





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput


def _A       (   __magic_name__  , __magic_name__=0.999  , __magic_name__="cosine"  , ):
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(__magic_name__	):
         return math.cos((t + 0.008) / 1.008 * math.pi / 2	) ** 2

   elif alpha_transform_type == "exp":

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

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

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







class  lowerCAmelCase							(       lowercase_							,							lowercase_ ):
  __lowerCamelCase		=      [e.name for e in KarrasDiffusionSchedulers]
  __lowerCamelCase		=      2







  @register_to_config
  def __init__(      self  :Optional[int]   ,							_lowercase  :int = 10_00   ,							_lowercase  :float = 0.00085   ,							_lowercase  :float = 0.012   ,							_lowercase  :str = "linear"   ,							_lowercase  :Optional[Union[np.ndarray, List[float]]] = None   ,							_lowercase  :str = "epsilon"   ,							_lowercase  :str = "linspace"   ,							_lowercase  :int = 0   ,							):






     '''simple docstring'''





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

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

     #  set all values
     self.set_timesteps(_lowercase   ,							_lowercase   ,							_lowercase )







  def   UpperCAmelCase					(      self  :Any   ,							_lowercase  :Tuple   ,							_lowercase  :List[Any]=None ):






     '''simple docstring'''





     if schedule_timesteps is None:
        lowercase__			       =  self.timesteps

     lowercase__			       =  (schedule_timesteps == timestep).nonzero()

     # The sigma index that is taken for the **very** first `step`
     # is always the second index (or the last index if there is only 1)
     # This way we can ensure we don't accidentally skip a sigma in
     # case we start in the middle of the denoising schedule (e.g. for image-to-image)
     if len(self._index_counter ) == 0:
        lowercase__			       =  1 if len(_lowercase ) > 1 else 0
     else:
        lowercase__			       =  timestep.cpu().item() if torch.is_tensor(_lowercase ) else timestep
        lowercase__			       =  self._index_counter[timestep_int]

     return indices[pos].item()







  @property
  def   UpperCAmelCase					(      self  :Union[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   UpperCAmelCase					(      self  :Dict   ,							_lowercase  :torch.FloatTensor   ,							_lowercase  :Union[float, torch.FloatTensor]   ,							):






     '''simple docstring'''





     lowercase__			       =  self.index_for_timestep(_lowercase )

     if self.state_in_first_order:
        lowercase__			       =  self.sigmas[step_index]
     else:
        lowercase__			       =  self.sigmas_interpol[step_index]

     lowercase__			       =  sample / ((sigma**2 + 1) ** 0.5)
     return sample







  def   UpperCAmelCase					(      self  :str   ,							_lowercase  :int   ,							_lowercase  :Union[str, torch.device] = None   ,							_lowercase  :Optional[int] = None   ,							):






     '''simple docstring'''





     lowercase__			       =  num_inference_steps

     lowercase__			       =  num_train_timesteps or self.config.num_train_timesteps

     # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
     if self.config.timestep_spacing == "linspace":
        lowercase__			       =  np.linspace(0   ,							num_train_timesteps - 1   ,							_lowercase   ,							dtype=_lowercase )[::-1].copy()
     elif self.config.timestep_spacing == "leading":
        lowercase__			       =  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
        lowercase__			       =  (np.arange(0   ,							_lowercase ) * step_ratio).round()[::-1].copy().astype(_lowercase )
        timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
        lowercase__			       =  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
        lowercase__			       =  (np.arange(_lowercase   ,							0   ,							-step_ratio )).round().copy().astype(_lowercase )
        timesteps -= 1
     else:
        raise ValueError(
            f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''' )

     lowercase__			       =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
     lowercase__			       =  torch.from_numpy(np.log(_lowercase ) ).to(_lowercase )

     lowercase__			       =  np.interp(_lowercase   ,							np.arange(0   ,							len(_lowercase ) )   ,							_lowercase )
     lowercase__			       =  np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
     lowercase__			       =  torch.from_numpy(_lowercase ).to(device=_lowercase )

     # interpolate sigmas
     lowercase__			       =  sigmas.log().lerp(sigmas.roll(1 ).log()   ,							0.5 ).exp()

     lowercase__			       =  torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2 ), sigmas[-1:]] )
     lowercase__			       =  torch.cat(
         [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2 ), sigmas_interpol[-1:]] )

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

     # interpolate timesteps
     lowercase__			       =  self.sigma_to_t(_lowercase ).to(_lowercase   ,							dtype=timesteps.dtype )
     lowercase__			       =  torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])   ,							dim=-1 ).flatten()

     lowercase__			       =  torch.cat([timesteps[:1], interleaved_timesteps] )

     lowercase__			       =  None

     # for exp beta schedules, such as the one for `pipeline_shap_e.py`
     # we need an index counter
     lowercase__			       =  defaultdict(_lowercase )







  def   UpperCAmelCase					(      self  :Optional[int]   ,							_lowercase  :Union[str, Any] ):






     '''simple docstring'''





     lowercase__			       =  sigma.log()

     # get distribution
     lowercase__			       =  log_sigma - self.log_sigmas[:, None]

     # get sigmas range
     lowercase__			       =  dists.ge(0 ).cumsum(dim=0 ).argmax(dim=0 ).clamp(max=self.log_sigmas.shape[0] - 2 )
     lowercase__			       =  low_idx + 1

     lowercase__			       =  self.log_sigmas[low_idx]
     lowercase__			       =  self.log_sigmas[high_idx]

     # interpolate sigmas
     lowercase__			       =  (low - log_sigma) / (low - high)
     lowercase__			       =  w.clamp(0   ,							1 )

     # transform interpolation to time range
     lowercase__			       =  (1 - w) * low_idx + w * high_idx
     lowercase__			       =  t.view(sigma.shape )
     return t







  @property
  def   UpperCAmelCase					(      self  :Optional[int] ):






     '''simple docstring'''





     return self.sample is None







  def   UpperCAmelCase					(      self  :str   ,							_lowercase  :Union[torch.FloatTensor, np.ndarray]   ,							_lowercase  :Union[float, torch.FloatTensor]   ,							_lowercase  :Union[torch.FloatTensor, np.ndarray]   ,							_lowercase  :bool = True   ,							):






     '''simple docstring'''





     lowercase__			       =  self.index_for_timestep(_lowercase )

     # advance index counter by 1
     lowercase__			       =  timestep.cpu().item() if torch.is_tensor(_lowercase ) else timestep
     self._index_counter[timestep_int] += 1

     if self.state_in_first_order:
        lowercase__			       =  self.sigmas[step_index]
        lowercase__			       =  self.sigmas_interpol[step_index + 1]
        lowercase__			       =  self.sigmas[step_index + 1]
     else:
        # 2nd order / KDPM2's method
        lowercase__			       =  self.sigmas[step_index - 1]
        lowercase__			       =  self.sigmas_interpol[step_index]
        lowercase__			       =  self.sigmas[step_index]

     # currently only gamma=0 is supported. This usually works best anyways.
     # We can support gamma in the future but then need to scale the timestep before
     # passing it to the model which requires a change in API
     lowercase__			       =  0
     lowercase__			       =  sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     if self.config.prediction_type == "epsilon":
        lowercase__			       =  sigma_hat if self.state_in_first_order else sigma_interpol
        lowercase__			       =  sample - sigma_input * model_output
     elif self.config.prediction_type == "v_prediction":
        lowercase__			       =  sigma_hat if self.state_in_first_order else sigma_interpol
        lowercase__			       =  model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
            sample / (sigma_input**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`''' )

     if self.state_in_first_order:
        # 2. Convert to an ODE derivative for 1st order
        lowercase__			       =  (sample - pred_original_sample) / sigma_hat
        # 3. delta timestep
        lowercase__			       =  sigma_interpol - sigma_hat

        # store for 2nd order step
        lowercase__			       =  sample
     else:
        # DPM-Solver-2
        # 2. Convert to an ODE derivative for 2nd order
        lowercase__			       =  (sample - pred_original_sample) / sigma_interpol

        # 3. delta timestep
        lowercase__			       =  sigma_next - sigma_hat

        lowercase__			       =  self.sample
        lowercase__			       =  None

     lowercase__			       =  sample + derivative * dt

     if not return_dict:
        return (prev_sample,)

     return SchedulerOutput(prev_sample=_lowercase )







  def   UpperCAmelCase					(      self  :str   ,							_lowercase  :torch.FloatTensor   ,							_lowercase  :torch.FloatTensor   ,							_lowercase  :torch.FloatTensor   ,							):






     '''simple docstring'''





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

     lowercase__			       =  [self.index_for_timestep(_lowercase   ,							_lowercase ) for t in timesteps]

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

     lowercase__			       =  original_samples + noise * sigma
     return noisy_samples







  def __len__(      self  :Any ):






     '''simple docstring'''





     return self.config.num_train_timesteps













from __future__ import annotations


def _A       (   __magic_name__  , __magic_name__	):
   lowercase__			       =  []
   create_all_state(1  , __magic_name__  , __magic_name__  , []  , __magic_name__	)
   return result


def _A       (   __magic_name__  , __magic_name__  , __magic_name__  , __magic_name__  , __magic_name__  , ):
   if level == 0:
      total_list.append(current_list[:]	)
      return

   for i in range(__magic_name__  , total_number - level + 2	):
      current_list.append(__magic_name__	)
      create_all_state(i + 1  , __magic_name__  , level - 1  , __magic_name__  , __magic_name__	)
      current_list.pop()


def _A       (   __magic_name__	):
   for i in total_list:
      print(*__magic_name__	)


if __name__ == "__main__":
  _snake_case           =			4
  _snake_case           =			2
  _snake_case           =			generate_all_combinations(n, k)
  print_all_state(total_list)






