code: 
  
  
  
  
  """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 :		str      							=    logging.get_logger(__name__)  # pylint: disable=invalid-name
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
  class 							lowerCamelCase		( _UpperCAmelCase				):
     lowercase       :  torch.FloatTensor
     lowercase       :  Optional[torch.FloatTensor]      =				None
  
  
  
  
  
  
  
  def 					A_			(		snake_case_     :       Tuple						,snake_case_     :       List[str]=0.999						,snake_case_     :       str="cosine"						,):
  
  
  
  
  
  
  
      '''simple docstring'''
      if alpha_transform_type == "cosine":
  
          def alpha_bar_fn(snake_case_     :       int    ):
              return math.cos((t + 0.008) / 1.008 * math.pi / 2    ) ** 2
  
      elif alpha_transform_type == "exp":
  
          def alpha_bar_fn(snake_case_     :       int    ):
              return math.exp(t * -12.0    )
  
      else:
          raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'    )
  
      UpperCamelCase				:   Optional[int]          =							[]
      for i in range(snake_case_    ):
          UpperCamelCase				:   List[str]          =							i / num_diffusion_timesteps
          UpperCamelCase				:   Optional[Any]          =							(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 							lowerCamelCase		( _UpperCAmelCase	,  _UpperCAmelCase				):
     lowercase       :  Union[str, Any]      =				[e.name for e in KarrasDiffusionSchedulers]
     lowercase       :  Optional[Any]      =				1
  
  
  
  
  
  
  
     @register_to_config
     def __init__(							self    ,      SCREAMING_SNAKE_CASE_ = 1000    ,      SCREAMING_SNAKE_CASE_ = 0.0001    ,      SCREAMING_SNAKE_CASE_ = 0.02    ,      SCREAMING_SNAKE_CASE_ = "linear"    ,      SCREAMING_SNAKE_CASE_ = None    ,      SCREAMING_SNAKE_CASE_ = "epsilon"    ,      SCREAMING_SNAKE_CASE_ = "linear"    ,      SCREAMING_SNAKE_CASE_ = False    ,      SCREAMING_SNAKE_CASE_ = "linspace"    ,      SCREAMING_SNAKE_CASE_ = 0    ,      ):
         if trained_betas is not None:
             UpperCamelCase				:   Tuple          =							torch.tensor(SCREAMING_SNAKE_CASE_    ,      dtype=torch.floataa )
         elif beta_schedule == "linear":
             UpperCamelCase				:   Optional[Any]          =							torch.linspace(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      dtype=torch.floataa )
         elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             UpperCamelCase				:   Optional[Any]          =							(
                 torch.linspace(beta_start**0.5    ,      beta_end**0.5    ,      SCREAMING_SNAKE_CASE_    ,      dtype=torch.floataa ) ** 2
             )
         elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             UpperCamelCase				:   Tuple          =							betas_for_alpha_bar(SCREAMING_SNAKE_CASE_ )
         else:
             raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}' )
  
         UpperCamelCase				:   Dict          =							1.0 - self.betas
         UpperCamelCase				:   Dict          =							torch.cumprod(self.alphas    ,      dim=0 )
  
         UpperCamelCase				:   int          =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
         UpperCamelCase				:   List[str]          =							np.concatenate([sigmas[::-1], [0.0]] ).astype(np.floataa )
         UpperCamelCase				:   str          =							torch.from_numpy(SCREAMING_SNAKE_CASE_ )
  
         # setable values
         UpperCamelCase				:   Tuple          =							None
         UpperCamelCase				:   Any          =							np.linspace(0    ,      num_train_timesteps - 1    ,      SCREAMING_SNAKE_CASE_    ,      dtype=SCREAMING_SNAKE_CASE_ )[::-1].copy()
         UpperCamelCase				:   Tuple          =							torch.from_numpy(SCREAMING_SNAKE_CASE_ )
         UpperCamelCase				:   Dict          =							False
         UpperCamelCase				:   Union[str, Any]          =							use_karras_sigmas
  
  
  
  
  
  
  
     @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    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
         if isinstance(SCREAMING_SNAKE_CASE_    ,      torch.Tensor ):
             UpperCamelCase				:   Dict          =							timestep.to(self.timesteps.device )
         UpperCamelCase				:   int          =							(self.timesteps == timestep).nonzero().item()
         UpperCamelCase				:   List[Any]          =							self.sigmas[step_index]
  
         UpperCamelCase				:   Optional[Any]          =							sample / ((sigma**2 + 1) ** 0.5)
  
         UpperCamelCase				:   List[str]          =							True
         return sample
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ = None ):
         UpperCamelCase				:   List[Any]          =							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				:   Optional[int]          =							np.linspace(0    ,      self.config.num_train_timesteps - 1    ,      SCREAMING_SNAKE_CASE_    ,      dtype=SCREAMING_SNAKE_CASE_ )[
                 ::-1
             ].copy()
         elif self.config.timestep_spacing == "leading":
             UpperCamelCase				:   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
             UpperCamelCase				:   List[str]          =							(np.arange(0    ,      SCREAMING_SNAKE_CASE_ ) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE_ )
             timesteps += self.config.steps_offset
         elif self.config.timestep_spacing == "trailing":
             UpperCamelCase				:   Optional[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
             UpperCamelCase				:   Optional[int]          =							(np.arange(self.config.num_train_timesteps    ,      0    ,      -step_ratio )).round().copy().astype(SCREAMING_SNAKE_CASE_ )
             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				:   Dict          =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
         UpperCamelCase				:   Optional[int]          =							np.log(SCREAMING_SNAKE_CASE_ )
  
         if self.config.interpolation_type == "linear":
             UpperCamelCase				:   int          =							np.interp(SCREAMING_SNAKE_CASE_    ,      np.arange(0    ,      len(SCREAMING_SNAKE_CASE_ ) )    ,      SCREAMING_SNAKE_CASE_ )
         elif self.config.interpolation_type == "log_linear":
             UpperCamelCase				:   Optional[Any]          =							torch.linspace(np.log(sigmas[-1] )    ,      np.log(sigmas[0] )    ,      num_inference_steps + 1 ).exp()
         else:
             raise ValueError(
                 f'{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'
                 """ 'linear' or 'log_linear'""" )
  
         if self.use_karras_sigmas:
             UpperCamelCase				:   str          =							self._convert_to_karras(in_sigmas=SCREAMING_SNAKE_CASE_    ,      num_inference_steps=self.num_inference_steps )
             UpperCamelCase				:   Tuple          =							np.array([self._sigma_to_t(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ) for sigma in sigmas] )
  
         UpperCamelCase				:   Any          =							np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
         UpperCamelCase				:   Optional[int]          =							torch.from_numpy(SCREAMING_SNAKE_CASE_ ).to(device=SCREAMING_SNAKE_CASE_ )
         if str(SCREAMING_SNAKE_CASE_ ).startswith("""mps""" ):
             # mps does not support float64
             UpperCamelCase				:   List[str]          =							torch.from_numpy(SCREAMING_SNAKE_CASE_ ).to(SCREAMING_SNAKE_CASE_    ,      dtype=torch.floataa )
         else:
             UpperCamelCase				:   int          =							torch.from_numpy(SCREAMING_SNAKE_CASE_ ).to(device=SCREAMING_SNAKE_CASE_ )
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
         # get log sigma
         UpperCamelCase				:   int          =							np.log(SCREAMING_SNAKE_CASE_ )
  
         # get distribution
         UpperCamelCase				:   int          =							log_sigma - log_sigmas[:, np.newaxis]
  
         # get sigmas range
         UpperCamelCase				:   List[str]          =							np.cumsum((dists >= 0)    ,      axis=0 ).argmax(axis=0 ).clip(max=log_sigmas.shape[0] - 2 )
         UpperCamelCase				:   int          =							low_idx + 1
  
         UpperCamelCase				:   List[str]          =							log_sigmas[low_idx]
         UpperCamelCase				:   str          =							log_sigmas[high_idx]
  
         # interpolate sigmas
         UpperCamelCase				:   Optional[Any]          =							(low - log_sigma) / (low - high)
         UpperCamelCase				:   Dict          =							np.clip(SCREAMING_SNAKE_CASE_    ,      0    ,      1 )
  
         # transform interpolation to time range
         UpperCamelCase				:   Any          =							(1 - w) * low_idx + w * high_idx
         UpperCamelCase				:   Any          =							t.reshape(sigma.shape )
         return t
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
         UpperCamelCase				:   float          =							in_sigmas[-1].item()
         UpperCamelCase				:   float          =							in_sigmas[0].item()
  
         UpperCamelCase				:   Tuple          =							7.0  # 7.0 is the value used in the paper
         UpperCamelCase				:   List[str]          =							np.linspace(0    ,      1    ,      SCREAMING_SNAKE_CASE_ )
         UpperCamelCase				:   int          =							sigma_min ** (1 / rho)
         UpperCamelCase				:   List[str]          =							sigma_max ** (1 / rho)
         UpperCamelCase				:   Union[str, Any]          =							(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
         return sigmas
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ = 0.0    ,      SCREAMING_SNAKE_CASE_ = 0.0    ,      SCREAMING_SNAKE_CASE_ = float("""inf""" )    ,      SCREAMING_SNAKE_CASE_ = 1.0    ,      SCREAMING_SNAKE_CASE_ = None    ,      SCREAMING_SNAKE_CASE_ = True    ,      ):
  
         if (
             isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ )
             or isinstance(SCREAMING_SNAKE_CASE_    ,      torch.IntTensor )
             or isinstance(SCREAMING_SNAKE_CASE_    ,      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(SCREAMING_SNAKE_CASE_    ,      torch.Tensor ):
             UpperCamelCase				:   Any          =							timestep.to(self.timesteps.device )
  
         UpperCamelCase				:   str          =							(self.timesteps == timestep).nonzero().item()
         UpperCamelCase				:   Any          =							self.sigmas[step_index]
  
         UpperCamelCase				:   Union[str, Any]          =							min(s_churn / (len(self.sigmas ) - 1)    ,      2**0.5 - 1 ) if s_tmin <= sigma <= s_tmax else 0.0
  
         UpperCamelCase				:   List[str]          =							randn_tensor(
             model_output.shape    ,      dtype=model_output.dtype    ,      device=model_output.device    ,      generator=SCREAMING_SNAKE_CASE_ )
  
         UpperCamelCase				:   Optional[Any]          =							noise * s_noise
         UpperCamelCase				:   str          =							sigma * (gamma + 1)
  
         if gamma > 0:
             UpperCamelCase				:   List[str]          =							sample + eps * (sigma_hat**2 - sigma**2) ** 0.5
  
         # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
         # NOTE: "original_sample" should not be an expected prediction_type but is left in for
         # backwards compatibility
         if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
             UpperCamelCase				:   Tuple          =							model_output
         elif self.config.prediction_type == "epsilon":
             UpperCamelCase				:   int          =							sample - sigma_hat * model_output
         elif self.config.prediction_type == "v_prediction":
             # * c_out + input * c_skip
             UpperCamelCase				:   Optional[int]          =							model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
         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
         UpperCamelCase				:   Any          =							(sample - pred_original_sample) / sigma_hat
  
         UpperCamelCase				:   int          =							self.sigmas[step_index + 1] - sigma_hat
  
         UpperCamelCase				:   Any          =							sample + derivative * dt
  
         if not return_dict:
             return (prev_sample,)
  
         return EulerDiscreteSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_    ,      pred_original_sample=SCREAMING_SNAKE_CASE_ )
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      ):
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         UpperCamelCase				:   Optional[Any]          =							self.sigmas.to(device=original_samples.device    ,      dtype=original_samples.dtype )
         if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE_ ):
             # mps does not support float64
             UpperCamelCase				:   List[Any]          =							self.timesteps.to(original_samples.device    ,      dtype=torch.floataa )
             UpperCamelCase				:   Dict          =							timesteps.to(original_samples.device    ,      dtype=torch.floataa )
         else:
             UpperCamelCase				:   Optional[int]          =							self.timesteps.to(original_samples.device )
             UpperCamelCase				:   int          =							timesteps.to(original_samples.device )
  
         UpperCamelCase				:   Tuple          =							[(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
         UpperCamelCase				:   Union[str, Any]          =							sigmas[step_indices].flatten()
         while len(sigma.shape ) < len(original_samples.shape ):
             UpperCamelCase				:   int          =							sigma.unsqueeze(-1 )
  
         UpperCamelCase				:   Tuple          =							original_samples + noise * sigma
         return noisy_samples
  
  
  
  
  
  
  
     def __len__(							self ):
         return self.config.num_train_timesteps
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  
  
  
  class 							lowerCamelCase		:
  
  
  
  
  
  
  
     def __init__(							self    ,      SCREAMING_SNAKE_CASE_=None ):
         UpperCamelCase				:   Optional[Any]          =							data
         UpperCamelCase				:   str          =							None
  
  
  
  
  
  
  
     def __repr__(							self ):
         UpperCamelCase				:   str          =							""""""
         UpperCamelCase				:   Any          =							self
         while temp:
             string_rep += f'<{temp.data}> ---> '
             UpperCamelCase				:   Optional[int]          =							temp.next
         string_rep += "<END>"
         return string_rep
  
  
  
  
  
  
  
  def 					A_			(		snake_case_     :       Tuple    ):
  
  
  
  
  
  
  
      '''simple docstring'''
  
      # if elements_list is empty
      if not elements_list:
          raise Exception("""The Elements List is empty"""    )
  
      # Set first element as Head
      UpperCamelCase				:   List[Any]          =							Node(elements_list[0]    )
      UpperCamelCase				:   str          =							head
      # Loop through elements from position 1
      for data in elements_list[1:]:
          UpperCamelCase				:   Optional[int]          =							Node(snake_case_    )
          UpperCamelCase				:   Optional[Any]          =							current.next
      return head
  
  
  __A :		List[Any]      							=    [1, 3, 5, 32, 44, 12, 43]
  print(F'''List: {list_data}''')
  print('''Creating Linked List from List.''')
  __A :		int      							=    make_linked_list(list_data)
  print('''Linked List:''')
  
  
  print(linked_list)
  
  
  
  
  