


from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)







@flax.struct.dataclass
class   __lowercase						:





							"""simple docstring"""







							_UpperCAmelCase						     =	4_2

							# setable values
							_UpperCAmelCase						     =	4_2
							_UpperCAmelCase						     =	4_2
							_UpperCAmelCase						     =	4_2
							_UpperCAmelCase						     =	None

							# running values
							_UpperCAmelCase						     =	None






							@classmethod
							def 				UpperCamelCase__    (			cls ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__					):





										"""simple docstring"""




										return cls(common=__UpperCamelCase ,	init_noise_sigma=__UpperCamelCase ,	timesteps=__UpperCamelCase ,	sigmas=__UpperCamelCase					)







@dataclass
class   __lowercase						(UpperCAmelCase_     ):





							"""simple docstring"""







							_UpperCAmelCase						     =	4_2







class   __lowercase						(UpperCAmelCase_  ,					UpperCAmelCase_     ):





							"""simple docstring"""







							_UpperCAmelCase						     =	[e.name for e in FlaxKarrasDiffusionSchedulers]

							_UpperCAmelCase						     =	4_2






							@property
							def 				UpperCamelCase__    (			self					):





										"""simple docstring"""




										return True






							@register_to_config
							def __init__(			self ,	lowerCAmelCase__ = 1_0_0_0 ,	lowerCAmelCase__ = 0.0_001 ,	lowerCAmelCase__ = 0.02 ,	lowerCAmelCase__ = "linear" ,	lowerCAmelCase__ = None ,	lowerCAmelCase__ = "epsilon" ,	lowerCAmelCase__ = jnp.floataa ,	):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				dtype






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ = None					):





										"""simple docstring"""




										if common is None:
													SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				CommonSchedulerState.create(self					)

										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				jnp.arange(0 ,	self.config.num_train_timesteps					).round()[::-1]
										SCREAMING_SNAKE_CASE_		:    int 		=				((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

										# standard deviation of the initial noise distribution
										SCREAMING_SNAKE_CASE_		:    int 		=				sigmas.max()

										return LMSDiscreteSchedulerState.create(
										    common=__UpperCamelCase ,	init_noise_sigma=__UpperCamelCase ,	timesteps=__UpperCamelCase ,	sigmas=__UpperCamelCase ,	)






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__					):





										"""simple docstring"""




										((SCREAMING_SNAKE_CASE_					)		,								)		:    int 		=				jnp.where(state.timesteps == timestep ,	size=1					)
										SCREAMING_SNAKE_CASE_		:    Any 		=				step_index[0]

										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				state.sigmas[step_index]
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				sample / ((sigma**2 + 1) ** 0.5)
										return sample






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__					):





										"""simple docstring"""




										def lms_derivative(lowerCAmelCase__					):
													SCREAMING_SNAKE_CASE_		:    Tuple 		=				1.0
													for k in range(__UpperCamelCase					):
																if current_order == k:
																			continue
																prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
													return prod

										SCREAMING_SNAKE_CASE_		:    List[str] 		=				integrate.quad(__UpperCamelCase ,	state.sigmas[t] ,	state.sigmas[t + 1] ,	epsrel=1E-4					)[0]

										return integrated_coeff






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ = ()					):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				jnp.linspace(self.config.num_train_timesteps - 1 ,	0 ,	__UpperCamelCase ,	dtype=self.dtype					)

										SCREAMING_SNAKE_CASE_		:    str 		=				jnp.floor(__UpperCamelCase					).astype(jnp.intaa					)
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				jnp.ceil(__UpperCamelCase					).astype(jnp.intaa					)

										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				jnp.mod(__UpperCamelCase ,	1.0					)

										SCREAMING_SNAKE_CASE_		:    Tuple 		=				((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				jnp.concatenate([sigmas, jnp.array([0.0] ,	dtype=self.dtype					)]					)

										SCREAMING_SNAKE_CASE_		:    int 		=				timesteps.astype(jnp.intaa					)

										# initial running values
										SCREAMING_SNAKE_CASE_		:    Dict 		=				jnp.zeros((0,) + shape ,	dtype=self.dtype					)

										return state.replace(
										    timesteps=__UpperCamelCase ,	sigmas=__UpperCamelCase ,	num_inference_steps=__UpperCamelCase ,	derivatives=__UpperCamelCase ,	)






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ = 4 ,	lowerCAmelCase__ = True ,	):





										"""simple docstring"""




										if state.num_inference_steps is None:
													raise ValueError(
													    'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'					)

										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				state.sigmas[timestep]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
													SCREAMING_SNAKE_CASE_		:    str 		=				sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													SCREAMING_SNAKE_CASE_		:    str 		=				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										else:
													raise ValueError(
													    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

										# 2. Convert to an ODE derivative
										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				(sample - pred_original_sample) / sigma
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				state.replace(derivatives=jnp.append(state.derivatives ,	__UpperCamelCase					)					)
										if len(state.derivatives					) > order:
													SCREAMING_SNAKE_CASE_		:    Dict 		=				state.replace(derivatives=jnp.delete(state.derivatives ,	0					)					)

										# 3. Compute linear multistep coefficients
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				min(timestep + 1 ,	__UpperCamelCase					)
										SCREAMING_SNAKE_CASE_		:    int 		=				[self.get_lms_coefficient(__UpperCamelCase ,	__UpperCamelCase ,	__UpperCamelCase ,	__UpperCamelCase					) for curr_order in range(__UpperCamelCase					)]

										# 4. Compute previous sample based on the derivatives path
										SCREAMING_SNAKE_CASE_		:    List[Any] 		=				sample + sum(
										    coeff * derivative for coeff, derivative in zip(__UpperCamelCase ,	reversed(state.derivatives					)					)					)

										if not return_dict:
													return (prev_sample, state)

										return FlaxLMSSchedulerOutput(prev_sample=__UpperCamelCase ,	state=__UpperCamelCase					)






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Tuple 		=				state.sigmas[timesteps].flatten()
										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				broadcast_to_shape_from_left(__UpperCamelCase ,	noise.shape					)

										SCREAMING_SNAKE_CASE_		:    int 		=				original_samples + noise * sigma

										return noisy_samples






							def __len__(			self					):





										"""simple docstring"""




										return self.config.num_train_timesteps



from itertools import compress, repeat
from math import ceil, sqrt






def 	a__ (							A__							):

			if num <= 2:
						return []
			if num == 3:
						return [2]

			# Odd sieve for numbers in range [3, num - 1]
			SCREAMING_SNAKE_CASE_		:    Any 		=				bytearray(B'\x01'							) * ((num >> 1) - 1)

			for i in range(3,			int(sqrt(A__							)							) + 1,			2							):
						if sieve[(i >> 1) - 1]:
									SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				i**2
									SCREAMING_SNAKE_CASE_		:    List[str] 		=				repeat(
									    0,			ceil((num - i_squared) / (i << 1)							)							)

			return [2] + list(compress(range(3,			A__,			2							),			A__							)							)


if __name__ == "__main__":
				import doctest

				doctest.testmod()





