code: 
  
  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    __A				(							lowerCAmelCase ):
      lowerCAmelCase_							:		torch.FloatTensor
      lowerCAmelCase_							:		Optional[torch.FloatTensor]						=							None
  
  
  
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase,      _UpperCAmelCase=0.9_9_9,      _UpperCAmelCase="cosine",      )					-> str:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      if alpha_transform_type == "cosine":
  
          def alpha_bar_fn(_UpperCAmelCase				):
              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(_UpperCAmelCase				):
              return math.exp(t * -1_2.0				)
  
      else:
          raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}"				)
  
      lowerCAmelCase				:			Any    			=      []
      for i in range(_UpperCAmelCase				):
          lowerCAmelCase				:			Optional[Any]    			=      i / num_diffusion_timesteps
          lowerCAmelCase				:			str    			=      (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(_UpperCAmelCase				) / alpha_bar_fn(_UpperCAmelCase				),      _UpperCAmelCase				)				)
      return torch.tensor(_UpperCAmelCase,      dtype=torch.floataa				)
  
  
  
  
  
  
  class    __A				(							lowerCAmelCase						,						lowerCAmelCase ):
      lowerCAmelCase_							:		str						=							[e.name for e in KarrasDiffusionSchedulers]
      lowerCAmelCase_							:		Optional[int]						=							1
  
  
  
  
  
  
      @register_to_config
      def __init__(	self			:    List[str]    ,				UpperCAmelCase_			:    int = 1000    ,				UpperCAmelCase_			:    float = 0.00_01    ,				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    ,				):
          if trained_betas is not None:
              lowerCAmelCase				:			List[Any]    			=      torch.tensor(UpperCAmelCase_    ,				dtype=torch.floataa    )
          elif beta_schedule == "linear":
              lowerCAmelCase				:			List[Any]    			=      torch.linspace(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				dtype=torch.floataa    )
          elif beta_schedule == "scaled_linear":
              # this schedule is very specific to the latent diffusion model.
              lowerCAmelCase				:			List[str]    			=      (
                  torch.linspace(beta_start**0.5    ,				beta_end**0.5    ,				UpperCAmelCase_    ,				dtype=torch.floataa    ) ** 2
              )
          elif beta_schedule == "squaredcos_cap_v2":
              # Glide cosine schedule
              lowerCAmelCase				:			Dict    			=      betas_for_alpha_bar(UpperCAmelCase_    )
          else:
              raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"    )
  
          lowerCAmelCase				:			Union[str, Any]    			=      1.0 - self.betas
          lowerCAmelCase				:			Tuple    			=      torch.cumprod(self.alphas    ,				dim=0    )
  
          lowerCAmelCase				:			Optional[int]    			=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
          lowerCAmelCase				:			str    			=      np.concatenate([sigmas[::-1], [0.0]]    ).astype(np.floataa    )
          lowerCAmelCase				:			Optional[Any]    			=      torch.from_numpy(UpperCAmelCase_    )
  
          # setable values
          lowerCAmelCase				:			Tuple    			=      None
          lowerCAmelCase				:			Dict    			=      use_karras_sigmas
          self.set_timesteps(UpperCAmelCase_    ,				UpperCAmelCase_    )
          lowerCAmelCase				:			List[Any]    			=      []
          lowerCAmelCase				:			Optional[int]    			=      False
  
  
  
  
  
  
      @property
      def 	lowercase__ (	self			:    Dict    ):
          # 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 	lowercase__ (	self			:    Any    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				UpperCAmelCase_			:    Union[float, torch.FloatTensor]    ):
          if isinstance(UpperCAmelCase_    ,				torch.Tensor    ):
              lowerCAmelCase				:			Dict    			=      timestep.to(self.timesteps.device    )
          lowerCAmelCase				:			Union[str, Any]    			=      (self.timesteps == timestep).nonzero().item()
          lowerCAmelCase				:			Dict    			=      self.sigmas[step_index]
          lowerCAmelCase				:			List[str]    			=      sample / ((sigma**2 + 1) ** 0.5)
          lowerCAmelCase				:			Optional[Any]    			=      True
          return sample
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Any    ,				UpperCAmelCase_			:    Any    ,				UpperCAmelCase_			:    Tuple    ,				UpperCAmelCase_			:    Optional[Any]    ):
  
          def lms_derivative(UpperCAmelCase_			:    int    ):
              lowerCAmelCase				:			str    			=      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
  
          lowerCAmelCase				:			List[str]    			=      integrate.quad(UpperCAmelCase_    ,				self.sigmas[t]    ,				self.sigmas[t + 1]    ,				epsrel=1E-4    )[0]
  
          return integrated_coeff
  
  
  
  
  
  
      def 	lowercase__ (	self			:    int    ,				UpperCAmelCase_			:    int    ,				UpperCAmelCase_			:    Union[str, torch.device] = None    ):
          lowerCAmelCase				:			Optional[int]    			=      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":
              lowerCAmelCase				:			Tuple    			=      np.linspace(0    ,				self.config.num_train_timesteps - 1    ,				UpperCAmelCase_    ,				dtype=UpperCAmelCase_    )[
                  ::-1
              ].copy()
          elif self.config.timestep_spacing == "leading":
              lowerCAmelCase				:			Any    			=      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
              lowerCAmelCase				:			Tuple    			=      (np.arange(0    ,				UpperCAmelCase_    ) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase_    )
              timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
              lowerCAmelCase				:			List[str]    			=      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
              lowerCAmelCase				:			Any    			=      (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'."    )
  
          lowerCAmelCase				:			List[Any]    			=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
          lowerCAmelCase				:			Any    			=      np.log(UpperCAmelCase_    )
          lowerCAmelCase				:			Dict    			=      np.interp(UpperCAmelCase_    ,				np.arange(0    ,				len(UpperCAmelCase_    )    )    ,				UpperCAmelCase_    )
  
          if self.use_karras_sigmas:
              lowerCAmelCase				:			List[Any]    			=      self._convert_to_karras(in_sigmas=UpperCAmelCase_    )
              lowerCAmelCase				:			List[Any]    			=      np.array([self._sigma_to_t(UpperCAmelCase_    ,				UpperCAmelCase_    ) for sigma in sigmas]    )
  
          lowerCAmelCase				:			Optional[int]    			=      np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
  
          lowerCAmelCase				:			str    			=      torch.from_numpy(UpperCAmelCase_    ).to(device=UpperCAmelCase_    )
          if str(UpperCAmelCase_    ).startswith('mps'    ):
              # mps does not support float64
              lowerCAmelCase				:			Tuple    			=      torch.from_numpy(UpperCAmelCase_    ).to(UpperCAmelCase_    ,				dtype=torch.floataa    )
          else:
              lowerCAmelCase				:			Optional[int]    			=      torch.from_numpy(UpperCAmelCase_    ).to(device=UpperCAmelCase_    )
  
          lowerCAmelCase				:			Any    			=      []
  
  
  
  
  
  
      def 	lowercase__ (	self			:    str    ,				UpperCAmelCase_			:    Optional[Any]    ,				UpperCAmelCase_			:    List[str]    ):
          # get log sigma
          lowerCAmelCase				:			Dict    			=      np.log(UpperCAmelCase_    )
  
          # get distribution
          lowerCAmelCase				:			Union[str, Any]    			=      log_sigma - log_sigmas[:, np.newaxis]
  
          # get sigmas range
          lowerCAmelCase				:			List[str]    			=      np.cumsum((dists >= 0)    ,				axis=0    ).argmax(axis=0    ).clip(max=log_sigmas.shape[0] - 2    )
          lowerCAmelCase				:			Optional[int]    			=      low_idx + 1
  
          lowerCAmelCase				:			Dict    			=      log_sigmas[low_idx]
          lowerCAmelCase				:			Union[str, Any]    			=      log_sigmas[high_idx]
  
          # interpolate sigmas
          lowerCAmelCase				:			Tuple    			=      (low - log_sigma) / (low - high)
          lowerCAmelCase				:			str    			=      np.clip(UpperCAmelCase_    ,				0    ,				1    )
  
          # transform interpolation to time range
          lowerCAmelCase				:			Optional[Any]    			=      (1 - w) * low_idx + w * high_idx
          lowerCAmelCase				:			List[str]    			=      t.reshape(sigma.shape    )
          return t
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Any    ,				UpperCAmelCase_			:    torch.FloatTensor    ):
          lowerCAmelCase				:			float    			=      in_sigmas[-1].item()
          lowerCAmelCase				:			float    			=      in_sigmas[0].item()
  
          lowerCAmelCase				:			int    			=      7.0  # 7.0 is the value used in the paper
          lowerCAmelCase				:			List[Any]    			=      np.linspace(0    ,				1    ,				self.num_inference_steps    )
          lowerCAmelCase				:			int    			=      sigma_min ** (1 / rho)
          lowerCAmelCase				:			List[str]    			=      sigma_max ** (1 / rho)
          lowerCAmelCase				:			Optional[int]    			=      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Optional[int]    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				UpperCAmelCase_			:    Union[float, torch.FloatTensor]    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				UpperCAmelCase_			:    int = 4    ,				UpperCAmelCase_			:    bool = True    ,				):
          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    ):
              lowerCAmelCase				:			Tuple    			=      timestep.to(self.timesteps.device    )
          lowerCAmelCase				:			List[str]    			=      (self.timesteps == timestep).nonzero().item()
          lowerCAmelCase				:			str    			=      self.sigmas[step_index]
  
          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
              lowerCAmelCase				:			str    			=      sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              lowerCAmelCase				:			Any    			=      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          elif self.config.prediction_type == "sample":
              lowerCAmelCase				:			int    			=      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
          lowerCAmelCase				:			Optional[Any]    			=      (sample - pred_original_sample) / sigma
          self.derivatives.append(UpperCAmelCase_    )
          if len(self.derivatives    ) > order:
              self.derivatives.pop(0    )
  
          # 3. Compute linear multistep coefficients
          lowerCAmelCase				:			str    			=      min(step_index + 1    ,				UpperCAmelCase_    )
          lowerCAmelCase				:			List[str]    			=      [self.get_lms_coefficient(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ) for curr_order in range(UpperCAmelCase_    )]
  
          # 4. Compute previous sample based on the derivatives path
          lowerCAmelCase				:			List[str]    			=      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			:    Optional[int]    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				UpperCAmelCase_			:    torch.FloatTensor    ,				):
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          lowerCAmelCase				:			Optional[int]    			=      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
              lowerCAmelCase				:			List[Any]    			=      self.timesteps.to(original_samples.device    ,				dtype=torch.floataa    )
              lowerCAmelCase				:			Union[str, Any]    			=      timesteps.to(original_samples.device    ,				dtype=torch.floataa    )
          else:
              lowerCAmelCase				:			List[Any]    			=      self.timesteps.to(original_samples.device    )
              lowerCAmelCase				:			str    			=      timesteps.to(original_samples.device    )
  
          lowerCAmelCase				:			Dict    			=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
          lowerCAmelCase				:			Optional[int]    			=      sigmas[step_indices].flatten()
          while len(sigma.shape    ) < len(original_samples.shape    ):
              lowerCAmelCase				:			Tuple    			=      sigma.unsqueeze(-1    )
  
          lowerCAmelCase				:			Any    			=      original_samples + noise * sigma
          return noisy_samples
  
  
  
  
  
  
      def __len__(	self			:    Dict    ):
          return self.config.num_train_timesteps
  
  
  
  
  
  
style_context: 
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available
  
  
  __A   :     Optional[int]      =			{
      '''configuration_splinter''': ['''SPLINTER_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''SplinterConfig'''],
      '''tokenization_splinter''': ['''SplinterTokenizer'''],
  }
  
  try:
   if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   __A   :     Optional[int]      =			['''SplinterTokenizerFast''']
  
  try:
   if not is_torch_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   __A   :     Union[str, Any]      =			[
       '''SPLINTER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''SplinterForQuestionAnswering''',
       '''SplinterForPreTraining''',
       '''SplinterLayer''',
       '''SplinterModel''',
       '''SplinterPreTrainedModel''',
   ]
  
  
  if TYPE_CHECKING:
   from .configuration_splinter import SPLINTER_PRETRAINED_CONFIG_ARCHIVE_MAP, SplinterConfig
   from .tokenization_splinter import SplinterTokenizer
  
   try:
    if not is_tokenizers_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .tokenization_splinter_fast import SplinterTokenizerFast
  
   try:
    if not is_torch_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_splinter import (
        SPLINTER_PRETRAINED_MODEL_ARCHIVE_LIST,
        SplinterForPreTraining,
        SplinterForQuestionAnswering,
        SplinterLayer,
        SplinterModel,
        SplinterPreTrainedModel,
    )
  
  
  else:
   import sys
  
   __A   :     Optional[Any]      =			_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
  
  
  
  
  
  