


'''simple docstring'''







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


a__  : Any				=	logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class  lowercase_					(   a__       ):
    __UpperCAmelCase             =     42
    __UpperCAmelCase             =     None







def _UpperCamelCase	(					__A				,      __A=0.999				,      __A="cosine"				,      )							->		Optional[int]:


      '''simple docstring'''



      if alpha_transform_type == "cosine":

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

      UpperCamelCase__  =    []
      for i in range(__A   ):
            UpperCamelCase__  =    i / num_diffusion_timesteps
            UpperCamelCase__  =    (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_					(   a__  ,						a__       ):
    __UpperCAmelCase             =     [e.name for e in KarrasDiffusionSchedulers]
    __UpperCAmelCase             =     1


    @register_to_config
    def __init__(					self  , a = 10_00  , a = 0.0001  , a = 0.02  , a = "linear"  , a = None  , a = "epsilon"  , a = "linspace"  , a = 0  , ):
          if trained_betas is not None:
                UpperCamelCase__  =    torch.tensor(a  , dtype=torch.floataa   )
          elif beta_schedule == "linear":
                UpperCamelCase__  =    torch.linspace(a  , a  , a  , 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  , a  , dtype=torch.floataa   ) ** 2
                )
          elif beta_schedule == "squaredcos_cap_v2":
                # Glide cosine schedule
                UpperCamelCase__  =    betas_for_alpha_bar(a   )
          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(a   )

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


    @property
    def        __a							(					self   ):
          # standard deviation of the initial noise distribution
          if self.config.timestep_spacing in ["linspace", "trailing"]:
                return self.sigmas.max()

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


    def        __a							(					self  , a  , a   ):
          if isinstance(a  , 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        __a							(					self  , a  , a = None   ):
          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  , a  , dtype=a   )[
                    ::-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  , a   ) * step_ratio).round()[::-1].copy().astype(a   )
                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(a   )
                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(a  , np.arange(0  , len(a   )   )  , a   )
          UpperCamelCase__  =    np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
          UpperCamelCase__  =    torch.from_numpy(a   ).to(device=a   )
          if str(a   ).startswith("mps"   ):
                # mps does not support float64
                UpperCamelCase__  =    torch.from_numpy(a   ).to(a  , dtype=torch.floataa   )
          else:
                UpperCamelCase__  =    torch.from_numpy(a   ).to(device=a   )


    def        __a							(					self  , a  , a  , a  , a = None  , a = True  , ):

          if (
              isinstance(a  , a   )
              or isinstance(a  , torch.IntTensor   )
              or isinstance(a  , 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(a  , 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=a  , generator=a   )

          UpperCamelCase__  =    prev_sample + noise * sigma_up

          if not return_dict:
                return (prev_sample,)

          return EulerAncestralDiscreteSchedulerOutput(
              prev_sample=a  , pred_original_sample=a   )


    def        __a							(					self  , a  , a  , a  , ):
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          UpperCamelCase__  =    self.sigmas.to(device=original_samples.device  , dtype=original_samples.dtype   )
          if original_samples.device.type == "mps" and torch.is_floating_point(a   ):
                # 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   ):
          return self.config.num_train_timesteps









'''simple docstring'''







from itertools import permutations







def _UpperCamelCase	(					)							->		Optional[int]:


      '''simple docstring'''



      UpperCamelCase__  =    list(map("".join				,      permutations("0123456789"   )   )   )
      return result[999999]


if __name__ == "__main__":
  print(solution())





