



'''simple docstring'''
class 							lowercase__			:





 def __init__(				self      :       List[Any]				,lowerCamelCase__      :       int				):







       '''simple docstring'''
       _UpperCamelCase      :	Union[str, Any]				       =     val
       # Number of nodes in left subtree
       _UpperCamelCase      :	Dict				       =     0
       _UpperCamelCase      :	str				       =     None
       _UpperCamelCase      :	int				       =     None
       _UpperCamelCase      :	Dict				       =     None





 def 			UpperCamelCase_						(				self      :       Optional[int]				,lowerCamelCase__      :       List[Any]				):







       '''simple docstring'''
       assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

       if self.val < other.val:
             _UpperCamelCase      :	int				       =     self.right
             _UpperCamelCase      :	Any				       =     None
             if self.right:
                   _UpperCamelCase      :	Optional[Any]				       =     other
             _UpperCamelCase      :	Union[str, Any]				       =     other
             _UpperCamelCase      :	List[Any]				       =     self.left_tree_size * 2 + 1
             return self
       else:
             _UpperCamelCase      :	str				       =     other.right
             _UpperCamelCase      :	List[Any]				       =     None
             if other.right:
                   _UpperCamelCase      :	Union[str, Any]				       =     self
             _UpperCamelCase      :	Optional[int]				       =     self
             _UpperCamelCase      :	Optional[int]				       =     other.left_tree_size * 2 + 1
             return other






class 							lowercase__			:





 def __init__(				self      :       List[str]				,lowerCamelCase__      :       Optional[int]=None				,lowerCamelCase__      :       str=None				,lowerCamelCase__      :       List[Any]=0				):







       '''simple docstring'''
       _UpperCamelCase      :	Any				       =     heap_size
       _UpperCamelCase      :	int				       =     bottom_root
       _UpperCamelCase      :	Any				       =     min_node





 def 			UpperCamelCase_						(				self      :       int				,lowerCamelCase__      :       int				):







       '''simple docstring'''

       # Empty heaps corner cases
       if other.size == 0:
             return None
       if self.size == 0:
             _UpperCamelCase      :	List[str]				       =     other.size
             _UpperCamelCase      :	Tuple				       =     other.bottom_root
             _UpperCamelCase      :	Tuple				       =     other.min_node
             return None
       # Update size
       _UpperCamelCase      :	Optional[Any]				       =     self.size + other.size

       # Update min.node
       if self.min_node.val > other.min_node.val:
             _UpperCamelCase      :	Optional[Any]				       =     other.min_node
       # Merge

       # Order roots by left_subtree_size
       _UpperCamelCase      :	Dict				       =     []
       _UpperCamelCase      :	Optional[Any]				       =     self.bottom_root, other.bottom_root
       while i or j:
             if i and ((not j) or i.left_tree_size < j.left_tree_size):
                   combined_roots_list.append((i, True)				)
                   _UpperCamelCase      :	Tuple				       =     i.parent
             else:
                   combined_roots_list.append((j, False)				)
                   _UpperCamelCase      :	Optional[Any]				       =     j.parent
        # Insert links between them
       for i in range(len(lowerCamelCase__				) - 1				):
             if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                   _UpperCamelCase      :	Dict				       =     combined_roots_list[i + 1][0]
                   _UpperCamelCase      :	Optional[int]				       =     combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
       _UpperCamelCase      :	Any				       =     combined_roots_list[0][0]
       while i.parent:
             if (
                 (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
             ) or (
                 i.left_tree_size == i.parent.left_tree_size
                 and i.left_tree_size != i.parent.parent.left_tree_size
             ):
                   # Neighbouring Nodes
                   _UpperCamelCase      :	Dict				       =     i.left
                   _UpperCamelCase      :	int				       =     i.parent.parent

                   # Merging trees
                   _UpperCamelCase      :	str				       =     i.merge_trees(i.parent				)

                   # Updating links
                   _UpperCamelCase      :	Union[str, Any]				       =     previous_node
                   _UpperCamelCase      :	List[Any]				       =     next_node
                   if previous_node:
                         _UpperCamelCase      :	List[str]				       =     i
                   if next_node:
                         _UpperCamelCase      :	Dict				       =     i
             else:
                   _UpperCamelCase      :	List[str]				       =     i.parent
        # Updating self.bottom_root
       while i.left:
             _UpperCamelCase      :	Union[str, Any]				       =     i.left
       _UpperCamelCase      :	Any				       =     i

       # Update other
       _UpperCamelCase      :	Optional[int]				       =     self.size
       _UpperCamelCase      :	Optional[Any]				       =     self.bottom_root
       _UpperCamelCase      :	str				       =     self.min_node

       # Return the merged heap
       return self





 def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       Dict				):







       '''simple docstring'''
       if self.size == 0:
             _UpperCamelCase      :	Tuple				       =     Node(lowerCamelCase__				)
             _UpperCamelCase      :	Optional[int]				       =     1
             _UpperCamelCase      :	Optional[int]				       =     self.bottom_root
       else:
             # Create new node
             _UpperCamelCase      :	List[Any]				       =     Node(lowerCamelCase__				)

             # Update size
             self.size += 1

             # update min_node
             if val < self.min_node.val:
                   _UpperCamelCase      :	List[str]				       =     new_node
             # Put new_node as a bottom_root in heap
             _UpperCamelCase      :	int				       =     new_node
             _UpperCamelCase      :	Tuple				       =     self.bottom_root
             _UpperCamelCase      :	Any				       =     new_node

             # Consecutively merge roots with same left_tree_size
             while (
                 self.bottom_root.parent
                 and self.bottom_root.left_tree_size
                 == self.bottom_root.parent.left_tree_size
             ):
                   # Next node
                   _UpperCamelCase      :	Any				       =     self.bottom_root.parent.parent

                   # Merge
                   _UpperCamelCase      :	int				       =     self.bottom_root.merge_trees(self.bottom_root.parent				)

                   # Update Links
                   _UpperCamelCase      :	Dict				       =     next_node
                   _UpperCamelCase      :	Optional[Any]				       =     None
                   if next_node:
                         _UpperCamelCase      :	Union[str, Any]				       =     self.bottom_root





 def 			UpperCamelCase_						(				self      :       Dict				):







       '''simple docstring'''
       return self.min_node.val





 def 			UpperCamelCase_						(				self      :       int				):







       '''simple docstring'''
       return self.size == 0





 def 			UpperCamelCase_						(				self      :       List[Any]				):







       '''simple docstring'''
       _UpperCamelCase      :	Tuple				       =     self.min_node.val

       # Last element in heap corner case
       if self.size == 1:
             # Update size
             _UpperCamelCase      :	Optional[Any]				       =     0

             # Update bottom root
             _UpperCamelCase      :	Any				       =     None

             # Update min_node
             _UpperCamelCase      :	List[str]				       =     None

             return min_value
       # No right subtree corner case
       # The structure of the tree implies that this should be the bottom root
       # and there is at least one other root
       if self.min_node.right is None:
             # Update size
             self.size -= 1

             # Update bottom root
             _UpperCamelCase      :	Union[str, Any]				       =     self.bottom_root.parent
             _UpperCamelCase      :	Union[str, Any]				       =     None

             # Update min_node
             _UpperCamelCase      :	Union[str, Any]				       =     self.bottom_root
             _UpperCamelCase      :	Union[str, Any]				       =     self.bottom_root.parent
             while i:
                   if i.val < self.min_node.val:
                         _UpperCamelCase      :	Union[str, Any]				       =     i
                   _UpperCamelCase      :	Optional[int]				       =     i.parent
             return min_value
       # General case
       # Find the BinomialHeap of the right subtree of min_node
       _UpperCamelCase      :	Dict				       =     self.min_node.right
       _UpperCamelCase      :	Dict				       =     None
       _UpperCamelCase      :	Tuple				       =     bottom_of_new
       _UpperCamelCase      :	Dict				       =     1

       # Size, min_node and bottom_root
       while bottom_of_new.left:
             _UpperCamelCase      :	Any				       =     size_of_new * 2 + 1
             _UpperCamelCase      :	Tuple				       =     bottom_of_new.left
             if bottom_of_new.val < min_of_new.val:
                   _UpperCamelCase      :	int				       =     bottom_of_new
        # Corner case of single root on top left path
       if (not self.min_node.left) and (not self.min_node.parent):
             _UpperCamelCase      :	Union[str, Any]				       =     size_of_new
             _UpperCamelCase      :	Union[str, Any]				       =     bottom_of_new
             _UpperCamelCase      :	Tuple				       =     min_of_new
             # print("Single root, multiple nodes case")
             return min_value
       # Remaining cases
       # Construct heap of right subtree
       _UpperCamelCase      :	Optional[Any]				       =     BinomialHeap(
           bottom_root=lowerCamelCase__				,min_node=lowerCamelCase__				,heap_size=lowerCamelCase__				)

       # Update size
       _UpperCamelCase      :	Union[str, Any]				       =     self.size - 1 - size_of_new

       # Neighbour nodes
       _UpperCamelCase      :	Union[str, Any]				       =     self.min_node.left
       _UpperCamelCase      :	Optional[Any]				       =     self.min_node.parent

       # Initialize new bottom_root and min_node
       _UpperCamelCase      :	Optional[int]				       =     previous_node or next_node
       _UpperCamelCase      :	Tuple				       =     next_node

       # Update links of previous_node and search below for new min_node and
       # bottom_root
       if previous_node:
             _UpperCamelCase      :	Dict				       =     next_node

             # Update bottom_root and search for min_node below
             _UpperCamelCase      :	int				       =     previous_node
             _UpperCamelCase      :	Tuple				       =     previous_node
             while self.bottom_root.left:
                   _UpperCamelCase      :	Union[str, Any]				       =     self.bottom_root.left
                   if self.bottom_root.val < self.min_node.val:
                         _UpperCamelCase      :	Any				       =     self.bottom_root
       if next_node:
             _UpperCamelCase      :	Any				       =     previous_node

             # Search for new min_node above min_node
             _UpperCamelCase      :	List[str]				       =     next_node
             while i:
                   if i.val < self.min_node.val:
                         _UpperCamelCase      :	List[Any]				       =     i
                   _UpperCamelCase      :	Dict				       =     i.parent
        # Merge heaps
       self.merge_heaps(lowerCamelCase__				)

       return min_value





 def 			UpperCamelCase_						(				self      :       Optional[int]				):







       '''simple docstring'''
       _UpperCamelCase      :	List[Any]				       =     self.bottom_root
       while top_root.parent:
             _UpperCamelCase      :	Tuple				       =     top_root.parent
       # preorder
       _UpperCamelCase      :	str				       =     []
       self.__traversal(lowerCamelCase__				,lowerCamelCase__				)
       return heap_pre_order





 def 			UpperCamelCase_						(				self      :       Dict				,lowerCamelCase__      :       Tuple				,lowerCamelCase__      :       Dict				,lowerCamelCase__      :       List[str]=0				):







       '''simple docstring'''
       if curr_node:
             preorder.append((curr_node.val, level)				)
             self.__traversal(curr_node.left				,lowerCamelCase__				,level + 1				)
             self.__traversal(curr_node.right				,lowerCamelCase__				,level + 1				)
       else:
             preorder.append(('#', level)				)





 def __str__(				self      :       List[Any]				):







       '''simple docstring'''
       if self.is_empty():
             return ""
       _UpperCamelCase      :	str				       =     self.pre_order()

       return "\n".join(('-' * level + str(lowerCamelCase__				)) for value, level in preorder_heap				)


# Unit Tests
if __name__ == "__main__":
     import doctest

     doctest.testmod()







'''simple docstring'''
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 							lowercase__			(							lowercase     ):
	lowercase__						       =    42
	lowercase__						       =    None






def A__					(  UpperCAmelCase_						,						UpperCAmelCase_=0.999						,						UpperCAmelCase_="cosine"						,						):
						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}'							)

						_UpperCamelCase      :	Tuple				       =     []
						for i in range(UpperCAmelCase_							):
												_UpperCamelCase      :	List[str]				       =     i / num_diffusion_timesteps
												_UpperCamelCase      :	Optional[int]				       =     (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 							lowercase__			(							lowercase		,      lowercase     ):
	lowercase__						       =    [e.name for e in KarrasDiffusionSchedulers]
	lowercase__						       =    1





	@register_to_config
	def __init__(				self      :       int				,lowerCamelCase__      :       int = 1000				,lowerCamelCase__      :       float = 0.0_0_0_1				,lowerCamelCase__      :       float = 0.0_2				,lowerCamelCase__      :       str = "linear"				,lowerCamelCase__      :       Optional[Union[np.ndarray, List[float]]] = None				,lowerCamelCase__      :       Optional[bool] = False				,lowerCamelCase__      :       str = "epsilon"				,lowerCamelCase__      :       str = "linspace"				,lowerCamelCase__      :       int = 0				,):







							'''simple docstring'''
							if trained_betas is not None:
													_UpperCamelCase      :	Union[str, Any]				       =     torch.tensor(lowerCamelCase__				,dtype=torch.floataa				)
							elif beta_schedule == "linear":
													_UpperCamelCase      :	Union[str, Any]				       =     torch.linspace(lowerCamelCase__				,lowerCamelCase__				,lowerCamelCase__				,dtype=torch.floataa				)
							elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													_UpperCamelCase      :	Optional[int]				       =     (
													    torch.linspace(beta_start**0.5				,beta_end**0.5				,lowerCamelCase__				,dtype=torch.floataa				) ** 2
													)
							elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													_UpperCamelCase      :	Dict				       =     betas_for_alpha_bar(lowerCamelCase__				)
							else:
													raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'				)

							_UpperCamelCase      :	List[Any]				       =     1.0 - self.betas
							_UpperCamelCase      :	int				       =     torch.cumprod(self.alphas				,dim=0				)

							_UpperCamelCase      :	Optional[int]				       =     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
							_UpperCamelCase      :	Any				       =     np.concatenate([sigmas[::-1], [0.0]]				).astype(np.floataa				)
							_UpperCamelCase      :	Optional[int]				       =     torch.from_numpy(lowerCamelCase__				)

							# setable values
							_UpperCamelCase      :	List[str]				       =     None
							_UpperCamelCase      :	List[Any]				       =     use_karras_sigmas
							self.set_timesteps(lowerCamelCase__				,lowerCamelCase__				)
							_UpperCamelCase      :	Any				       =     []
							_UpperCamelCase      :	Tuple				       =     False





	@property
	def 			UpperCamelCase_						(				self      :       Union[str, Any]				):







							'''simple docstring'''
							# 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 			UpperCamelCase_						(				self      :       Optional[int]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				):







							'''simple docstring'''
							if isinstance(lowerCamelCase__				,torch.Tensor				):
													_UpperCamelCase      :	List[str]				       =     timestep.to(self.timesteps.device				)
							_UpperCamelCase      :	Optional[Any]				       =     (self.timesteps == timestep).nonzero().item()
							_UpperCamelCase      :	Any				       =     self.sigmas[step_index]
							_UpperCamelCase      :	Dict				       =     sample / ((sigma**2 + 1) ** 0.5)
							_UpperCamelCase      :	Optional[Any]				       =     True
							return sample





	def 			UpperCamelCase_						(				self      :       List[Any]				,lowerCamelCase__      :       Optional[int]				,lowerCamelCase__      :       int				,lowerCamelCase__      :       Optional[Any]				):







							'''simple docstring'''

							def lms_derivative(lowerCamelCase__      :       str				):
													_UpperCamelCase      :	Any				       =     1.0
													for k in range(lowerCamelCase__				):
																			if current_order == k:
																									continue
																			prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
													return prod

							_UpperCamelCase      :	Union[str, Any]				       =     integrate.quad(lowerCamelCase__				,self.sigmas[t]				,self.sigmas[t + 1]				,epsrel=1E-4				)[0]

							return integrated_coeff





	def 			UpperCamelCase_						(				self      :       Dict				,lowerCamelCase__      :       int				,lowerCamelCase__      :       Union[str, torch.device] = None				):







							'''simple docstring'''
							_UpperCamelCase      :	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":
													_UpperCamelCase      :	int				       =     np.linspace(0				,self.config.num_train_timesteps - 1				,lowerCamelCase__				,dtype=lowerCamelCase__				)[
													    ::-1
													].copy()
							elif self.config.timestep_spacing == "leading":
													_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      :	str				       =     (np.arange(0				,lowerCamelCase__				) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__				)
													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[Any]				       =     (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\'.'				)

							_UpperCamelCase      :	Optional[Any]				       =     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
							_UpperCamelCase      :	Optional[Any]				       =     np.log(lowerCamelCase__				)
							_UpperCamelCase      :	Dict				       =     np.interp(lowerCamelCase__				,np.arange(0				,len(lowerCamelCase__				)				)				,lowerCamelCase__				)

							if self.use_karras_sigmas:
													_UpperCamelCase      :	Optional[int]				       =     self._convert_to_karras(in_sigmas=lowerCamelCase__				)
													_UpperCamelCase      :	str				       =     np.array([self._sigma_to_t(lowerCamelCase__				,lowerCamelCase__				) for sigma in sigmas]				)

							_UpperCamelCase      :	List[str]				       =     np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)

							_UpperCamelCase      :	Any				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)
							if str(lowerCamelCase__				).startswith('mps'				):
													# mps does not support float64
													_UpperCamelCase      :	Optional[Any]				       =     torch.from_numpy(lowerCamelCase__				).to(lowerCamelCase__				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Any				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)

							_UpperCamelCase      :	Union[str, Any]				       =     []





	def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       Any				,lowerCamelCase__      :       List[str]				):







							'''simple docstring'''
							# get log sigma
							_UpperCamelCase      :	Tuple				       =     np.log(lowerCamelCase__				)

							# get distribution
							_UpperCamelCase      :	Dict				       =     log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							_UpperCamelCase      :	Optional[int]				       =     np.cumsum((dists >= 0)				,axis=0				).argmax(axis=0				).clip(max=log_sigmas.shape[0] - 2				)
							_UpperCamelCase      :	str				       =     low_idx + 1

							_UpperCamelCase      :	Optional[int]				       =     log_sigmas[low_idx]
							_UpperCamelCase      :	Union[str, Any]				       =     log_sigmas[high_idx]

							# interpolate sigmas
							_UpperCamelCase      :	List[Any]				       =     (low - log_sigma) / (low - high)
							_UpperCamelCase      :	int				       =     np.clip(lowerCamelCase__				,0				,1				)

							# transform interpolation to time range
							_UpperCamelCase      :	Dict				       =     (1 - w) * low_idx + w * high_idx
							_UpperCamelCase      :	Dict				       =     t.reshape(sigma.shape				)
							return t





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				):







							'''simple docstring'''
							_UpperCamelCase      :	float				       =     in_sigmas[-1].item()
							_UpperCamelCase      :	float				       =     in_sigmas[0].item()

							_UpperCamelCase      :	List[str]				       =     7.0  # 7.0 is the value used in the paper
							_UpperCamelCase      :	str				       =     np.linspace(0				,1				,self.num_inference_steps				)
							_UpperCamelCase      :	Dict				       =     sigma_min ** (1 / rho)
							_UpperCamelCase      :	Optional[Any]				       =     sigma_max ** (1 / rho)
							_UpperCamelCase      :	int				       =     (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       int = 4				,lowerCamelCase__      :       bool = True				,):







							'''simple docstring'''
							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(lowerCamelCase__				,torch.Tensor				):
													_UpperCamelCase      :	Union[str, Any]				       =     timestep.to(self.timesteps.device				)
							_UpperCamelCase      :	Any				       =     (self.timesteps == timestep).nonzero().item()
							_UpperCamelCase      :	Optional[int]				       =     self.sigmas[step_index]

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
													_UpperCamelCase      :	Dict				       =     sample - sigma * model_output
							elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													_UpperCamelCase      :	str				       =     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
							elif self.config.prediction_type == "sample":
													_UpperCamelCase      :	Any				       =     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
							_UpperCamelCase      :	List[Any]				       =     (sample - pred_original_sample) / sigma
							self.derivatives.append(lowerCamelCase__				)
							if len(self.derivatives				) > order:
													self.derivatives.pop(0				)

							# 3. Compute linear multistep coefficients
							_UpperCamelCase      :	List[Any]				       =     min(step_index + 1				,lowerCamelCase__				)
							_UpperCamelCase      :	Optional[int]				       =     [self.get_lms_coefficient(lowerCamelCase__				,lowerCamelCase__				,lowerCamelCase__				) for curr_order in range(lowerCamelCase__				)]

							# 4. Compute previous sample based on the derivatives path
							_UpperCamelCase      :	int				       =     sample + sum(
							    coeff * derivative for coeff, derivative in zip(lowerCamelCase__				,reversed(self.derivatives				)				)				)

							if not return_dict:
													return (prev_sample,)

							return LMSDiscreteSchedulerOutput(prev_sample=lowerCamelCase__				,pred_original_sample=lowerCamelCase__				)





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,):







							'''simple docstring'''
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							_UpperCamelCase      :	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
													_UpperCamelCase      :	str				       =     self.timesteps.to(original_samples.device				,dtype=torch.floataa				)
													_UpperCamelCase      :	Optional[Any]				       =     timesteps.to(original_samples.device				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Union[str, Any]				       =     self.timesteps.to(original_samples.device				)
													_UpperCamelCase      :	Union[str, Any]				       =     timesteps.to(original_samples.device				)

							_UpperCamelCase      :	Union[str, Any]				       =     [(schedule_timesteps == t).nonzero().item() for t in timesteps]

							_UpperCamelCase      :	Optional[int]				       =     sigmas[step_indices].flatten()
							while len(sigma.shape				) < len(original_samples.shape				):
													_UpperCamelCase      :	int				       =     sigma.unsqueeze(-1				)

							_UpperCamelCase      :	str				       =     original_samples + noise * sigma
							return noisy_samples





	def __len__(				self      :       List[Any]				):







							'''simple docstring'''
							return self.config.num_train_timesteps


