





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


_UpperCAmelCase										=					logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 				_UpperCamelCase       (						lowerCAmelCase_  ):
       _UpperCamelCase					:       torch.FloatTensor
       _UpperCamelCase					:       Optional[torch.FloatTensor]       = None




def 			lowerCAmelCase_			(				UpperCamelCase_       ,		UpperCamelCase_=0.9_99       ,		UpperCamelCase_="cosine"       ,		)  ->		List[str]:
       if alpha_transform_type == "cosine":

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

       elif alpha_transform_type == "exp":

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

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

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







class 				_UpperCamelCase       (						lowerCAmelCase_	,    lowerCAmelCase_  ):
       _UpperCamelCase					:       List[Any]       = [e.name for e in KarrasDiffusionSchedulers]
       _UpperCamelCase					:       Dict       = 1

       @register_to_config
       def __init__(		self:			int       , _SCREAMING_SNAKE_CASE:			int = 1000       , _SCREAMING_SNAKE_CASE:			float = 0.00_01       , _SCREAMING_SNAKE_CASE:			float = 0.02       , _SCREAMING_SNAKE_CASE:			str = "linear"       , _SCREAMING_SNAKE_CASE:			Optional[Union[np.ndarray, List[float]]] = None       , _SCREAMING_SNAKE_CASE:			str = "epsilon"       , _SCREAMING_SNAKE_CASE:			str = "linspace"       , _SCREAMING_SNAKE_CASE:			int = 0       , )							->			Any:




              """simple docstring"""


              if trained_betas is not None:
                     UpperCamelCase_ 							=	torch.tensor(_SCREAMING_SNAKE_CASE       , dtype=torch.floataa		)
              elif beta_schedule == "linear":
                     UpperCamelCase_ 							=	torch.linspace(_SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE       , dtype=torch.floataa		)
              elif beta_schedule == "scaled_linear":
                     # this schedule is very specific to the latent diffusion model.
                     UpperCamelCase_ 							=	(
                         torch.linspace(beta_start**0.5       , beta_end**0.5       , _SCREAMING_SNAKE_CASE       , dtype=torch.floataa		) ** 2
                     )
              elif beta_schedule == "squaredcos_cap_v2":
                     # Glide cosine schedule
                     UpperCamelCase_ 							=	betas_for_alpha_bar(_SCREAMING_SNAKE_CASE		)
              else:
                     raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''		)

              UpperCamelCase_ 							=	1.0 - self.betas
              UpperCamelCase_ 							=	torch.cumprod(self.alphas       , dim=0		)

              UpperCamelCase_ 							=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
              UpperCamelCase_ 							=	np.concatenate([sigmas[::-1], [0.0]]		).astype(np.floataa		)
              UpperCamelCase_ 							=	torch.from_numpy(_SCREAMING_SNAKE_CASE		)

              # setable values
              UpperCamelCase_ 							=	None
              UpperCamelCase_ 							=	np.linspace(0       , num_train_timesteps - 1       , _SCREAMING_SNAKE_CASE       , dtype=_SCREAMING_SNAKE_CASE		)[::-1].copy()
              UpperCamelCase_ 							=	torch.from_numpy(_SCREAMING_SNAKE_CASE		)
              UpperCamelCase_ 							=	False

       @property
       def lowercase			(		self:			List[str]		)							->			Any:




              """simple docstring"""


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

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

       def lowercase			(		self:			Optional[int]       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , _SCREAMING_SNAKE_CASE:			Union[float, torch.FloatTensor]		)							->			torch.FloatTensor:




              """simple docstring"""


              if isinstance(_SCREAMING_SNAKE_CASE       , torch.Tensor		):
                     UpperCamelCase_ 							=	timestep.to(self.timesteps.device		)
              UpperCamelCase_ 							=	(self.timesteps == timestep).nonzero().item()
              UpperCamelCase_ 							=	self.sigmas[step_index]
              UpperCamelCase_ 							=	sample / ((sigma**2 + 1) ** 0.5)
              UpperCamelCase_ 							=	True
              return sample

       def lowercase			(		self:			Union[str, Any]       , _SCREAMING_SNAKE_CASE:			int       , _SCREAMING_SNAKE_CASE:			Union[str, torch.device] = None		)							->			List[str]:




              """simple docstring"""


              UpperCamelCase_ 							=	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":
                     UpperCamelCase_ 							=	np.linspace(0       , self.config.num_train_timesteps - 1       , _SCREAMING_SNAKE_CASE       , dtype=_SCREAMING_SNAKE_CASE		)[
                         ::-1
                     ].copy()
              elif self.config.timestep_spacing == "leading":
                     UpperCamelCase_ 							=	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
                     UpperCamelCase_ 							=	(np.arange(0       , _SCREAMING_SNAKE_CASE		) * step_ratio).round()[::-1].copy().astype(_SCREAMING_SNAKE_CASE		)
                     timesteps += self.config.steps_offset
              elif self.config.timestep_spacing == "trailing":
                     UpperCamelCase_ 							=	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
                     UpperCamelCase_ 							=	(np.arange(self.config.num_train_timesteps       , 0       , -step_ratio		)).round().copy().astype(_SCREAMING_SNAKE_CASE		)
                     timesteps -= 1
              else:
                     raise ValueError(
                         f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''		)

              UpperCamelCase_ 							=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
              UpperCamelCase_ 							=	np.interp(_SCREAMING_SNAKE_CASE       , np.arange(0       , len(_SCREAMING_SNAKE_CASE		)		)       , _SCREAMING_SNAKE_CASE		)
              UpperCamelCase_ 							=	np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)
              UpperCamelCase_ 							=	torch.from_numpy(_SCREAMING_SNAKE_CASE		).to(device=_SCREAMING_SNAKE_CASE		)
              if str(_SCREAMING_SNAKE_CASE		).startswith("mps"		):
                     # mps does not support float64
                     UpperCamelCase_ 							=	torch.from_numpy(_SCREAMING_SNAKE_CASE		).to(_SCREAMING_SNAKE_CASE       , dtype=torch.floataa		)
              else:
                     UpperCamelCase_ 							=	torch.from_numpy(_SCREAMING_SNAKE_CASE		).to(device=_SCREAMING_SNAKE_CASE		)

       def lowercase			(		self:			Optional[int]       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , _SCREAMING_SNAKE_CASE:			Union[float, torch.FloatTensor]       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , _SCREAMING_SNAKE_CASE:			Optional[torch.Generator] = None       , _SCREAMING_SNAKE_CASE:			bool = True       , )							->			Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:




              """simple docstring"""


              if (
                  isinstance(_SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE		)
                  or isinstance(_SCREAMING_SNAKE_CASE       , torch.IntTensor		)
                  or isinstance(_SCREAMING_SNAKE_CASE       , 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(_SCREAMING_SNAKE_CASE       , torch.Tensor		):
                     UpperCamelCase_ 							=	timestep.to(self.timesteps.device		)

              UpperCamelCase_ 							=	(self.timesteps == timestep).nonzero().item()
              UpperCamelCase_ 							=	self.sigmas[step_index]

              # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
              if self.config.prediction_type == "epsilon":
                     UpperCamelCase_ 							=	sample - sigma * model_output
              elif self.config.prediction_type == "v_prediction":
                     # * c_out + input * c_skip
                     UpperCamelCase_ 							=	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`'''		)

              UpperCamelCase_ 							=	self.sigmas[step_index]
              UpperCamelCase_ 							=	self.sigmas[step_index + 1]
              UpperCamelCase_ 							=	(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
              UpperCamelCase_ 							=	(sigma_to**2 - sigma_up**2) ** 0.5

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

              UpperCamelCase_ 							=	sigma_down - sigma

              UpperCamelCase_ 							=	sample + derivative * dt

              UpperCamelCase_ 							=	model_output.device
              UpperCamelCase_ 							=	randn_tensor(model_output.shape       , dtype=model_output.dtype       , device=_SCREAMING_SNAKE_CASE       , generator=_SCREAMING_SNAKE_CASE		)

              UpperCamelCase_ 							=	prev_sample + noise * sigma_up

              if not return_dict:
                     return (prev_sample,)

              return EulerAncestralDiscreteSchedulerOutput(
                  prev_sample=_SCREAMING_SNAKE_CASE       , pred_original_sample=_SCREAMING_SNAKE_CASE		)

       def lowercase			(		self:			Union[str, Any]       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , _SCREAMING_SNAKE_CASE:			torch.FloatTensor       , )							->			torch.FloatTensor:




              """simple docstring"""


              UpperCamelCase_ 							=	self.sigmas.to(device=original_samples.device       , dtype=original_samples.dtype		)
              if original_samples.device.type == "mps" and torch.is_floating_point(_SCREAMING_SNAKE_CASE		):
                     # mps does not support float64
                     UpperCamelCase_ 							=	self.timesteps.to(original_samples.device       , dtype=torch.floataa		)
                     UpperCamelCase_ 							=	timesteps.to(original_samples.device       , dtype=torch.floataa		)
              else:
                     UpperCamelCase_ 							=	self.timesteps.to(original_samples.device		)
                     UpperCamelCase_ 							=	timesteps.to(original_samples.device		)

              UpperCamelCase_ 							=	[(schedule_timesteps == t).nonzero().item() for t in timesteps]

              UpperCamelCase_ 							=	sigmas[step_indices].flatten()
              while len(sigma.shape		) < len(original_samples.shape		):
                     UpperCamelCase_ 							=	sigma.unsqueeze(-1		)

              UpperCamelCase_ 							=	original_samples + noise * sigma
              return noisy_samples



       def __len__(		self:			Any		)							->			List[str]:




              """simple docstring"""


              return self.config.num_train_timesteps








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




def 			lowerCAmelCase_			(				UpperCamelCase_	)  ->		list[int]:

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

       # Odd sieve for numbers in range [3, num - 1]
       UpperCamelCase_ 							=	bytearray(b"\x01"	) * ((num >> 1) - 1)

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

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()

