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
  
  
  _lowerCamelCase				:	Any				    =       logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  
  
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
  class 							__UpperCAmelCase  (       A__						):
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    42
  		__lowerCAmelCase 				=    None
  
  
  
  
  
  
  def    __a (     UpperCAmelCase       ,			UpperCAmelCase=0.999       ,			UpperCAmelCase="cosine"       ,			)      ->Any:
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if alpha_transform_type == "cosine":
  
  		def alpha_bar_fn(UpperCAmelCase    ):
  			return math.cos((t + 0.008) / 1.008 * math.pi / 2    ) ** 2
  
  	elif alpha_transform_type == "exp":
  
  		def alpha_bar_fn(UpperCAmelCase    ):
  			return math.exp(t * -12.0    )
  
  	else:
  		raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""    )
  
  	A							  =      []
  	for i in range(UpperCAmelCase    ):
  		A							  =      i / num_diffusion_timesteps
  		A							  =      (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 							__UpperCAmelCase  (       A__		,					A__						):
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    [e.name for e in KarrasDiffusionSchedulers]
  		__lowerCAmelCase 				=    1
  
  
  
  
  
  
  
  		@register_to_config
  		def __init__(self						:      int      ,      _lowerCAmelCase						:      int = 1000      ,      _lowerCAmelCase						:      float = 0.0_001      ,      _lowerCAmelCase						:      float = 0.02      ,      _lowerCAmelCase						:      str = "linear"      ,      _lowerCAmelCase						:      Optional[Union[np.ndarray, List[float]]] = None      ,      _lowerCAmelCase						:      str = "epsilon"      ,      _lowerCAmelCase						:      str = "linear"      ,      _lowerCAmelCase						:      Optional[bool] = False      ,      _lowerCAmelCase						:      str = "linspace"      ,      _lowerCAmelCase						:      int = 0      ,      ):
  			if trained_betas is not None:
  				A							  =      torch.tensor(_lowerCAmelCase      ,      dtype=torch.floataa      )
  			elif beta_schedule == "linear":
  				A							  =      torch.linspace(_lowerCAmelCase      ,      _lowerCAmelCase      ,      _lowerCAmelCase      ,      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      ,      _lowerCAmelCase      ,      dtype=torch.floataa      ) ** 2
  				)
  			elif beta_schedule == "squaredcos_cap_v2":
  				# Glide cosine schedule
  				A							  =      betas_for_alpha_bar(_lowerCAmelCase      )
  			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      )
  
  			A							  =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
  			A							  =      np.concatenate([sigmas[::-1], [0.0]]      ).astype(np.floataa      )
  			A							  =      torch.from_numpy(_lowerCAmelCase      )
  
  			# setable values
  			A							  =      None
  			A							  =      np.linspace(0      ,      num_train_timesteps - 1      ,      _lowerCAmelCase      ,      dtype=_lowerCAmelCase      )[::-1].copy()
  			A							  =      torch.from_numpy(_lowerCAmelCase      )
  			A							  =      False
  			A							  =      use_karras_sigmas
  
  
  
  
  
  
  
  		@property
  		def        A     (self						:      Tuple      ):
  			# 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						:      Optional[Any]      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      Union[float, torch.FloatTensor]      ):
  			if isinstance(_lowerCAmelCase      ,      torch.Tensor      ):
  				A							  =      timestep.to(self.timesteps.device      )
  			A							  =      (self.timesteps == timestep).nonzero().item()
  			A							  =      self.sigmas[step_index]
  
  			A							  =      sample / ((sigma**2 + 1) ** 0.5)
  
  			A							  =      True
  			return sample
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      int      ,      _lowerCAmelCase						:      Union[str, torch.device] = None      ):
  			A							  =      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":
  				A							  =      np.linspace(0      ,      self.config.num_train_timesteps - 1      ,      _lowerCAmelCase      ,      dtype=_lowerCAmelCase      )[
  				    ::-1
  				].copy()
  			elif self.config.timestep_spacing == "leading":
  				A							  =      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
  				A							  =      (np.arange(0      ,      _lowerCAmelCase      ) * step_ratio).round()[::-1].copy().astype(_lowerCAmelCase      )
  				timesteps += self.config.steps_offset
  			elif self.config.timestep_spacing == "trailing":
  				A							  =      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
  				A							  =      (np.arange(self.config.num_train_timesteps      ,      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							  =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
  			A							  =      np.log(_lowerCAmelCase      )
  
  			if self.config.interpolation_type == "linear":
  				A							  =      np.interp(_lowerCAmelCase      ,      np.arange(0      ,      len(_lowerCAmelCase      )      )      ,      _lowerCAmelCase      )
  			elif self.config.interpolation_type == "log_linear":
  				A							  =      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:
  				A							  =      self._convert_to_karras(in_sigmas=_lowerCAmelCase      ,      num_inference_steps=self.num_inference_steps      )
  				A							  =      np.array([self._sigma_to_t(_lowerCAmelCase      ,      _lowerCAmelCase      ) for sigma in sigmas]      )
  
  			A							  =      np.concatenate([sigmas, [0.0]]      ).astype(np.floataa      )
  			A							  =      torch.from_numpy(_lowerCAmelCase      ).to(device=_lowerCAmelCase      )
  			if str(_lowerCAmelCase      ).startswith("""mps"""      ):
  				# mps does not support float64
  				A							  =      torch.from_numpy(_lowerCAmelCase      ).to(_lowerCAmelCase      ,      dtype=torch.floataa      )
  			else:
  				A							  =      torch.from_numpy(_lowerCAmelCase      ).to(device=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      List[str]      ,      _lowerCAmelCase						:      Tuple      ,      _lowerCAmelCase						:      Union[str, Any]      ):
  			# get log sigma
  			A							  =      np.log(_lowerCAmelCase      )
  
  			# get distribution
  			A							  =      log_sigma - log_sigmas[:, np.newaxis]
  
  			# get sigmas range
  			A							  =      np.cumsum((dists >= 0)      ,      axis=0      ).argmax(axis=0      ).clip(max=log_sigmas.shape[0] - 2      )
  			A							  =      low_idx + 1
  
  			A							  =      log_sigmas[low_idx]
  			A							  =      log_sigmas[high_idx]
  
  			# interpolate sigmas
  			A							  =      (low - log_sigma) / (low - high)
  			A							  =      np.clip(_lowerCAmelCase      ,      0      ,      1      )
  
  			# transform interpolation to time range
  			A							  =      (1 - w) * low_idx + w * high_idx
  			A							  =      t.reshape(sigma.shape      )
  			return t
  
  
  
  
  
  
  
  		def        A     (self						:      List[Any]      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      List[Any]      ):
  			A							  =      in_sigmas[-1].item()
  			A							  =      in_sigmas[0].item()
  
  			A							  =      7.0  # 7.0 is the value used in the paper
  			A							  =      np.linspace(0      ,      1      ,      _lowerCAmelCase      )
  			A							  =      sigma_min ** (1 / rho)
  			A							  =      sigma_max ** (1 / rho)
  			A							  =      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
  			return sigmas
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[int]      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      Union[float, torch.FloatTensor]      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      float = 0.0      ,      _lowerCAmelCase						:      float = 0.0      ,      _lowerCAmelCase						:      float = float("""inf"""      )      ,      _lowerCAmelCase						:      float = 1.0      ,      _lowerCAmelCase						:      Optional[torch.Generator] = None      ,      _lowerCAmelCase						:      bool = True      ,      ):
  
  			if (
  			    isinstance(_lowerCAmelCase      ,      _lowerCAmelCase      )
  			    or isinstance(_lowerCAmelCase      ,      torch.IntTensor      )
  			    or isinstance(_lowerCAmelCase      ,      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(_lowerCAmelCase      ,      torch.Tensor      ):
  				A							  =      timestep.to(self.timesteps.device      )
  
  			A							  =      (self.timesteps == timestep).nonzero().item()
  			A							  =      self.sigmas[step_index]
  
  			A							  =      min(s_churn / (len(self.sigmas      ) - 1)      ,      2**0.5 - 1      ) if s_tmin <= sigma <= s_tmax else 0.0
  
  			A							  =      randn_tensor(
  			    model_output.shape      ,      dtype=model_output.dtype      ,      device=model_output.device      ,      generator=_lowerCAmelCase      )
  
  			A							  =      noise * s_noise
  			A							  =      sigma * (gamma + 1)
  
  			if gamma > 0:
  				A							  =      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":
  				A							  =      model_output
  			elif self.config.prediction_type == "epsilon":
  				A							  =      sample - sigma_hat * model_output
  			elif self.config.prediction_type == "v_prediction":
  				# * c_out + input * c_skip
  				A							  =      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
  			A							  =      (sample - pred_original_sample) / sigma_hat
  
  			A							  =      self.sigmas[step_index + 1] - sigma_hat
  
  			A							  =      sample + derivative * dt
  
  			if not return_dict:
  				return (prev_sample,)
  
  			return EulerDiscreteSchedulerOutput(prev_sample=_lowerCAmelCase      ,      pred_original_sample=_lowerCAmelCase      )
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      _lowerCAmelCase						:      torch.FloatTensor      ,      ):
  			# Make sure sigmas and timesteps have the same device and dtype as original_samples
  			A							  =      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							  =      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							  =      [(schedule_timesteps == t).nonzero().item() 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						:      Any      ):
  			return self.config.num_train_timesteps
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  
  from __future__ import annotations
  
  
  
  class 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(self						:      Any      ,      _lowerCAmelCase						:      int      ):
  			A							  =      value
  			A							  =      None
  			A							  =      None
  
  
  
  
  
  
  class 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    42
  
  
  
  
  
  
  
  		def __init__(self						:      List[str]      ):
  			A							  =      0
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int      ):
  			if node is None:
  				return
  
  			if path_sum == self.target:
  				self.paths += 1
  
  			if node.left:
  				self.depth_first_search(node.left      ,      path_sum + node.left.value      )
  			if node.right:
  				self.depth_first_search(node.right      ,      path_sum + node.right.value      )
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int | None = None      ):
  			if node is None:
  				return 0
  			if target is not None:
  				A							  =      target
  
  			self.depth_first_search(_lowerCAmelCase      ,      node.value      )
  			self.path_sum(node.left      )
  			self.path_sum(node.right      )
  
  			return self.paths
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  