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

import numpy as np
import torch
from scipy import integrate

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




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 	UpperCAmelCase_      (			_A					):


  '''simple docstring'''







  a__   	=		42
  a__   	=		None







def a__   (	UpperCAmelCase__,					UpperCAmelCase__=0.999,					UpperCAmelCase__="cosine",					):






  '''simple docstring'''





  if alpha_transform_type == "cosine":

    def alpha_bar_fn(UpperCAmelCase__ ):
      return math.cos((t + 0.008) / 1.008 * 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}''' )

  __magic_name__    					=	[]
  for i in range(A_ ):
    __magic_name__    					=	i / num_diffusion_timesteps
    __magic_name__    					=	(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 	UpperCAmelCase_      (			_A  ,	_A					):


  '''simple docstring'''







  a__   	=		[e.name for e in KarrasDiffusionSchedulers]
  a__   	=		1
  @register_to_config
  def __init__(			self      :			Tuple      ,							UpperCamelCase__      :			int = 1000      ,							UpperCamelCase__      :			float = 0.0001      ,							UpperCamelCase__      :			float = 0.02      ,							UpperCamelCase__      :			str = "linear"      ,							UpperCamelCase__      :			Optional[Union[np.ndarray, List[float]]] = None      ,							UpperCamelCase__      :			Optional[bool] = False      ,							UpperCamelCase__      :			str = "epsilon"      ,							UpperCamelCase__      :			str = "linspace"      ,							UpperCamelCase__      :			int = 0      ,							)      ->     Any:







    """simple docstring"""






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

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

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

    # setable values
    __magic_name__    					=	None
    __magic_name__    					=	use_karras_sigmas
    self.set_timesteps(UpperCamelCase__      ,							UpperCamelCase__   )
    __magic_name__    					=	[]
    __magic_name__    					=	False
  @property
  def 							_lowercase							(			self      :			Tuple   )      ->     Tuple:







    """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      :			Dict      ,							UpperCamelCase__      :			torch.FloatTensor      ,							UpperCamelCase__      :			Union[float, torch.FloatTensor]   )      ->     torch.FloatTensor:







    """simple docstring"""






    if isinstance(UpperCamelCase__      ,							torch.Tensor   ):
      __magic_name__    					=	timestep.to(self.timesteps.device   )
    __magic_name__    					=	(self.timesteps == timestep).nonzero().item()
    __magic_name__    					=	self.sigmas[step_index]
    __magic_name__    					=	sample / ((sigma**2 + 1) ** 0.5)
    __magic_name__    					=	True
    return sample
  def 							_lowercase							(			self      :			List[Any]      ,							UpperCamelCase__      :			int      ,							UpperCamelCase__      :			Optional[int]      ,							UpperCamelCase__      :			Any   )      ->     Any:







    """simple docstring"""






    def lms_derivative(UpperCamelCase__      :			Tuple   ):
      __magic_name__    					=	1.0
      for k in range(UpperCamelCase__   ):
        if current_order == k:
          continue
        prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
      return prod

    __magic_name__    					=	integrate.quad(UpperCamelCase__      ,							self.sigmas[t]      ,							self.sigmas[t + 1]      ,							epsrel=1E-4   )[0]

    return integrated_coeff
  def 							_lowercase							(			self      :			Optional[Any]      ,							UpperCamelCase__      :			int      ,							UpperCamelCase__      :			Union[str, torch.device] = None   )      ->     Dict:







    """simple docstring"""






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

    __magic_name__    					=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
    __magic_name__    					=	np.log(UpperCamelCase__   )
    __magic_name__    					=	np.interp(UpperCamelCase__      ,							np.arange(0      ,							len(UpperCamelCase__   )   )      ,							UpperCamelCase__   )

    if self.use_karras_sigmas:
      __magic_name__    					=	self._convert_to_karras(in_sigmas=UpperCamelCase__   )
      __magic_name__    					=	np.array([self._sigma_to_t(UpperCamelCase__      ,							UpperCamelCase__   ) for sigma in sigmas]   )

    __magic_name__    					=	np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )

    __magic_name__    					=	torch.from_numpy(UpperCamelCase__   ).to(device=UpperCamelCase__   )
    if str(UpperCamelCase__   ).startswith("""mps"""   ):
      # mps does not support float64
      __magic_name__    					=	torch.from_numpy(UpperCamelCase__   ).to(UpperCamelCase__      ,							dtype=torch.floataa   )
    else:
      __magic_name__    					=	torch.from_numpy(UpperCamelCase__   ).to(device=UpperCamelCase__   )

    __magic_name__    					=	[]
  def 							_lowercase							(			self      :			Tuple      ,							UpperCamelCase__      :			Dict      ,							UpperCamelCase__      :			List[Any]   )      ->     Union[str, Any]:







    """simple docstring"""






    __magic_name__    					=	np.log(UpperCamelCase__   )

    # get distribution
    __magic_name__    					=	log_sigma - log_sigmas[:, np.newaxis]

    # get sigmas range
    __magic_name__    					=	np.cumsum((dists >= 0)      ,							axis=0   ).argmax(axis=0   ).clip(max=log_sigmas.shape[0] - 2   )
    __magic_name__    					=	low_idx + 1

    __magic_name__    					=	log_sigmas[low_idx]
    __magic_name__    					=	log_sigmas[high_idx]

    # interpolate sigmas
    __magic_name__    					=	(low - log_sigma) / (low - high)
    __magic_name__    					=	np.clip(UpperCamelCase__      ,							0      ,							1   )

    # transform interpolation to time range
    __magic_name__    					=	(1 - w) * low_idx + w * high_idx
    __magic_name__    					=	t.reshape(sigma.shape   )
    return t
  def 							_lowercase							(			self      :			Union[str, Any]      ,							UpperCamelCase__      :			torch.FloatTensor   )      ->     torch.FloatTensor:







    """simple docstring"""






    __magic_name__    					=	in_sigmas[-1].item()
    __magic_name__    					=	in_sigmas[0].item()

    __magic_name__    					=	7.0  # 7.0 is the value used in the paper
    __magic_name__    					=	np.linspace(0      ,							1      ,							self.num_inference_steps   )
    __magic_name__    					=	sigma_min ** (1 / rho)
    __magic_name__    					=	sigma_max ** (1 / rho)
    __magic_name__    					=	(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
    return sigmas
  def 							_lowercase							(			self      :			List[str]      ,							UpperCamelCase__      :			torch.FloatTensor      ,							UpperCamelCase__      :			Union[float, torch.FloatTensor]      ,							UpperCamelCase__      :			torch.FloatTensor      ,							UpperCamelCase__      :			int = 4      ,							UpperCamelCase__      :			bool = True      ,							)      ->     Union[LMSDiscreteSchedulerOutput, Tuple]:







    """simple docstring"""






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

    if isinstance(UpperCamelCase__      ,							torch.Tensor   ):
      __magic_name__    					=	timestep.to(self.timesteps.device   )
    __magic_name__    					=	(self.timesteps == timestep).nonzero().item()
    __magic_name__    					=	self.sigmas[step_index]

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
      __magic_name__    					=	sample - sigma * model_output
    elif self.config.prediction_type == "v_prediction":
      # * c_out + input * c_skip
      __magic_name__    					=	model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
    elif self.config.prediction_type == "sample":
      __magic_name__    					=	model_output
    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
    __magic_name__    					=	(sample - pred_original_sample) / sigma
    self.derivatives.append(UpperCamelCase__   )
    if len(self.derivatives   ) > order:
      self.derivatives.pop(0   )

    # 3. Compute linear multistep coefficients
    __magic_name__    					=	min(step_index + 1      ,							UpperCamelCase__   )
    __magic_name__    					=	[self.get_lms_coefficient(UpperCamelCase__      ,							UpperCamelCase__      ,							UpperCamelCase__   ) for curr_order in range(UpperCamelCase__   )]

    # 4. Compute previous sample based on the derivatives path
    __magic_name__    					=	sample + sum(
        coeff * derivative for coeff, derivative in zip(UpperCamelCase__      ,							reversed(self.derivatives   )   )   )

    if not return_dict:
      return (prev_sample,)

    return LMSDiscreteSchedulerOutput(prev_sample=UpperCamelCase__      ,							pred_original_sample=UpperCamelCase__   )
  def 							_lowercase							(			self      :			Tuple      ,							UpperCamelCase__      :			torch.FloatTensor      ,							UpperCamelCase__      :			torch.FloatTensor      ,							UpperCamelCase__      :			torch.FloatTensor      ,							)      ->     torch.FloatTensor:







    """simple docstring"""






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

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

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

    __magic_name__    					=	original_samples + noise * sigma
    return noisy_samples





  def __len__(			self      :			str   )      ->     Dict:







    """simple docstring"""






    return self.config.num_train_timesteps



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

def a__   (	A_ ):






  '''simple docstring'''





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

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

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

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()

