code: 
  
  
  
  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 ..utils import randn_tensor
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
  
  
  
  
  def     UpperCAmelCase__ (							__snake_case						,				__snake_case=0.9_99						,				__snake_case="cosine"						,				)   -> Union[str, Any]:
    if alpha_transform_type == "cosine":
  
      def alpha_bar_fn(__snake_case							):
        return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2							) ** 2
  
    elif alpha_transform_type == "exp":
  
      def alpha_bar_fn(__snake_case							):
        return math.exp(t * -12.0							)
  
    else:
      raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}'''							)
  
    _A           =    []
    for i in range(__snake_case							):
      _A           =    i / num_diffusion_timesteps
      _A           =    (i + 1) / num_diffusion_timesteps
      betas.append(min(1 - alpha_bar_fn(__snake_case							) / alpha_bar_fn(__snake_case							)						,				__snake_case							)							)
    return torch.tensor(__snake_case						,				dtype=torch.floataa							)
  
  
  
  class 		_snake_case      (			lowerCamelCase					,lowerCamelCase				):
  
  
  
  
  
   """simple docstring"""
  
  
  
   lowerCamelCase_          =			[e.name for e in KarrasDiffusionSchedulers]
   lowerCamelCase_          =			2
   @register_to_config
   def __init__(						self	,    a = 1_0_0_0	,    a = 0.00_085	,    a = 0.012	,    a = "linear"	,    a = None	,    a = "epsilon"	,    a = "linspace"	,    a = 0	,    )	->							Dict:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if trained_betas is not None:
       _A           =    torch.tensor(a	,    dtype=torch.floataa					)
     elif beta_schedule == "linear":
       _A           =    torch.linspace(a	,    a	,    a	,    dtype=torch.floataa					)
     elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       _A           =    (
           torch.linspace(beta_start**0.5	,    beta_end**0.5	,    a	,    dtype=torch.floataa					) ** 2
       )
     elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       _A           =    betas_for_alpha_bar(a					)
     else:
       raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''					)
  
     _A           =    1.0 - self.betas
     _A           =    torch.cumprod(self.alphas	,    dim=0					)
  
     #  set all values
     self.set_timesteps(a	,    a	,    a					)
   def lowercase_		(						self	,    a	,    a=None					)	->							Optional[Any]:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if schedule_timesteps is None:
       _A           =    self.timesteps
  
     _A           =    (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           =    1 if len(a					) > 1 else 0
     else:
       _A           =    timestep.cpu().item() if torch.is_tensor(a					) else timestep
       _A           =    self._index_counter[timestep_int]
  
     return indices[pos].item()
   @property
   def lowercase_		(						self					)	->							List[str]:
  
  
  
  
     """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	,    a	,    a	,    )	->							torch.FloatTensor:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _A           =    self.index_for_timestep(a					)
  
     if self.state_in_first_order:
       _A           =    self.sigmas[step_index]
     else:
       _A           =    self.sigmas_interpol[step_index - 1]
  
     _A           =    sample / ((sigma**2 + 1) ** 0.5)
     return sample
   def lowercase_		(						self	,    a	,    a = None	,    a = None	,    )	->							Tuple:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _A           =    num_inference_steps
  
     _A           =    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           =    np.linspace(0	,    num_train_timesteps - 1	,    a	,    dtype=a					)[::-1].copy()
     elif self.config.timestep_spacing == "leading":
       _A           =    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           =    (np.arange(0	,    a					) * step_ratio).round()[::-1].copy().astype(a					)
       timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
       _A           =    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           =    (np.arange(a	,    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\'.'''					)
  
     _A           =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
     _A           =    torch.from_numpy(np.log(a					)					).to(a					)
  
     _A           =    np.interp(a	,    np.arange(0	,    len(a					)					)	,    a					)
     _A           =    np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
     _A           =    torch.from_numpy(a					).to(device=a					)
  
     # compute up and down sigmas
     _A           =    sigmas.roll(-1					)
     _A           =    0.0
     _A           =    (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
     _A           =    (sigmas_next**2 - sigmas_up**2) ** 0.5
     _A           =    0.0
  
     # compute interpolated sigmas
     _A           =    sigmas.log().lerp(sigmas_down.log()	,    0.5					).exp()
     _A           =    0.0
  
     # set sigmas
     _A           =    torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
     _A           =    torch.cat(
         [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)
     _A           =    torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2					), sigmas_up[-1:]]					)
     _A           =    torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2					), sigmas_down[-1:]]					)
  
     if str(a					).startswith('''mps'''					):
       # mps does not support float64
       _A           =    torch.from_numpy(a					).to(a	,    dtype=torch.floataa					)
     else:
       _A           =    torch.from_numpy(a					).to(a					)
  
     _A           =    self.sigma_to_t(a					).to(a	,    dtype=timesteps.dtype					)
     _A           =    torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])	,    dim=-1					).flatten()
  
     _A           =    torch.cat([timesteps[:1], interleaved_timesteps]					)
  
     _A           =    None
  
     # for exp beta schedules, such as the one for `pipeline_shap_e.py`
     # we need an index counter
     _A           =    defaultdict(a					)
   def lowercase_		(						self	,    a					)	->							Any:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _A           =    sigma.log()
  
     # get distribution
     _A           =    log_sigma - self.log_sigmas[:, None]
  
     # get sigmas range
     _A           =    dists.ge(0					).cumsum(dim=0					).argmax(dim=0					).clamp(max=self.log_sigmas.shape[0] - 2					)
     _A           =    low_idx + 1
  
     _A           =    self.log_sigmas[low_idx]
     _A           =    self.log_sigmas[high_idx]
  
     # interpolate sigmas
     _A           =    (low - log_sigma) / (low - high)
     _A           =    w.clamp(0	,    1					)
  
     # transform interpolation to time range
     _A           =    (1 - w) * low_idx + w * high_idx
     _A           =    t.view(sigma.shape					)
     return t
   @property
   def lowercase_		(						self					)	->							Union[str, Any]:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     return self.sample is None
   def lowercase_		(						self	,    a	,    a	,    a	,    a = None	,    a = True	,    )	->							Union[SchedulerOutput, Tuple]:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _A           =    self.index_for_timestep(a					)
  
     # advance index counter by 1
     _A           =    timestep.cpu().item() if torch.is_tensor(a					) else timestep
     self._index_counter[timestep_int] += 1
  
     if self.state_in_first_order:
       _A           =    self.sigmas[step_index]
       _A           =    self.sigmas_interpol[step_index]
       _A           =    self.sigmas_up[step_index]
       _A           =    self.sigmas_down[step_index - 1]
     else:
       # 2nd order / KPDM2's method
       _A           =    self.sigmas[step_index - 1]
       _A           =    self.sigmas_interpol[step_index - 1]
       _A           =    self.sigmas_up[step_index - 1]
       _A           =    self.sigmas_down[step_index - 1]
  
     # 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           =    0
     _A           =    sigma * (gamma + 1)  # Note: sigma_hat == sigma for now
  
     _A           =    model_output.device
     _A           =    randn_tensor(model_output.shape	,    dtype=model_output.dtype	,    device=a	,    generator=a					)
  
     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     if self.config.prediction_type == "epsilon":
       _A           =    sigma_hat if self.state_in_first_order else sigma_interpol
       _A           =    sample - sigma_input * model_output
     elif self.config.prediction_type == "v_prediction":
       _A           =    sigma_hat if self.state_in_first_order else sigma_interpol
       _A           =    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           =    (sample - pred_original_sample) / sigma_hat
       # 3. delta timestep
       _A           =    sigma_interpol - sigma_hat
  
       # store for 2nd order step
       _A           =    sample
       _A           =    dt
       _A           =    sample + derivative * dt
     else:
       # DPM-Solver-2
       # 2. Convert to an ODE derivative for 2nd order
       _A           =    (sample - pred_original_sample) / sigma_interpol
       # 3. delta timestep
       _A           =    sigma_down - sigma_hat
  
       _A           =    self.sample
       _A           =    None
  
       _A           =    sample + derivative * dt
       _A           =    prev_sample + noise * sigma_up
  
     if not return_dict:
       return (prev_sample,)
  
     return SchedulerOutput(prev_sample=a					)
   def lowercase_		(						self	,    a	,    a	,    a	,    )	->							torch.FloatTensor:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _A           =    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
       _A           =    self.timesteps.to(original_samples.device	,    dtype=torch.floataa					)
       _A           =    timesteps.to(original_samples.device	,    dtype=torch.floataa					)
     else:
       _A           =    self.timesteps.to(original_samples.device					)
       _A           =    timesteps.to(original_samples.device					)
  
     _A           =    [self.index_for_timestep(a	,    a					) for t in timesteps]
  
     _A           =    sigmas[step_indices].flatten()
     while len(sigma.shape					) < len(original_samples.shape					):
       _A           =    sigma.unsqueeze(-1					)
  
     _A           =    original_samples + noise * sigma
     return noisy_samples
  
  
  
   def __len__(						self					)	->							Optional[int]:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     return self.config.num_train_timesteps
style_context: 
  
  
  
  def     UpperCAmelCase__ (							__snake_case						,				__snake_case = 1_000							)   -> str:
    if (not isinstance(__snake_case						,				__snake_case							)) or (digit_position <= 0):
      raise ValueError('''Digit position must be a positive integer'''							)
    elif (not isinstance(__snake_case						,				__snake_case							)) or (precision < 0):
      raise ValueError('''Precision must be a nonnegative integer'''							)
  
    # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
    # accurate
    _A           =    (
        4 * _subsum(__snake_case						,				1						,				__snake_case							)
        - 2 * _subsum(__snake_case						,				4						,				__snake_case							)
        - _subsum(__snake_case						,				5						,				__snake_case							)
        - _subsum(__snake_case						,				6						,				__snake_case							)
    )
  
    # return the first hex digit of the fractional part of the result
    return hex(int((sum_result % 1) * 16							)							)[2:]
  
  
  
  
  def     UpperCAmelCase__ (							__snake_case						,				__snake_case						,				__snake_case							)   -> float:
    _A           =    0.0
    for sum_index in range(digit_pos_to_extract + precision							):
      _A           =    8 * sum_index + denominator_addend
      if sum_index < digit_pos_to_extract:
        # if the exponential term is an integer and we mod it by the denominator
        # before dividing, only the integer part of the sum will change;
        # the fractional part will not
        _A           =    pow(
            16						,				digit_pos_to_extract - 1 - sum_index						,				__snake_case							)
      else:
        _A           =    pow(16						,				digit_pos_to_extract - 1 - sum_index							)
      total += exponential_term / denominator
    return total
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()