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 					UpperCamelCase	(     snake_case__      ):
  					__UpperCamelCase						=   42
  					__UpperCamelCase						=   None
  
  
  
  
  def 							_lowerCamelCase(				__snake_case						,						__snake_case=0.9_9_9						,						__snake_case="cosine"						,						)  ->   Tuple:
  		if alpha_transform_type == "cosine":
  
  				def alpha_bar_fn(__snake_case	):
  						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(__snake_case	):
  						return math.exp(t * -1_2.0	)
  
  		else:
  				raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""	)
  
  		__snake_case		       =     []
  		for i in range(__snake_case	):
  				__snake_case		       =     i / num_diffusion_timesteps
  				__snake_case		       =     (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 					UpperCamelCase	(     snake_case__			,      snake_case__      ):
  					__UpperCamelCase						=   [e.name for e in KarrasDiffusionSchedulers]
  					__UpperCamelCase						=   1
  
  
  
  
  					@register_to_config
  					def __init__( self :					str      ,_lowerCAmelCase :					int = 1_000      ,_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:
  									__snake_case		       =     torch.tensor(_lowerCAmelCase      ,dtype=torch.floataa						)
  							elif beta_schedule == "linear":
  									__snake_case		       =     torch.linspace(_lowerCAmelCase      ,_lowerCAmelCase      ,_lowerCAmelCase      ,dtype=torch.floataa						)
  							elif beta_schedule == "scaled_linear":
  									# this schedule is very specific to the latent diffusion model.
  									__snake_case		       =     (
  									    torch.linspace(beta_start**0.5      ,beta_end**0.5      ,_lowerCAmelCase      ,dtype=torch.floataa						) ** 2
  									)
  							elif beta_schedule == "squaredcos_cap_v2":
  									# Glide cosine schedule
  									__snake_case		       =     betas_for_alpha_bar(_lowerCAmelCase						)
  							else:
  									raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""						)
  
  							__snake_case		       =     1.0 - self.betas
  							__snake_case		       =     torch.cumprod(self.alphas      ,dim=0						)
  
  							__snake_case		       =     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
  							__snake_case		       =     np.concatenate([sigmas[::-1], [0.0]]						).astype(np.floataa						)
  							__snake_case		       =     torch.from_numpy(_lowerCAmelCase						)
  
  							# setable values
  							__snake_case		       =     None
  							__snake_case		       =     use_karras_sigmas
  							self.set_timesteps(_lowerCAmelCase      ,_lowerCAmelCase						)
  							__snake_case		       =     []
  							__snake_case		       =     False
  
  
  
  
  					@property
  					def 							UpperCamelCase_						( self :					Dict						):
  
  
  							"""simple docstring"""
  
  
  
  
  							if self.config.timestep_spacing in ["linspace", "trailing"]:
  									return self.sigmas.max()
  
  							return (self.sigmas.max() ** 2 + 1) ** 0.5
  
  
  
  
  					def 							UpperCamelCase_						( self :					Tuple      ,_lowerCAmelCase :					torch.FloatTensor      ,_lowerCAmelCase :					Union[float, torch.FloatTensor]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							if isinstance(_lowerCAmelCase      ,torch.Tensor						):
  									__snake_case		       =     timestep.to(self.timesteps.device						)
  							__snake_case		       =     (self.timesteps == timestep).nonzero().item()
  							__snake_case		       =     self.sigmas[step_index]
  							__snake_case		       =     sample / ((sigma**2 + 1) ** 0.5)
  							__snake_case		       =     True
  							return sample
  
  
  
  
  					def 							UpperCamelCase_						( self :					int      ,_lowerCAmelCase :					Dict      ,_lowerCAmelCase :					Tuple      ,_lowerCAmelCase :					Dict						):
  
  
  							"""simple docstring"""
  
  
  
  
  							def lms_derivative(_lowerCAmelCase :					Union[str, Any]						):
  									__snake_case		       =     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
  
  							__snake_case		       =     integrate.quad(_lowerCAmelCase      ,self.sigmas[t]      ,self.sigmas[t + 1]      ,epsrel=1E-4						)[0]
  
  							return integrated_coeff
  
  
  
  
  					def 							UpperCamelCase_						( self :					Optional[Any]      ,_lowerCAmelCase :					int      ,_lowerCAmelCase :					Union[str, torch.device] = None						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     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":
  									__snake_case		       =     np.linspace(0      ,self.config.num_train_timesteps - 1      ,_lowerCAmelCase      ,dtype=_lowerCAmelCase						)[
  									    ::-1
  									].copy()
  							elif self.config.timestep_spacing == "leading":
  									__snake_case		       =     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
  									__snake_case		       =     (np.arange(0      ,_lowerCAmelCase						) * step_ratio).round()[::-1].copy().astype(_lowerCAmelCase						)
  									timesteps += self.config.steps_offset
  							elif self.config.timestep_spacing == "trailing":
  									__snake_case		       =     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
  									__snake_case		       =     (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'."""						)
  
  							__snake_case		       =     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
  							__snake_case		       =     np.log(_lowerCAmelCase						)
  							__snake_case		       =     np.interp(_lowerCAmelCase      ,np.arange(0      ,len(_lowerCAmelCase						)						)      ,_lowerCAmelCase						)
  
  							if self.use_karras_sigmas:
  									__snake_case		       =     self._convert_to_karras(in_sigmas=_lowerCAmelCase						)
  									__snake_case		       =     np.array([self._sigma_to_t(_lowerCAmelCase      ,_lowerCAmelCase						) for sigma in sigmas]						)
  
  							__snake_case		       =     np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
  
  							__snake_case		       =     torch.from_numpy(_lowerCAmelCase						).to(device=_lowerCAmelCase						)
  							if str(_lowerCAmelCase						).startswith("mps"						):
  									# mps does not support float64
  									__snake_case		       =     torch.from_numpy(_lowerCAmelCase						).to(_lowerCAmelCase      ,dtype=torch.floataa						)
  							else:
  									__snake_case		       =     torch.from_numpy(_lowerCAmelCase						).to(device=_lowerCAmelCase						)
  
  							__snake_case		       =     []
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[str]      ,_lowerCAmelCase :					str      ,_lowerCAmelCase :					Tuple						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     np.log(_lowerCAmelCase						)
  
  							# get distribution
  							__snake_case		       =     log_sigma - log_sigmas[:, np.newaxis]
  
  							# get sigmas range
  							__snake_case		       =     np.cumsum((dists >= 0)      ,axis=0						).argmax(axis=0						).clip(max=log_sigmas.shape[0] - 2						)
  							__snake_case		       =     low_idx + 1
  
  							__snake_case		       =     log_sigmas[low_idx]
  							__snake_case		       =     log_sigmas[high_idx]
  
  							# interpolate sigmas
  							__snake_case		       =     (low - log_sigma) / (low - high)
  							__snake_case		       =     np.clip(_lowerCAmelCase      ,0      ,1						)
  
  							# transform interpolation to time range
  							__snake_case		       =     (1 - w) * low_idx + w * high_idx
  							__snake_case		       =     t.reshape(sigma.shape						)
  							return t
  
  
  
  
  					def 							UpperCamelCase_						( self :					Optional[Any]      ,_lowerCAmelCase :					torch.FloatTensor						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     in_sigmas[-1].item()
  							__snake_case		       =     in_sigmas[0].item()
  
  							__snake_case		       =     7.0  # 7.0 is the value used in the paper
  							__snake_case		       =     np.linspace(0      ,1      ,self.num_inference_steps						)
  							__snake_case		       =     sigma_min ** (1 / rho)
  							__snake_case		       =     sigma_max ** (1 / rho)
  							__snake_case		       =     (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
  							return sigmas
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[str]      ,_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						):
  									__snake_case		       =     timestep.to(self.timesteps.device						)
  							__snake_case		       =     (self.timesteps == timestep).nonzero().item()
  							__snake_case		       =     self.sigmas[step_index]
  
  							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
  							if self.config.prediction_type == "epsilon":
  									__snake_case		       =     sample - sigma * model_output
  							elif self.config.prediction_type == "v_prediction":
  									# * c_out + input * c_skip
  									__snake_case		       =     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
  							elif self.config.prediction_type == "sample":
  									__snake_case		       =     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
  							__snake_case		       =     (sample - pred_original_sample) / sigma
  							self.derivatives.append(_lowerCAmelCase						)
  							if len(self.derivatives						) > order:
  									self.derivatives.pop(0						)
  
  							# 3. Compute linear multistep coefficients
  							__snake_case		       =     min(step_index + 1      ,_lowerCAmelCase						)
  							__snake_case		       =     [self.get_lms_coefficient(_lowerCAmelCase      ,_lowerCAmelCase      ,_lowerCAmelCase						) for curr_order in range(_lowerCAmelCase						)]
  
  							# 4. Compute previous sample based on the derivatives path
  							__snake_case		       =     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 :					List[str]      ,_lowerCAmelCase :					torch.FloatTensor      ,_lowerCAmelCase :					torch.FloatTensor      ,_lowerCAmelCase :					torch.FloatTensor      ,):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     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
  									__snake_case		       =     self.timesteps.to(original_samples.device      ,dtype=torch.floataa						)
  									__snake_case		       =     timesteps.to(original_samples.device      ,dtype=torch.floataa						)
  							else:
  									__snake_case		       =     self.timesteps.to(original_samples.device						)
  									__snake_case		       =     timesteps.to(original_samples.device						)
  
  							__snake_case		       =     [(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
  							__snake_case		       =     sigmas[step_indices].flatten()
  							while len(sigma.shape						) < len(original_samples.shape						):
  									__snake_case		       =     sigma.unsqueeze(-1						)
  
  							__snake_case		       =     original_samples + noise * sigma
  							return noisy_samples
  
  
  
  
  
  
  
  					def __len__( self :					Union[str, Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							return self.config.num_train_timesteps
  
  
  
  
  
  
style_context: from __future__ import annotations
  
  from collections.abc import Iterable
  from dataclasses import dataclass
  from typing import Any
  
  
  
  
  class 					UpperCamelCase	:
  					__UpperCamelCase						=   ("""_front""", """_back""", """_len""")
  
  
  
  
  					@dataclass
  					class 					UpperCamelCase	:
  										__UpperCamelCase						=   None
  										__UpperCamelCase						=   None
  										__UpperCamelCase						=   None
  
  
  
  
  					class 					UpperCamelCase	:
  										__UpperCamelCase						=   ("""_cur""",)
  
  
  
  
  										def __init__( self :					Dict      ,_lowerCAmelCase :					Deque._Node | None						):
  
  
  												"""simple docstring"""
  
  
  
  
  												__snake_case		       =     cur
  
  
  
  
  										def __iter__( self :					Dict						):
  
  
  												"""simple docstring"""
  
  
  
  
  												return self
  
  
  
  
  
  
  
  										def 							UpperCamelCase_						( self :					Optional[Any]						):
  
  
  												"""simple docstring"""
  
  
  
  
  												if self._cur is None:
  														# finished iterating
  														raise StopIteration
  												__snake_case		       =     self._cur.val
  												__snake_case		       =     self._cur.next_node
  
  												return val
  
  
  
  
  					def __init__( self :					Optional[int]      ,_lowerCAmelCase :					Iterable[Any] | None = None						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     None
  							__snake_case		       =     None
  							__snake_case		       =     0
  
  							if iterable is not None:
  									# append every value to the deque
  									for val in iterable:
  											self.append(_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					int      ,_lowerCAmelCase :					Any						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     self._Node(_lowerCAmelCase      ,_lowerCAmelCase      ,_lowerCAmelCase						)
  							if self.is_empty():
  									# front = back
  									__snake_case		       =     __snake_case		       =     node
  									__snake_case		       =     1
  							else:
  									# connect nodes
  									__snake_case		       =     node
  									__snake_case		       =     self._back
  									__snake_case		       =     node  # assign new back to the new node
  
  									self._len += 1
  
  									# make sure there were no errors
  									assert not self.is_empty(), "Error on appending value."
  
  
  
  
  					def 							UpperCamelCase_						( self :					Any      ,_lowerCAmelCase :					Any						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     self._Node(_lowerCAmelCase      ,_lowerCAmelCase      ,_lowerCAmelCase						)
  							if self.is_empty():
  									# front = back
  									__snake_case		       =     __snake_case		       =     node
  									__snake_case		       =     1
  							else:
  									# connect nodes
  									__snake_case		       =     self._front
  									__snake_case		       =     node
  									__snake_case		       =     node  # assign new front to the new node
  
  									self._len += 1
  
  									# make sure there were no errors
  									assert not self.is_empty(), "Error on appending value."
  
  
  
  
  					def 							UpperCamelCase_						( self :					int      ,_lowerCAmelCase :					Iterable[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							for val in iterable:
  									self.append(_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					Optional[int]      ,_lowerCAmelCase :					Iterable[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							for val in iterable:
  									self.appendleft(_lowerCAmelCase						)
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							assert not self.is_empty(), "Deque is empty."
  
  							__snake_case		       =     self._back
  							__snake_case		       =     self._back.prev_node  # set new back
  							# drop the last node - python will deallocate memory automatically
  							__snake_case		       =     None
  
  							self._len -= 1
  
  							return topop.val
  
  
  
  
  					def 							UpperCamelCase_						( self :					List[str]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							assert not self.is_empty(), "Deque is empty."
  
  							__snake_case		       =     self._front
  							__snake_case		       =     self._front.next_node  # set new front and drop the first node
  							__snake_case		       =     None
  
  							self._len -= 1
  
  							return topop.val
  
  
  
  
  					def 							UpperCamelCase_						( self :					int						):
  
  
  							"""simple docstring"""
  
  
  
  
  							return self._front is None
  
  
  
  
  					def __len__( self :					Tuple						):
  
  
  							"""simple docstring"""
  
  
  
  
  							return self._len
  
  
  
  
  					def __eq__( self :					Union[str, Any]      ,_lowerCAmelCase :					object						):
  
  
  							"""simple docstring"""
  
  
  
  
  							if not isinstance(_lowerCAmelCase      ,_lowerCAmelCase						):
  									return NotImplemented
  
  							__snake_case		       =     self._front
  							__snake_case		       =     other._front
  
  							# if the length of the dequeues are not the same, they are not equal
  							if len(self						) != len(_lowerCAmelCase						):
  									return False
  
  							while me is not None and oth is not None:
  									# compare every value
  									if me.val != oth.val:
  											return False
  									__snake_case		       =     me.next_node
  									__snake_case		       =     oth.next_node
  
  							return True
  
  
  
  
  					def __iter__( self :					Tuple						):
  
  
  							"""simple docstring"""
  
  
  
  
  							return Deque._Iterator(self._front						)
  
  
  
  
  
  
  
  					def __repr__( self :					List[Any]						):
  
  
  							"""simple docstring"""
  
  
  
  
  							__snake_case		       =     []
  							__snake_case		       =     self._front
  							while aux is not None:
  									# append the values in a list to display
  									values_list.append(aux.val						)
  									__snake_case		       =     aux.next_node
  
  							return F"""[{", ".join(repr(_lowerCAmelCase						) for val in values_list						)}]"""
  
  
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  
  
  
  
  
  