
"""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 				A_  (__a					, __a=0.999					, __a="cosine"					, ):

					'''simple docstring'''





					if alpha_transform_type == "cosine":

										def alpha_bar_fn(__a					):
															return math.cos((t + 0.008) / 1.008 * math.pi / 2					) ** 2

					elif alpha_transform_type == "exp":

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

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

					A_								=    []
					for i in range(__a					):
										A_								=    i / num_diffusion_timesteps
										A_								=    (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 __lowerCAmelCase					(       _lowercase  ,					_lowercase   ):




			"""simple docstring"""







			snake_case						   =					[e.name for e in KarrasDiffusionSchedulers]
			snake_case						   =					2




			@register_to_config
			def __init__(					self    :       int							, _snake_case    :       int = 1_000							, _snake_case    :       float = 0.0_0_0_8_5							, _snake_case    :       float = 0.0_1_2							, _snake_case    :       str = "linear"							, _snake_case    :       Optional[Union[np.ndarray, List[float]]] = None							, _snake_case    :       str = "epsilon"							, _snake_case    :       str = "linspace"							, _snake_case    :       int = 0							, )   ->			Optional[Any]:







								"""simple docstring"""
								if trained_betas is not None:
													A_								=    torch.tensor(_snake_case							, dtype=torch.floataa						)
								elif beta_schedule == "linear":
													A_								=    torch.linspace(_snake_case							, _snake_case							, _snake_case							, 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							, _snake_case							, dtype=torch.floataa						) ** 2
													)
								elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													A_								=    betas_for_alpha_bar(_snake_case						)
								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						)

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




			def   lowerCamelCase__  (					self    :       Any							, _snake_case    :       str							, _snake_case    :       Tuple=None						)   ->			Optional[Any]:







								"""simple docstring"""
								if schedule_timesteps is None:
													A_								=    self.timesteps

								A_								=    (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_								=    1 if len(_snake_case						) > 1 else 0
								else:
													A_								=    timestep.cpu().item() if torch.is_tensor(_snake_case						) else timestep
													A_								=    self._index_counter[timestep_int]

								return indices[pos].item()




			@property
			def   lowerCamelCase__  (					self    :       Tuple						)   ->			Dict:







								"""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   lowerCamelCase__  (					self    :       List[str]							, _snake_case    :       torch.FloatTensor							, _snake_case    :       Union[float, torch.FloatTensor]							, )   ->			torch.FloatTensor:







								"""simple docstring"""
								A_								=    self.index_for_timestep(_snake_case						)

								if self.state_in_first_order:
													A_								=    self.sigmas[step_index]
								else:
													A_								=    self.sigmas_interpol[step_index]

								A_								=    sample / ((sigma**2 + 1) ** 0.5)
								return sample




			def   lowerCamelCase__  (					self    :       List[Any]							, _snake_case    :       int							, _snake_case    :       Union[str, torch.device] = None							, _snake_case    :       Optional[int] = None							, )   ->			Any:







								"""simple docstring"""
								A_								=    num_inference_steps

								A_								=    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_								=    np.linspace(0							, num_train_timesteps - 1							, _snake_case							, dtype=_snake_case						)[::-1].copy()
								elif self.config.timestep_spacing == "leading":
													A_								=    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							, _snake_case						) * step_ratio).round()[::-1].copy().astype(_snake_case						)
													timesteps += self.config.steps_offset
								elif self.config.timestep_spacing == "trailing":
													A_								=    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(_snake_case							, 0							, -step_ratio						)).round().copy().astype(_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_								=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
								A_								=    torch.from_numpy(np.log(_snake_case						)						).to(_snake_case						)

								A_								=    np.interp(_snake_case							, np.arange(0							, len(_snake_case						)						)							, _snake_case						)
								A_								=    np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
								A_								=    torch.from_numpy(_snake_case						).to(device=_snake_case						)

								# interpolate sigmas
								A_								=    sigmas.log().lerp(sigmas.roll(1						).log()							, 0.5						).exp()

								A_								=    torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2						), sigmas[-1:]]						)
								A_								=    torch.cat(
								    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2						), sigmas_interpol[-1:]]						)

								if str(_snake_case						).startswith("mps"						):
													# mps does not support float64
													A_								=    torch.from_numpy(_snake_case						).to(_snake_case							, dtype=torch.floataa						)
								else:
													A_								=    torch.from_numpy(_snake_case						).to(_snake_case						)

								# interpolate timesteps
								A_								=    self.sigma_to_t(_snake_case						).to(_snake_case							, dtype=timesteps.dtype						)
								A_								=    torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])							, dim=-1						).flatten()

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

								A_								=    None

								# for exp beta schedules, such as the one for `pipeline_shap_e.py`
								# we need an index counter
								A_								=    defaultdict(_snake_case						)




			def   lowerCamelCase__  (					self    :       Optional[Any]							, _snake_case    :       Optional[int]						)   ->			Optional[Any]:







								"""simple docstring"""
								# get log sigma
								A_								=    sigma.log()

								# get distribution
								A_								=    log_sigma - self.log_sigmas[:, None]

								# get sigmas range
								A_								=    dists.ge(0						).cumsum(dim=0						).argmax(dim=0						).clamp(max=self.log_sigmas.shape[0] - 2						)
								A_								=    low_idx + 1

								A_								=    self.log_sigmas[low_idx]
								A_								=    self.log_sigmas[high_idx]

								# interpolate sigmas
								A_								=    (low - log_sigma) / (low - high)
								A_								=    w.clamp(0							, 1						)

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




			@property
			def   lowerCamelCase__  (					self    :       Union[str, Any]						)   ->			Tuple:







								"""simple docstring"""
								return self.sample is None




			def   lowerCamelCase__  (					self    :       int							, _snake_case    :       Union[torch.FloatTensor, np.ndarray]							, _snake_case    :       Union[float, torch.FloatTensor]							, _snake_case    :       Union[torch.FloatTensor, np.ndarray]							, _snake_case    :       bool = True							, )   ->			Union[SchedulerOutput, Tuple]:







								"""simple docstring"""
								A_								=    self.index_for_timestep(_snake_case						)

								# advance index counter by 1
								A_								=    timestep.cpu().item() if torch.is_tensor(_snake_case						) else timestep
								self._index_counter[timestep_int] += 1

								if self.state_in_first_order:
													A_								=    self.sigmas[step_index]
													A_								=    self.sigmas_interpol[step_index + 1]
													A_								=    self.sigmas[step_index + 1]
								else:
													# 2nd order / KDPM2's method
													A_								=    self.sigmas[step_index - 1]
													A_								=    self.sigmas_interpol[step_index]
													A_								=    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_								=    0
								A_								=    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_								=    sigma_hat if self.state_in_first_order else sigma_interpol
													A_								=    sample - sigma_input * model_output
								elif self.config.prediction_type == "v_prediction":
													A_								=    sigma_hat if self.state_in_first_order else sigma_interpol
													A_								=    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_								=    (sample - pred_original_sample) / sigma_hat
													# 3. delta timestep
													A_								=    sigma_interpol - sigma_hat

													# store for 2nd order step
													A_								=    sample
								else:
													# DPM-Solver-2
													# 2. Convert to an ODE derivative for 2nd order
													A_								=    (sample - pred_original_sample) / sigma_interpol

													# 3. delta timestep
													A_								=    sigma_next - sigma_hat

													A_								=    self.sample
													A_								=    None

								A_								=    sample + derivative * dt

								if not return_dict:
													return (prev_sample,)

								return SchedulerOutput(prev_sample=_snake_case						)




			def   lowerCamelCase__  (					self    :       List[Any]							, _snake_case    :       torch.FloatTensor							, _snake_case    :       torch.FloatTensor							, _snake_case    :       torch.FloatTensor							, )   ->			torch.FloatTensor:







								"""simple docstring"""
								# 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(_snake_case						):
													# 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_								=    [self.index_for_timestep(_snake_case							, _snake_case						) 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    :       Union[str, Any]						)   ->			Tuple:







								"""simple docstring"""
								return self.config.num_train_timesteps






"""simple docstring"""





import operator
def 				A_  (__a					, __a = False					, __a = None					):

					'''simple docstring'''





					A_								=    operator.lt if reverse else operator.gt
					A_								=    solution or []

					if not arr:
										return solution

					A_								=    [arr.pop(0					)]
					for i, item in enumerate(__a					):
										if _operator(__a					, sublist[-1]					):
															sublist.append(__a					)
															arr.pop(__a					)

    #  merging sublist into solution list
					if not solution:
										solution.extend(__a					)
					else:
										while sublist:
															A_								=    sublist.pop(0					)
															for i, xx in enumerate(__a					):
																				if not _operator(__a					, __a					):
																									solution.insert(__a					, __a					)
																									break
															else:
																				solution.append(__a					)

					strand_sort(__a					, __a					, __a					)
					return solution


if __name__ == "__main__":
		assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
		assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]




