


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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


lowerCAmelCase__ :			List[str]         =logging.get_logger(__name__)  # pylint: disable=invalid-name







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class   __lowercase						(__SCREAMING_SNAKE_CASE     ):





							"""simple docstring"""







							_UpperCAmelCase						     =	4_2
							_UpperCAmelCase						     =	None







def 	a__ (							A__,			A__=0.9_99,			A__="cosine",			):
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(A__							):
									return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2							) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(A__							):
									return math.exp(t * -12.0							)

			else:
						raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}'''							)

			SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				[]
			for i in range(A__							):
						SCREAMING_SNAKE_CASE_		:    int 		=				i / num_diffusion_timesteps
						SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				(i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(A__							) / alpha_bar_fn(A__							),			A__							)							)
			return torch.tensor(A__,			dtype=torch.floataa							)







class   __lowercase						(__SCREAMING_SNAKE_CASE  ,					__SCREAMING_SNAKE_CASE     ):





							"""simple docstring"""







							_UpperCAmelCase						     =	[e.name for e in KarrasDiffusionSchedulers]
							_UpperCAmelCase						     =	1






							@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__ = "linspace" ,	lowerCAmelCase__ = 0 ,	):





										"""simple docstring"""




										if trained_betas is not None:
													SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				torch.tensor(lowerCAmelCase__ ,	dtype=torch.floataa					)
										elif beta_schedule == "linear":
													SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				torch.linspace(lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	dtype=torch.floataa					)
										elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				(
													    torch.linspace(beta_start**0.5 ,	beta_end**0.5 ,	lowerCAmelCase__ ,	dtype=torch.floataa					) ** 2
													)
										elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				betas_for_alpha_bar(lowerCAmelCase__					)
										else:
													raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''					)

										SCREAMING_SNAKE_CASE_		:    str 		=				1.0 - self.betas
										SCREAMING_SNAKE_CASE_		:    List[str] 		=				torch.cumprod(self.alphas ,	dim=0					)

										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				np.concatenate([sigmas[::-1], [0.0]]					).astype(np.floataa					)
										SCREAMING_SNAKE_CASE_		:    int 		=				torch.from_numpy(lowerCAmelCase__					)

										# setable values
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				None
										SCREAMING_SNAKE_CASE_		:    int 		=				np.linspace(0 ,	num_train_timesteps - 1 ,	lowerCAmelCase__ ,	dtype=lowerCAmelCase__					)[::-1].copy()
										SCREAMING_SNAKE_CASE_		:    int 		=				torch.from_numpy(lowerCAmelCase__					)
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				False






							@property
							def 				UpperCamelCase__    (			self					):





										"""simple docstring"""




										if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

										return (self.sigmas.max() ** 2 + 1) ** 0.5






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__					):





										"""simple docstring"""




										if isinstance(lowerCAmelCase__ ,	torch.Tensor					):
													SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				timestep.to(self.timesteps.device					)
										SCREAMING_SNAKE_CASE_		:    Dict 		=				(self.timesteps == timestep).nonzero().item()
										SCREAMING_SNAKE_CASE_		:    str 		=				self.sigmas[step_index]
										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				sample / ((sigma**2 + 1) ** 0.5)
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				True
										return sample






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ = None					):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				num_inference_steps

										# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
										if self.config.timestep_spacing == "linspace":
													SCREAMING_SNAKE_CASE_		:    List[Any] 		=				np.linspace(0 ,	self.config.num_train_timesteps - 1 ,	lowerCAmelCase__ ,	dtype=lowerCAmelCase__					)[
													    ::-1
													].copy()
										elif self.config.timestep_spacing == "leading":
													SCREAMING_SNAKE_CASE_		:    List[Any] 		=				self.config.num_train_timesteps // self.num_inference_steps
													# creates integer timesteps by multiplying by ratio
													# casting to int to avoid issues when num_inference_step is power of 3
													SCREAMING_SNAKE_CASE_		:    int 		=				(np.arange(0 ,	lowerCAmelCase__					) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__					)
													timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
													SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				self.config.num_train_timesteps / self.num_inference_steps
													# creates integer timesteps by multiplying by ratio
													# casting to int to avoid issues when num_inference_step is power of 3
													SCREAMING_SNAKE_CASE_		:    int 		=				(np.arange(self.config.num_train_timesteps ,	0 ,	-step_ratio					)).round().copy().astype(lowerCAmelCase__					)
													timesteps -= 1
										else:
													raise ValueError(
													    F'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''					)

										SCREAMING_SNAKE_CASE_		:    List[Any] 		=				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				np.interp(lowerCAmelCase__ ,	np.arange(0 ,	len(lowerCAmelCase__					)					) ,	lowerCAmelCase__					)
										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				torch.from_numpy(lowerCAmelCase__					).to(device=lowerCAmelCase__					)
										if str(lowerCAmelCase__					).startswith('mps'					):
													# mps does not support float64
													SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				torch.from_numpy(lowerCAmelCase__					).to(lowerCAmelCase__ ,	dtype=torch.floataa					)
										else:
													SCREAMING_SNAKE_CASE_		:    List[Any] 		=				torch.from_numpy(lowerCAmelCase__					).to(device=lowerCAmelCase__					)






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ ,	lowerCAmelCase__ = None ,	lowerCAmelCase__ = True ,	):





										"""simple docstring"""




										if (
										    isinstance(lowerCAmelCase__ ,	lowerCAmelCase__					)
										    or isinstance(lowerCAmelCase__ ,	torch.IntTensor					)
										    or isinstance(lowerCAmelCase__ ,	torch.LongTensor					)
										):
													raise ValueError(
													    (
													        'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
													        ' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'
													        ' one of the `scheduler.timesteps` as a timestep.'
													    ) ,	)

										if not self.is_scale_input_called:
													logger.warning(
													    'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
													    'See `StableDiffusionPipeline` for a usage example.'					)

										if isinstance(lowerCAmelCase__ ,	torch.Tensor					):
													SCREAMING_SNAKE_CASE_		:    Tuple 		=				timestep.to(self.timesteps.device					)

										SCREAMING_SNAKE_CASE_		:    str 		=				(self.timesteps == timestep).nonzero().item()
										SCREAMING_SNAKE_CASE_		:    List[str] 		=				self.sigmas[step_index]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
													SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													SCREAMING_SNAKE_CASE_		:    Tuple 		=				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										elif self.config.prediction_type == "sample":
													raise NotImplementedError('prediction_type not implemented yet: sample'					)
										else:
													raise ValueError(
													    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				self.sigmas[step_index]
										SCREAMING_SNAKE_CASE_		:    Dict 		=				self.sigmas[step_index + 1]
										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
										SCREAMING_SNAKE_CASE_		:    Tuple 		=				(sigma_to**2 - sigma_up**2) ** 0.5

										# 2. Convert to an ODE derivative
										SCREAMING_SNAKE_CASE_		:    Any 		=				(sample - pred_original_sample) / sigma

										SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				sigma_down - sigma

										SCREAMING_SNAKE_CASE_		:    int 		=				sample + derivative * dt

										SCREAMING_SNAKE_CASE_		:    Any 		=				model_output.device
										SCREAMING_SNAKE_CASE_		:    List[str] 		=				randn_tensor(model_output.shape ,	dtype=model_output.dtype ,	device=lowerCAmelCase__ ,	generator=lowerCAmelCase__					)

										SCREAMING_SNAKE_CASE_		:    Dict 		=				prev_sample + noise * sigma_up

										if not return_dict:
													return (prev_sample,)

										return EulerAncestralDiscreteSchedulerOutput(
										    prev_sample=lowerCAmelCase__ ,	pred_original_sample=lowerCAmelCase__					)






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





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Dict 		=				self.sigmas.to(device=original_samples.device ,	dtype=original_samples.dtype					)
										if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase__					):
													# mps does not support float64
													SCREAMING_SNAKE_CASE_		:    str 		=				self.timesteps.to(original_samples.device ,	dtype=torch.floataa					)
													SCREAMING_SNAKE_CASE_		:    str 		=				timesteps.to(original_samples.device ,	dtype=torch.floataa					)
										else:
													SCREAMING_SNAKE_CASE_		:    Tuple 		=				self.timesteps.to(original_samples.device					)
													SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				timesteps.to(original_samples.device					)

										SCREAMING_SNAKE_CASE_		:    Any 		=				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

										SCREAMING_SNAKE_CASE_		:    Tuple 		=				sigmas[step_indices].flatten()
										while len(sigma.shape					) < len(original_samples.shape					):
													SCREAMING_SNAKE_CASE_		:    List[Any] 		=				sigma.unsqueeze(-1					)

										SCREAMING_SNAKE_CASE_		:    Optional[Any] 		=				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()





