

"""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 			_snake_case     :
						# setable values
						__snake_case 			=     None
						__snake_case 			=     None
						__snake_case 			=     None







						@classmethod
						def        _UpperCamelCase    (cls							)			->						Optional[Any]:
											return cls()



@dataclass
class 			_snake_case     (						UpperCamelCase       ):
						__snake_case 			=     42
						__snake_case 			=     42
						__snake_case 			=     None



class 			_snake_case     (						UpperCamelCase						,			UpperCamelCase       ):







						@property
						def        _UpperCamelCase    (self							)			->						Union[str, Any]:
											return True







						@register_to_config
						def __init__(self     ,							UpperCAmelCase_ = 2_0_0_0     ,							UpperCAmelCase_ = 0.1_5     ,							UpperCAmelCase_ = 0.0_1     ,							UpperCAmelCase_ = 1_3_4_8.0     ,							UpperCAmelCase_ = 1e-5     ,							UpperCAmelCase_ = 1     ,							)			->						Union[str, Any]:
											pass







						def        _UpperCamelCase    (self							)			->						List[Any]:
											__lowercase												=			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        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = ()     ,							UpperCAmelCase_ = None							)			->						ScoreSdeVeSchedulerState:
											__lowercase												=			sampling_eps if sampling_eps is not None else self.config.sampling_eps

											__lowercase												=			jnp.linspace(1     ,							UpperCAmelCase_     ,							UpperCAmelCase_							)
											return state.replace(timesteps=UpperCAmelCase_							)







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = None     ,							UpperCAmelCase_ = None     ,							UpperCAmelCase_ = None     ,							)			->						ScoreSdeVeSchedulerState:
											__lowercase												=			sigma_min if sigma_min is not None else self.config.sigma_min
											__lowercase												=			sigma_max if sigma_max is not None else self.config.sigma_max
											__lowercase												=			sampling_eps if sampling_eps is not None else self.config.sampling_eps
											if state.timesteps is None:
																__lowercase												=			self.set_timesteps(UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_							)

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

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







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_							)			->						List[Any]:
											return jnp.where(timesteps == 0     ,							jnp.zeros_like(UpperCAmelCase_							)     ,							state.discrete_sigmas[timesteps - 1]							)







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = True     ,							)			->						Union[FlaxSdeVeOutput, Tuple]:
											if state.timesteps is None:
																raise ValueError(
																    '''`state.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''							)

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

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

											#  equation 6: sample noise for the diffusion term of
											__lowercase												=			random.split(UpperCAmelCase_     ,							num=1							)
											__lowercase												=			random.normal(key=UpperCAmelCase_     ,							shape=sample.shape							)
											__lowercase												=			sample - drift  # subtract because `dt` is a small negative timestep
											# TODO is the variable diffusion the correct scaling term for the noise?
											__lowercase												=			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        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = True     ,							)			->						Union[FlaxSdeVeOutput, Tuple]:
											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												=			random.split(UpperCAmelCase_     ,							num=1							)
											__lowercase												=			random.normal(key=UpperCAmelCase_     ,							shape=sample.shape							)

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

											# compute corrected sample: model_output term and noise term
											__lowercase												=			step_size.flatten()
											__lowercase												=			broadcast_to_shape_from_left(UpperCAmelCase_     ,							sample.shape							)
											__lowercase												=			sample + step_size * model_output
											__lowercase												=			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							)			->						List[Any]:
											return self.config.num_train_timesteps





"""simple docstring"""

def 				__UpperCamelCase   (    a__: int ,	a__: int = 10_00			)				->			str:




					"""simple docstring"""



					if (not isinstance(a__ ,	a__			)) or (digit_position <= 0):
										raise ValueError('''Digit position must be a positive integer'''			)
					elif (not isinstance(a__ ,	a__			)) or (precision < 0):
										raise ValueError('''Precision must be a nonnegative integer'''			)

					# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
					# accurate
					__lowercase												=			(
					    4 * _subsum(a__ ,	1 ,	a__			)
					    - 2 * _subsum(a__ ,	4 ,	a__			)
					    - _subsum(a__ ,	5 ,	a__			)
					    - _subsum(a__ ,	6 ,	a__			)
					)

					# return the first hex digit of the fractional part of the result
					return hex(int((sum_result % 1) * 16			)			)[2:]





def 				__UpperCamelCase   (    a__: int ,	a__: int ,	a__: int			)				->			float:




					"""simple docstring"""



					__lowercase												=			0.0
					for sum_index in range(digit_pos_to_extract + precision			):
										__lowercase												=			8 * sum_index + denominator_addend
										if sum_index < digit_pos_to_extract:
															# if the exponential term is an integer and we mod it by the denominator
															# before dividing, only the integer part of the sum will change;
															# the fractional part will not
															__lowercase												=			pow(
															    16 ,	digit_pos_to_extract - 1 - sum_index ,	a__			)
										else:
															__lowercase												=			pow(16 ,	digit_pos_to_extract - 1 - sum_index			)
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()


