






'''simple docstring'''







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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput





def 		_UpperCAmelCase   (							__A							:   Union[str, Any]						,		__A							:   List[Any]=0.999						,		__A							:   Optional[Any]="cosine"						,		):
				if alpha_transform_type == "cosine":

								def alpha_bar_fn(__A							:   Optional[int]      ):
												return math.cos((t + 0.008) / 1.008 * math.pi / 2      ) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(__A							:   int      ):
												return math.exp(t * -12.0      )

				else:
								raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'      )

				a_		:  Any											=      []
				for i in range(__A      ):
								a_		:  List[Any]											=      i / num_diffusion_timesteps
								a_		:  str											=      (i + 1) / num_diffusion_timesteps
								betas.append(min(1 - alpha_bar_fn(__A      ) / alpha_bar_fn(__A      )						,		__A      )      )
				return torch.tensor(__A						,		dtype=torch.floataa      )





class 	SCREAMING_SNAKE_CASE					(					SCREAMING_SNAKE_CASE_	,   SCREAMING_SNAKE_CASE_       ):
			snake_case__  =				[e.name for e in KarrasDiffusionSchedulers]
			snake_case__  =				2






			@register_to_config
			def __init__( self      :			Tuple  ,						__SCREAMING_SNAKE_CASE      :			int = 1000  ,						__SCREAMING_SNAKE_CASE      :			float = 0.0_0085  ,						__SCREAMING_SNAKE_CASE      :			float = 0.012  ,						__SCREAMING_SNAKE_CASE      :			str = "linear"  ,						__SCREAMING_SNAKE_CASE      :			Optional[Union[np.ndarray, List[float]]] = None  ,						__SCREAMING_SNAKE_CASE      :			str = "epsilon"  ,						__SCREAMING_SNAKE_CASE      :			str = "linspace"  ,						__SCREAMING_SNAKE_CASE      :			int = 0  ,						)			->			Optional[Any]:
							if trained_betas is not None:
											a_		:  List[str]											=      torch.tensor(__SCREAMING_SNAKE_CASE  ,						dtype=torch.floataa					)
							elif beta_schedule == "linear":
											a_		:  Optional[int]											=      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.
											a_		:  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
											a_		:  Any											=      betas_for_alpha_bar(__SCREAMING_SNAKE_CASE					)
							else:
											raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'					)

							a_		:  str											=      1.0 - self.betas
							a_		:  Dict											=      torch.cumprod(self.alphas  ,						dim=0					)

							#  set all values
							self.set_timesteps(__SCREAMING_SNAKE_CASE  ,						__SCREAMING_SNAKE_CASE  ,						__SCREAMING_SNAKE_CASE					)






			def 			SCREAMING_SNAKE_CASE      ( self      :			List[Any]  ,						__SCREAMING_SNAKE_CASE      :			Any  ,						__SCREAMING_SNAKE_CASE      :			Tuple=None					)			->			str:
							if schedule_timesteps is None:
											a_		:  Any											=      self.timesteps

							a_		:  str											=      (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_		:  List[str]											=      1 if len(__SCREAMING_SNAKE_CASE					) > 1 else 0
							else:
											a_		:  List[str]											=      timestep.cpu().item() if torch.is_tensor(__SCREAMING_SNAKE_CASE					) else timestep
											a_		:  Union[str, Any]											=      self._index_counter[timestep_int]

							return indices[pos].item()






			@property
			def 			SCREAMING_SNAKE_CASE      ( self      :			List[Any]					)			->			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 			SCREAMING_SNAKE_CASE      ( self      :			Optional[int]  ,						__SCREAMING_SNAKE_CASE      :			torch.FloatTensor  ,						__SCREAMING_SNAKE_CASE      :			Union[float, torch.FloatTensor]  ,						)			->			torch.FloatTensor:
							a_		:  Tuple											=      self.index_for_timestep(__SCREAMING_SNAKE_CASE					)

							if self.state_in_first_order:
											a_		:  int											=      self.sigmas[step_index]
							else:
											a_		:  str											=      self.sigmas_interpol[step_index]

							a_		:  Optional[Any]											=      sample / ((sigma**2 + 1) ** 0.5)
							return sample






			def 			SCREAMING_SNAKE_CASE      ( self      :			Union[str, Any]  ,						__SCREAMING_SNAKE_CASE      :			int  ,						__SCREAMING_SNAKE_CASE      :			Union[str, torch.device] = None  ,						__SCREAMING_SNAKE_CASE      :			Optional[int] = None  ,						)			->			str:
							a_		:  List[Any]											=      num_inference_steps

							a_		:  Dict											=      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_		:  Optional[int]											=      np.linspace(0  ,						num_train_timesteps - 1  ,						__SCREAMING_SNAKE_CASE  ,						dtype=__SCREAMING_SNAKE_CASE					)[::-1].copy()
							elif self.config.timestep_spacing == "leading":
											a_		:  Optional[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_		:  int											=      (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":
											a_		:  int											=      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(__SCREAMING_SNAKE_CASE  ,						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\'.'					)

							a_		:  List[Any]											=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
							a_		:  Optional[Any]											=      torch.from_numpy(np.log(__SCREAMING_SNAKE_CASE					)					).to(__SCREAMING_SNAKE_CASE					)

							a_		:  Dict											=      np.interp(__SCREAMING_SNAKE_CASE  ,						np.arange(0  ,						len(__SCREAMING_SNAKE_CASE					)					)  ,						__SCREAMING_SNAKE_CASE					)
							a_		:  Optional[Any]											=      np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
							a_		:  List[Any]											=      torch.from_numpy(__SCREAMING_SNAKE_CASE					).to(device=__SCREAMING_SNAKE_CASE					)

							# interpolate sigmas
							a_		:  List[Any]											=      sigmas.log().lerp(sigmas.roll(1					).log()  ,						0.5					).exp()

							a_		:  List[Any]											=      torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
							a_		:  Dict											=      torch.cat(
							    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)

							if str(__SCREAMING_SNAKE_CASE					).startswith('''mps'''					):
											# mps does not support float64
											a_		:  List[str]											=      torch.from_numpy(__SCREAMING_SNAKE_CASE					).to(__SCREAMING_SNAKE_CASE  ,						dtype=torch.floataa					)
							else:
											a_		:  str											=      torch.from_numpy(__SCREAMING_SNAKE_CASE					).to(__SCREAMING_SNAKE_CASE					)

							# interpolate timesteps
							a_		:  int											=      self.sigma_to_t(__SCREAMING_SNAKE_CASE					).to(__SCREAMING_SNAKE_CASE  ,						dtype=timesteps.dtype					)
							a_		:  Optional[int]											=      torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])  ,						dim=-1					).flatten()

							a_		:  Tuple											=      torch.cat([timesteps[:1], interleaved_timesteps]					)

							a_		:  List[str]											=      None

							# for exp beta schedules, such as the one for `pipeline_shap_e.py`
							# we need an index counter
							a_		:  int											=      defaultdict(__SCREAMING_SNAKE_CASE					)






			def 			SCREAMING_SNAKE_CASE      ( self      :			str  ,						__SCREAMING_SNAKE_CASE      :			str					)			->			Dict:
							# get log sigma
							a_		:  Optional[Any]											=      sigma.log()

							# get distribution
							a_		:  Union[str, Any]											=      log_sigma - self.log_sigmas[:, None]

							# get sigmas range
							a_		:  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_		:  Tuple											=      self.log_sigmas[low_idx]
							a_		:  str											=      self.log_sigmas[high_idx]

							# interpolate sigmas
							a_		:  int											=      (low - log_sigma) / (low - high)
							a_		:  Optional[Any]											=      w.clamp(0  ,						1					)

							# transform interpolation to time range
							a_		:  int											=      (1 - w) * low_idx + w * high_idx
							a_		:  str											=      t.view(sigma.shape					)
							return t






			@property
			def 			SCREAMING_SNAKE_CASE      ( self      :			Optional[Any]					)			->			Optional[Any]:
							return self.sample is None






			def 			SCREAMING_SNAKE_CASE      ( self      :			str  ,						__SCREAMING_SNAKE_CASE      :			Union[torch.FloatTensor, np.ndarray]  ,						__SCREAMING_SNAKE_CASE      :			Union[float, torch.FloatTensor]  ,						__SCREAMING_SNAKE_CASE      :			Union[torch.FloatTensor, np.ndarray]  ,						__SCREAMING_SNAKE_CASE      :			bool = True  ,						)			->			Union[SchedulerOutput, Tuple]:
							a_		:  Dict											=      self.index_for_timestep(__SCREAMING_SNAKE_CASE					)

							# advance index counter by 1
							a_		:  int											=      timestep.cpu().item() if torch.is_tensor(__SCREAMING_SNAKE_CASE					) else timestep
							self._index_counter[timestep_int] += 1

							if self.state_in_first_order:
											a_		:  List[Any]											=      self.sigmas[step_index]
											a_		:  Optional[Any]											=      self.sigmas_interpol[step_index + 1]
											a_		:  Optional[Any]											=      self.sigmas[step_index + 1]
							else:
											# 2nd order / KDPM2's method
											a_		:  List[Any]											=      self.sigmas[step_index - 1]
											a_		:  List[str]											=      self.sigmas_interpol[step_index]
											a_		:  Tuple											=      self.sigmas[step_index]

							# 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_		:  Union[str, Any]											=      0
							a_		:  List[Any]											=      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
											a_		:  Tuple											=      sigma_hat if self.state_in_first_order else sigma_interpol
											a_		:  List[str]											=      sample - sigma_input * model_output
							elif self.config.prediction_type == "v_prediction":
											a_		:  Optional[Any]											=      sigma_hat if self.state_in_first_order else sigma_interpol
											a_		:  Dict											=      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_		:  Tuple											=      (sample - pred_original_sample) / sigma_hat
											# 3. delta timestep
											a_		:  Union[str, Any]											=      sigma_interpol - sigma_hat

											# store for 2nd order step
											a_		:  Dict											=      sample
							else:
											# DPM-Solver-2
											# 2. Convert to an ODE derivative for 2nd order
											a_		:  Optional[Any]											=      (sample - pred_original_sample) / sigma_interpol

											# 3. delta timestep
											a_		:  int											=      sigma_next - sigma_hat

											a_		:  List[str]											=      self.sample
											a_		:  str											=      None

							a_		:  Dict											=      sample + derivative * dt

							if not return_dict:
											return (prev_sample,)

							return SchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE					)






			def 			SCREAMING_SNAKE_CASE      ( self      :			str  ,						__SCREAMING_SNAKE_CASE      :			torch.FloatTensor  ,						__SCREAMING_SNAKE_CASE      :			torch.FloatTensor  ,						__SCREAMING_SNAKE_CASE      :			torch.FloatTensor  ,						)			->			torch.FloatTensor:
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							a_		:  Optional[int]											=      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
											a_		:  List[Any]											=      self.timesteps.to(original_samples.device  ,						dtype=torch.floataa					)
											a_		:  List[str]											=      timesteps.to(original_samples.device  ,						dtype=torch.floataa					)
							else:
											a_		:  Any											=      self.timesteps.to(original_samples.device					)
											a_		:  Union[str, Any]											=      timesteps.to(original_samples.device					)

							a_		:  Any											=      [self.index_for_timestep(__SCREAMING_SNAKE_CASE  ,						__SCREAMING_SNAKE_CASE					) for t in timesteps]

							a_		:  Dict											=      sigmas[step_indices].flatten()
							while len(sigma.shape					) < len(original_samples.shape					):
											a_		:  Union[str, Any]											=      sigma.unsqueeze(-1					)

							a_		:  Optional[Any]											=      original_samples + noise * sigma
							return noisy_samples







			def __len__( self      :			str					)			->			Optional[int]:
							return self.config.num_train_timesteps












'''simple docstring'''







from __future__ import annotations





def 		_UpperCAmelCase   (							__A							:   list[int]      ):
				a_		:  int											=      len(__A      ) // 2

				# choose the middle 3 elements
				a_		:  Dict											=      lst[m - 1 : m + 2]

				# if middle element is peak
				if three[1] > three[0] and three[1] > three[2]:
								return three[1]

				# if increasing, recurse on right
				elif three[0] < three[2]:
								if len(lst[:m]      ) == 2:
												m -= 1
								return peak(lst[m:]      )

				# decreasing
				else:
								if len(lst[:m]      ) == 2:
												m += 1
								return peak(lst[:m]      )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




