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       (UpperCamelCase__  :						Optional[Any]       ,							UpperCamelCase__  :						int=0.9_99       ,							UpperCamelCase__  :						Union[str, Any]="cosine"       ,							):
         if alpha_transform_type == "cosine":
  
                def alpha_bar_fn(UpperCamelCase__  :						Union[str, Any]		):
                       return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2		) ** 2
  
         elif alpha_transform_type == "exp":
  
                def alpha_bar_fn(UpperCamelCase__  :						Optional[int]		):
                       return math.exp(t * -12.0		)
  
         else:
                raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}"		)
  
         _A   : Union[str, Any]       					=				[]
         for i in range(UpperCamelCase__		):
                _A   : str       					=				i / num_diffusion_timesteps
                _A   : Optional[Any]       					=				(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   lowerCAmelCase__ (       a  ,					a):
  
  
  
  
       '''simple docstring'''
       __SCREAMING_SNAKE_CASE						    =				[e.name for e in KarrasDiffusionSchedulers]
       __SCREAMING_SNAKE_CASE						    =				2
  
  
       @register_to_config
       def __init__(		self				,		__lowerCamelCase = 1_0_0_0				,		__lowerCamelCase = 0.0_0_0_8_5				,		__lowerCamelCase = 0.0_1_2				,		__lowerCamelCase = "linear"				,		__lowerCamelCase = None				,		__lowerCamelCase = "epsilon"				,		__lowerCamelCase = "linspace"				,		__lowerCamelCase = 0				,		)    ->       int:
              if trained_betas is not None:
                     _A   : str       					=				torch.tensor(__lowerCamelCase				,		dtype=torch.floataa)
              elif beta_schedule == "linear":
                     _A   : Optional[Any]       					=				torch.linspace(__lowerCamelCase				,		__lowerCamelCase				,		__lowerCamelCase				,		dtype=torch.floataa)
              elif beta_schedule == "scaled_linear":
                     # this schedule is very specific to the latent diffusion model.
                     _A   : str       					=				(
                         torch.linspace(beta_start**0.5				,		beta_end**0.5				,		__lowerCamelCase				,		dtype=torch.floataa) ** 2
                     )
              elif beta_schedule == "squaredcos_cap_v2":
                     # Glide cosine schedule
                     _A   : int       					=				betas_for_alpha_bar(__lowerCamelCase)
              else:
                     raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}")
  
              _A   : str       					=				1.0 - self.betas
              _A   : Union[str, Any]       					=				torch.cumprod(self.alphas				,		dim=0)
  
              #  set all values
              self.set_timesteps(__lowerCamelCase				,		__lowerCamelCase				,		__lowerCamelCase)
  
  
       def 				_lowerCamelCase				(		self				,		__lowerCamelCase				,		__lowerCamelCase=None)    ->       Union[str, Any]:
              if schedule_timesteps is None:
                     _A   : str       					=				self.timesteps
  
              _A   : Tuple       					=				(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   : Any       					=				1 if len(__lowerCamelCase) > 1 else 0
              else:
                     _A   : int       					=				timestep.cpu().item() if torch.is_tensor(__lowerCamelCase) else timestep
                     _A   : int       					=				self._index_counter[timestep_int]
  
              return indices[pos].item()
  
  
       @property
       def 				_lowerCamelCase				(		self)    ->       int:
              # 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 				_lowerCamelCase				(		self				,		__lowerCamelCase				,		__lowerCamelCase				,		)    ->       torch.FloatTensor:
              _A   : List[str]       					=				self.index_for_timestep(__lowerCamelCase)
  
              if self.state_in_first_order:
                     _A   : Union[str, Any]       					=				self.sigmas[step_index]
              else:
                     _A   : Union[str, Any]       					=				self.sigmas_interpol[step_index - 1]
  
              _A   : Dict       					=				sample / ((sigma**2 + 1) ** 0.5)
              return sample
  
  
       def 				_lowerCamelCase				(		self				,		__lowerCamelCase				,		__lowerCamelCase = None				,		__lowerCamelCase = None				,		)    ->       List[str]:
              _A   : Dict       					=				num_inference_steps
  
              _A   : List[str]       					=				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   : Any       					=				np.linspace(0				,		num_train_timesteps - 1				,		__lowerCamelCase				,		dtype=__lowerCamelCase)[::-1].copy()
              elif self.config.timestep_spacing == "leading":
                     _A   : List[str]       					=				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   : Optional[int]       					=				(np.arange(0				,		__lowerCamelCase) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase)
                     timesteps += self.config.steps_offset
              elif self.config.timestep_spacing == "trailing":
                     _A   : 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   : Optional[int]       					=				(np.arange(__lowerCamelCase				,		0				,		-step_ratio)).round().copy().astype(__lowerCamelCase)
                     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[Any]       					=				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
              _A   : Union[str, Any]       					=				torch.from_numpy(np.log(__lowerCamelCase)).to(__lowerCamelCase)
  
              _A   : List[Any]       					=				np.interp(__lowerCamelCase				,		np.arange(0				,		len(__lowerCamelCase))				,		__lowerCamelCase)
              _A   : Union[str, Any]       					=				np.concatenate([sigmas, [0.0]]).astype(np.floataa)
              _A   : List[Any]       					=				torch.from_numpy(__lowerCamelCase).to(device=__lowerCamelCase)
  
              # compute up and down sigmas
              _A   : Union[str, Any]       					=				sigmas.roll(-1)
              _A   : List[str]       					=				0.0
              _A   : List[str]       					=				(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
              _A   : Optional[int]       					=				(sigmas_next**2 - sigmas_up**2) ** 0.5
              _A   : Tuple       					=				0.0
  
              # compute interpolated sigmas
              _A   : str       					=				sigmas.log().lerp(sigmas_down.log()				,		0.5).exp()
              _A   : List[Any]       					=				0.0
  
              # set sigmas
              _A   : str       					=				torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2), sigmas[-1:]])
              _A   : List[Any]       					=				torch.cat(
                  [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2), sigmas_interpol[-1:]])
              _A   : Tuple       					=				torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2), sigmas_up[-1:]])
              _A   : Any       					=				torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2), sigmas_down[-1:]])
  
              if str(__lowerCamelCase).startswith("mps"):
                     # mps does not support float64
                     _A   : Optional[Any]       					=				torch.from_numpy(__lowerCamelCase).to(__lowerCamelCase				,		dtype=torch.floataa)
              else:
                     _A   : Dict       					=				torch.from_numpy(__lowerCamelCase).to(__lowerCamelCase)
  
              _A   : Union[str, Any]       					=				self.sigma_to_t(__lowerCamelCase).to(__lowerCamelCase				,		dtype=timesteps.dtype)
              _A   : Optional[int]       					=				torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])				,		dim=-1).flatten()
  
              _A   : Optional[Any]       					=				torch.cat([timesteps[:1], interleaved_timesteps])
  
              _A   : Optional[Any]       					=				None
  
              # for exp beta schedules, such as the one for `pipeline_shap_e.py`
              # we need an index counter
              _A   : Optional[Any]       					=				defaultdict(__lowerCamelCase)
  
  
       def 				_lowerCamelCase				(		self				,		__lowerCamelCase)    ->       Tuple:
              # get log sigma
              _A   : Optional[int]       					=				sigma.log()
  
              # get distribution
              _A   : Optional[Any]       					=				log_sigma - self.log_sigmas[:, None]
  
              # get sigmas range
              _A   : Optional[Any]       					=				dists.ge(0).cumsum(dim=0).argmax(dim=0).clamp(max=self.log_sigmas.shape[0] - 2)
              _A   : List[str]       					=				low_idx + 1
  
              _A   : int       					=				self.log_sigmas[low_idx]
              _A   : Any       					=				self.log_sigmas[high_idx]
  
              # interpolate sigmas
              _A   : Optional[int]       					=				(low - log_sigma) / (low - high)
              _A   : int       					=				w.clamp(0				,		1)
  
              # transform interpolation to time range
              _A   : List[Any]       					=				(1 - w) * low_idx + w * high_idx
              _A   : Optional[int]       					=				t.view(sigma.shape)
              return t
  
  
       @property
       def 				_lowerCamelCase				(		self)    ->       str:
              return self.sample is None
  
  
       def 				_lowerCamelCase				(		self				,		__lowerCamelCase				,		__lowerCamelCase				,		__lowerCamelCase				,		__lowerCamelCase = None				,		__lowerCamelCase = True				,		)    ->       Union[SchedulerOutput, Tuple]:
              _A   : List[str]       					=				self.index_for_timestep(__lowerCamelCase)
  
              # advance index counter by 1
              _A   : Optional[int]       					=				timestep.cpu().item() if torch.is_tensor(__lowerCamelCase) else timestep
              self._index_counter[timestep_int] += 1
  
              if self.state_in_first_order:
                     _A   : int       					=				self.sigmas[step_index]
                     _A   : Optional[int]       					=				self.sigmas_interpol[step_index]
                     _A   : List[str]       					=				self.sigmas_up[step_index]
                     _A   : str       					=				self.sigmas_down[step_index - 1]
              else:
                     # 2nd order / KPDM2's method
                     _A   : Union[str, Any]       					=				self.sigmas[step_index - 1]
                     _A   : Dict       					=				self.sigmas_interpol[step_index - 1]
                     _A   : str       					=				self.sigmas_up[step_index - 1]
                     _A   : Optional[Any]       					=				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   : Dict       					=				0
              _A   : int       					=				sigma * (gamma + 1)  # Note: sigma_hat == sigma for now
  
              _A   : List[str]       					=				model_output.device
              _A   : int       					=				randn_tensor(model_output.shape				,		dtype=model_output.dtype				,		device=__lowerCamelCase				,		generator=__lowerCamelCase)
  
              # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
              if self.config.prediction_type == "epsilon":
                     _A   : List[str]       					=				sigma_hat if self.state_in_first_order else sigma_interpol
                     _A   : Optional[Any]       					=				sample - sigma_input * model_output
              elif self.config.prediction_type == "v_prediction":
                     _A   : Any       					=				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   : Union[str, Any]       					=				(sample - pred_original_sample) / sigma_hat
                     # 3. delta timestep
                     _A   : List[Any]       					=				sigma_interpol - sigma_hat
  
                     # store for 2nd order step
                     _A   : str       					=				sample
                     _A   : Optional[int]       					=				dt
                     _A   : Optional[int]       					=				sample + derivative * dt
              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   : str       					=				sigma_down - sigma_hat
  
                     _A   : Optional[Any]       					=				self.sample
                     _A   : Tuple       					=				None
  
                     _A   : Optional[Any]       					=				sample + derivative * dt
                     _A   : Optional[int]       					=				prev_sample + noise * sigma_up
  
              if not return_dict:
                     return (prev_sample,)
  
              return SchedulerOutput(prev_sample=__lowerCamelCase)
  
  
       def 				_lowerCamelCase				(		self				,		__lowerCamelCase				,		__lowerCamelCase				,		__lowerCamelCase				,		)    ->       torch.FloatTensor:
              # Make sure sigmas and timesteps have the same device and dtype as original_samples
              _A   : Tuple       					=				self.sigmas.to(device=original_samples.device				,		dtype=original_samples.dtype)
              if original_samples.device.type == "mps" and torch.is_floating_point(__lowerCamelCase):
                     # mps does not support float64
                     _A   : Optional[Any]       					=				self.timesteps.to(original_samples.device				,		dtype=torch.floataa)
                     _A   : Tuple       					=				timesteps.to(original_samples.device				,		dtype=torch.floataa)
              else:
                     _A   : Optional[Any]       					=				self.timesteps.to(original_samples.device)
                     _A   : List[Any]       					=				timesteps.to(original_samples.device)
  
              _A   : List[Any]       					=				[self.index_for_timestep(__lowerCamelCase				,		__lowerCamelCase) for t in timesteps]
  
              _A   : Any       					=				sigmas[step_indices].flatten()
              while len(sigma.shape) < len(original_samples.shape):
                     _A   : Optional[int]       					=				sigma.unsqueeze(-1)
  
              _A   : List[str]       					=				original_samples + noise * sigma
              return noisy_samples
  
  
       def __len__(		self)    ->       Union[str, Any]:
              return self.config.num_train_timesteps
  
style_context: 
  
  
  lowerCAmelCase__   	=				'\n# Transformers installation\n! pip install transformers datasets evaluate\n# To install from source instead of the last release, comment the command above and uncomment the following one.\n# ! pip install git+https://github.com/huggingface/transformers.git\n'
  
  lowerCAmelCase__   	=				[{'type': 'code', 'content': INSTALL_CONTENT}]
  lowerCAmelCase__   	=				{
      '{processor_class}': 'FakeProcessorClass',
      '{model_class}': 'FakeModelClass',
      '{object_class}': 'FakeObjectClass',
  }
  