									return state.replace(timesteps=__UpperCamelCase		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase = None   ,	__UpperCamelCase = None   ,	__UpperCamelCase = None   ,	)					->  ScoreSdeVeSchedulerState:



									'''simple docstring'''







									snake_case__ :     Dict 							=				sigma_min if sigma_min is not None else self.config.sigma_min
									snake_case__ :     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__ :     Dict 							=				self.set_timesteps(__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)

									snake_case__ :     Optional[int] 							=				jnp.exp(jnp.linspace(jnp.log(__UpperCamelCase		)   ,	jnp.log(__UpperCamelCase		)   ,	__UpperCamelCase		)		)
									snake_case__ :     Union[str, Any] 							=				jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]		)

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




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  Optional[Any]:



									'''simple docstring'''







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




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase = True   ,	)					->  Union[FlaxSdeVeOutput, Tuple]:



									'''simple docstring'''







									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__ :     Dict 							=				(timestep * (len(state.timesteps		) - 1)).long()

									snake_case__ :     List[str] 							=				state.discrete_sigmas[timesteps]
									snake_case__ :     Dict 							=				self.get_adjacent_sigma(__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									snake_case__ :     List[Any] 							=				jnp.zeros_like(__UpperCamelCase		)
									snake_case__ :     Union[str, 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(__UpperCamelCase   ,	sample.shape		)
									snake_case__ :     Union[str, Any] 							=				drift - diffusion**2 * model_output

									#  equation 6: sample noise for the diffusion term of
									snake_case__ :     Tuple 							=				random.split(__UpperCamelCase   ,	num=1		)
									snake_case__ :     str 							=				random.normal(key=__UpperCamelCase   ,	shape=sample.shape		)
									snake_case__ :     str 							=				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=__UpperCamelCase   ,	prev_sample_mean=__UpperCamelCase   ,	state=__UpperCamelCase		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase = True   ,	)					->  Union[FlaxSdeVeOutput, Tuple]:



									'''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
									snake_case__ :     Tuple 							=				random.split(__UpperCamelCase   ,	num=1		)
									snake_case__ :     Tuple 							=				random.normal(key=__UpperCamelCase   ,	shape=sample.shape		)

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

									# compute corrected sample: model_output term and noise term
									snake_case__ :     Union[str, Any] 							=				step_size.flatten()
									snake_case__ :     Dict 							=				broadcast_to_shape_from_left(__UpperCamelCase   ,	sample.shape		)
									snake_case__ :     List[Any] 							=				sample + step_size * model_output
									snake_case__ :     List[Any] 							=				prev_sample_mean + ((step_size * 2) ** 0.5) * noise

									if not return_dict:
													return (prev_sample, state)

									return FlaxSdeVeOutput(prev_sample=__UpperCamelCase   ,	state=__UpperCamelCase		)




					def __len__(       self		)					->  Dict:



									'''simple docstring'''







									return self.config.num_train_timesteps



def 			UpperCamelCase__						(    A__   )       -> int:
				if number != int(A__   ):
								raise ValueError('factorial() only accepts integral values'   )
				if number < 0:
								raise ValueError('factorial() not defined for negative values'   )
				snake_case__ :     Optional[Any] 							=				1
				for i in range(1      ,			number + 1   ):
								value *= i
				return value
def 			UpperCamelCase__						(    A__   )       -> int:
				if not isinstance(A__      ,			A__   ):
								raise ValueError('factorial() only accepts integral values'   )
				if n < 0:
								raise ValueError('factorial() not defined for negative values'   )
				return 1 if n == 0 or n == 1 else n * factorial(n - 1   )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				lowerCAmelCase__					:       Any		=       int(input('''Enter a positive integer: ''').strip() or 0)
				print(F'''factorial{n} is {factorial(n)}''')


