"""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        __UpperCAmelCase						:
				# setable values
				A__				:       Optional[jnp.ndarray]  							=	None
				A__				:       Optional[jnp.ndarray]  							=	None
				A__				:       Optional[jnp.ndarray]  							=	None

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






@dataclass
class        __UpperCAmelCase						(     __lowerCAmelCase     ):
				A__				:       ScoreSdeVeSchedulerState
				A__				:       jnp.ndarray
				A__				:       Optional[jnp.ndarray]  							=	None






class        __UpperCAmelCase						(     __lowerCAmelCase				,				__lowerCAmelCase     ):

				@property
				def 		_a     (				self				):
										return True

				@register_to_config
				def __init__(				self     ,			_lowerCamelCase = 2000     ,			_lowerCamelCase = 0.1_5     ,			_lowerCamelCase = 0.0_1     ,			_lowerCamelCase = 1_3_4_8.0     ,			_lowerCamelCase = 1E-5     ,			_lowerCamelCase = 1     ,			):
										pass

				def 		_a     (				self				):
										lowerCamelCase__ =ScoreSdeVeSchedulerState.create()
										return self.set_sigmas(
										    _lowerCamelCase     ,			self.config.num_train_timesteps     ,			self.config.sigma_min     ,			self.config.sigma_max     ,			self.config.sampling_eps     ,			)

				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase = ()     ,			_lowerCamelCase = None				):
										lowerCamelCase__ =sampling_eps if sampling_eps is not None else self.config.sampling_eps

										lowerCamelCase__ =jnp.linspace(1     ,			_lowerCamelCase     ,			_lowerCamelCase				)
										return state.replace(timesteps=_lowerCamelCase				)

				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase = None     ,			_lowerCamelCase = None     ,			_lowerCamelCase = None     ,			):
										lowerCamelCase__ =sigma_min if sigma_min is not None else self.config.sigma_min
										lowerCamelCase__ =sigma_max if sigma_max is not None else self.config.sigma_max
										lowerCamelCase__ =sampling_eps if sampling_eps is not None else self.config.sampling_eps
										if state.timesteps is None:
																lowerCamelCase__ =self.set_timesteps(_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase				)

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

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

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

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

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

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

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

				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase = 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
										lowerCamelCase__ =random.split(_lowerCamelCase     ,			num=1				)
										lowerCamelCase__ =random.normal(key=_lowerCamelCase     ,			shape=sample.shape				)

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

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

										if not return_dict:
																return (prev_sample, state)

										return FlaxSdeVeOutput(prev_sample=_lowerCamelCase     ,			state=_lowerCamelCase				)






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



"""simple docstring"""


from __future__ import annotations

from collections.abc import Generator





def       lowerCamelCase_			( __lowerCAmelCase    )							-> Generator[int, None, None]:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ) or n < 1:
												raise Exception("Sequence only defined for positive integers"    )

						yield n
						while n != 1:
												if n % 2 == 0:
																		n //= 2
												else:
																		lowerCamelCase__ =3 * n + 1
												yield n





def       lowerCamelCase_			( )							-> List[str]:




						'''simple docstring'''



						lowerCamelCase__ =43
						lowerCamelCase__ =tuple(collatz_sequence(__lowerCAmelCase    )    )
						print(__lowerCAmelCase    )
						print(F'''Collatz sequence from {n} took {len(__lowerCAmelCase    )} steps.'''    )


if __name__ == "__main__":
	main()


