





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	(		SCREAMING_SNAKE_CASE					:       Optional[Any]	,	SCREAMING_SNAKE_CASE					:       str=0.9_9_9	,	SCREAMING_SNAKE_CASE					:       List[str]="cosine"	,	):





  """simple docstring"""



  if alpha_transform_type == "cosine":

    def alpha_bar_fn(SCREAMING_SNAKE_CASE					:       Union[str, Any]						):
      return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2						) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(SCREAMING_SNAKE_CASE					:       Any						):
      return math.exp(t * -1_2.0						)

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

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







class     __lowerCAmelCase	(   UpperCAmelCase_						,    UpperCAmelCase_):
      _lowercase    : Union[str, Any]            =      [e.name for e in KarrasDiffusionSchedulers]
      _lowercase    : Dict            =      2







      @register_to_config
      def __init__(   self		,				lowerCAmelCase__ = 1_0_0_0		,				lowerCAmelCase__ = 0.0_00_85		,				lowerCAmelCase__ = 0.0_12		,				lowerCAmelCase__ = "linear"		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = "epsilon"		,				lowerCAmelCase__ = "linspace"		,				lowerCAmelCase__ = 0		,				)       ->						Optional[int]:



        '''simple docstring'''




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

        a__     : Any  =1.0 - self.betas
        a__     : Optional[int]  =torch.cumprod(self.alphas		,				dim=0							)

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







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__=None							)       ->						Any:



        '''simple docstring'''




        if schedule_timesteps is None:
          a__     : Dict  =self.timesteps

        a__     : List[str]  =(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:
          a__     : int  =1 if len(__lowercase							) > 1 else 0
        else:
          a__     : str  =timestep.cpu().item() if torch.is_tensor(__lowercase							) else timestep
          a__     : Union[str, Any]  =self._index_counter[timestep_int]

        return indices[pos].item()







      @property
      def        _lowercase  (   self							)       ->						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		,				lowerCAmelCase__		,				lowerCAmelCase__		,				)       ->						torch.FloatTensor:



        '''simple docstring'''




        a__     : Dict  =self.index_for_timestep(__lowercase							)

        if self.state_in_first_order:
          a__     : Dict  =self.sigmas[step_index]
        else:
          a__     : int  =self.sigmas_interpol[step_index]

        a__     : Tuple  =sample / ((sigma**2 + 1) ** 0.5)
        return sample







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = None		,				)       ->						Tuple:



        '''simple docstring'''




        a__     : Optional[Any]  =num_inference_steps

        a__     : Any  =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":
          a__     : List[Any]  =np.linspace(0		,				num_train_timesteps - 1		,				__lowercase		,				dtype=__lowercase							)[::-1].copy()
        elif self.config.timestep_spacing == "leading":
          a__     : Dict  =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
          a__     : List[str]  =(np.arange(0		,				__lowercase							) * step_ratio).round()[::-1].copy().astype(__lowercase							)
          timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
          a__     : Optional[Any]  =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
          a__     : Dict  =(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\'.'''							)

        a__     : List[str]  =np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
        a__     : Tuple  =torch.from_numpy(np.log(__lowercase							)							).to(__lowercase							)

        a__     : Union[str, Any]  =np.interp(__lowercase		,				np.arange(0		,				len(__lowercase							)							)		,				__lowercase							)
        a__     : Any  =np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
        a__     : Optional[Any]  =torch.from_numpy(__lowercase							).to(device=__lowercase							)

        # interpolate sigmas
        a__     : Optional[int]  =sigmas.log().lerp(sigmas.roll(1							).log()		,				0.5							).exp()

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

        if str(__lowercase							).startswith("mps"							):
          # mps does not support float64
          a__     : Any  =torch.from_numpy(__lowercase							).to(__lowercase		,				dtype=torch.floataa							)
        else:
          a__     : List[str]  =torch.from_numpy(__lowercase							).to(__lowercase							)

        # interpolate timesteps
        a__     : int  =self.sigma_to_t(__lowercase							).to(__lowercase		,				dtype=timesteps.dtype							)
        a__     : Union[str, Any]  =torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])		,				dim=-1							).flatten()

        a__     : Optional[Any]  =torch.cat([timesteps[:1], interleaved_timesteps]							)

        a__     : Union[str, Any]  =None

        # for exp beta schedules, such as the one for `pipeline_shap_e.py`
        # we need an index counter
        a__     : str  =defaultdict(__lowercase							)







      def        _lowercase  (   self		,				lowerCAmelCase__							)       ->						List[str]:



        '''simple docstring'''




        a__     : Optional[Any]  =sigma.log()

        # get distribution
        a__     : Optional[Any]  =log_sigma - self.log_sigmas[:, None]

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

        a__     : str  =self.log_sigmas[low_idx]
        a__     : List[str]  =self.log_sigmas[high_idx]

        # interpolate sigmas
        a__     : Tuple  =(low - log_sigma) / (low - high)
        a__     : List[str]  =w.clamp(0		,				1							)

        # transform interpolation to time range
        a__     : Tuple  =(1 - w) * low_idx + w * high_idx
        a__     : Optional[int]  =t.view(sigma.shape							)
        return t







      @property
      def        _lowercase  (   self							)       ->						Union[str, Any]:



        '''simple docstring'''




        return self.sample is None







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__ = True		,				)       ->						Union[SchedulerOutput, Tuple]:



        '''simple docstring'''




        a__     : Union[str, Any]  =self.index_for_timestep(__lowercase							)

        # advance index counter by 1
        a__     : int  =timestep.cpu().item() if torch.is_tensor(__lowercase							) else timestep
        self._index_counter[timestep_int] += 1

        if self.state_in_first_order:
          a__     : List[Any]  =self.sigmas[step_index]
          a__     : List[str]  =self.sigmas_interpol[step_index + 1]
          a__     : Optional[Any]  =self.sigmas[step_index + 1]
        else:
          # 2nd order / KDPM2's method
          a__     : List[Any]  =self.sigmas[step_index - 1]
          a__     : List[Any]  =self.sigmas_interpol[step_index]
          a__     : str  =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
        a__     : str  =0
        a__     : Optional[int]  =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":
          a__     : Optional[Any]  =sigma_hat if self.state_in_first_order else sigma_interpol
          a__     : List[Any]  =sample - sigma_input * model_output
        elif self.config.prediction_type == "v_prediction":
          a__     : Dict  =sigma_hat if self.state_in_first_order else sigma_interpol
          a__     : List[Any]  =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
          a__     : List[Any]  =(sample - pred_original_sample) / sigma_hat
          # 3. delta timestep
          a__     : Union[str, Any]  =sigma_interpol - sigma_hat

          # store for 2nd order step
          a__     : Any  =sample
        else:
          # DPM-Solver-2
          # 2. Convert to an ODE derivative for 2nd order
          a__     : Union[str, Any]  =(sample - pred_original_sample) / sigma_interpol

          # 3. delta timestep
          a__     : Tuple  =sigma_next - sigma_hat

          a__     : Tuple  =self.sample
          a__     : int  =None

        a__     : Optional[Any]  =sample + derivative * dt

        if not return_dict:
          return (prev_sample,)

        return SchedulerOutput(prev_sample=__lowercase							)







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				)       ->						torch.FloatTensor:



        '''simple docstring'''




        a__     : Any  =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
          a__     : Dict  =self.timesteps.to(original_samples.device		,				dtype=torch.floataa							)
          a__     : Optional[Any]  =timesteps.to(original_samples.device		,				dtype=torch.floataa							)
        else:
          a__     : Any  =self.timesteps.to(original_samples.device							)
          a__     : List[str]  =timesteps.to(original_samples.device							)

        a__     : List[Any]  =[self.index_for_timestep(__lowercase		,				__lowercase							) for t in timesteps]

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

        a__     : Optional[int]  =original_samples + noise * sigma
        return noisy_samples







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



        '''simple docstring'''




        return self.config.num_train_timesteps













UpperCAmelCase     :     Dict							=	[0, 2, 4, 6, 8]
UpperCAmelCase     :     Tuple							=	[1, 3, 5, 7, 9]
def 					_A	(		SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       list[int]	,	SCREAMING_SNAKE_CASE					:       int						):





  """simple docstring"""



  if remaining_length == 0:
    if digits[0] == 0 or digits[-1] == 0:
      return 0

    for i in range(length // 2 - 1	,	-1	,	-1						):
      remainder += digits[i] + digits[length - i - 1]

      if remainder % 2 == 0:
        return 0

      remainder //= 10

    return 1

  if remaining_length == 1:
    if remainder % 2 == 0:
      return 0

    a__     : str  =0
    for digit in range(10						):
      a__     : int  =digit
      result += reversible_numbers(
          0	,	(remainder + 2 * digit) // 10	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
    return result

  a__     : List[str]  =0
  for digita in range(10						):
    a__     : Optional[int]  =digita

    if (remainder + digita) % 2 == 0:
      a__     : Dict  =ODD_DIGITS
    else:
      a__     : Any  =EVEN_DIGITS

    for digita in other_parity_digits:
      a__     : Union[str, Any]  =digita
      result += reversible_numbers(
          remaining_length - 2	,	(remainder + digita + digita) // 10	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	)
  return result
def 					_A	(		SCREAMING_SNAKE_CASE					:       int = 9						):





  """simple docstring"""



  a__     : List[str]  =0
  for length in range(1	,	max_power + 1						):
    result += reversible_numbers(SCREAMING_SNAKE_CASE	,	0	,	[0] * length	,	SCREAMING_SNAKE_CASE						)
  return result


if __name__ == "__main__":
     print(F"""{solution() = }""")






