
"""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


snake_case    =		logging.get_logger(__name__)  # pylint: disable=invalid-name




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class      UpperCamelCase	(       __magic_name__      ):

				"""simple docstring"""



				UpperCAmelCase_				:      torch.FloatTensor
				UpperCAmelCase_				:      Optional[torch.FloatTensor]						  =				None






def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_=0.999,     SCREAMING_SNAKE_CASE_="cosine",     ):
					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

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

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

					SCREAMING_SNAKE_CASE				=	[]
					for i in range(SCREAMING_SNAKE_CASE_			):
										SCREAMING_SNAKE_CASE				=	i / num_diffusion_timesteps
										SCREAMING_SNAKE_CASE				=	(i + 1) / num_diffusion_timesteps
										betas.append(min(1 - alpha_bar_fn(SCREAMING_SNAKE_CASE_			) / alpha_bar_fn(SCREAMING_SNAKE_CASE_			),     SCREAMING_SNAKE_CASE_			)			)
					return torch.tensor(SCREAMING_SNAKE_CASE_,     dtype=torch.floataa			)




class      UpperCamelCase	(       __magic_name__  ,      __magic_name__      ):

				"""simple docstring"""



				UpperCAmelCase_				:      int						  =				[e.name for e in KarrasDiffusionSchedulers]
				UpperCAmelCase_				:      List[str]						  =				1


				@register_to_config
				def __init__(				self		,	lowercase__ = 1000		,	lowercase__ = 0.0_001		,	lowercase__ = 0.02		,	lowercase__ = "linear"		,	lowercase__ = None		,	lowercase__ = "epsilon"		,	lowercase__ = "linear"		,	lowercase__ = False		,	lowercase__ = "linspace"		,	lowercase__ = 0		,	)    ->    Any:
									"""simple docstring"""







									if trained_betas is not None:
														SCREAMING_SNAKE_CASE				=	torch.tensor(lowercase__		,	dtype=torch.floataa			)
									elif beta_schedule == "linear":
														SCREAMING_SNAKE_CASE				=	torch.linspace(lowercase__		,	lowercase__		,	lowercase__		,	dtype=torch.floataa			)
									elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														SCREAMING_SNAKE_CASE				=	(
														    torch.linspace(beta_start**0.5		,	beta_end**0.5		,	lowercase__		,	dtype=torch.floataa			) ** 2
														)
									elif beta_schedule == "squaredcos_cap_v2":
														# Glide cosine schedule
														SCREAMING_SNAKE_CASE				=	betas_for_alpha_bar(lowercase__			)
									else:
														raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''			)

									SCREAMING_SNAKE_CASE				=	1.0 - self.betas
									SCREAMING_SNAKE_CASE				=	torch.cumprod(self.alphas		,	dim=0			)

									SCREAMING_SNAKE_CASE				=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
									SCREAMING_SNAKE_CASE				=	np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
									SCREAMING_SNAKE_CASE				=	torch.from_numpy(lowercase__			)

									# setable values
									SCREAMING_SNAKE_CASE				=	None
									SCREAMING_SNAKE_CASE				=	np.linspace(0		,	num_train_timesteps - 1		,	lowercase__		,	dtype=lowercase__			)[::-1].copy()
									SCREAMING_SNAKE_CASE				=	torch.from_numpy(lowercase__			)
									SCREAMING_SNAKE_CASE				=	False
									SCREAMING_SNAKE_CASE				=	use_karras_sigmas


				@property
				def 							A					(				self			)    ->    Tuple:
									"""simple docstring"""







									if self.config.timestep_spacing in ["linspace", "trailing"]:
														return self.sigmas.max()

									return (self.sigmas.max() ** 2 + 1) ** 0.5


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    torch.FloatTensor:
									"""simple docstring"""







									if isinstance(lowercase__		,	torch.Tensor			):
														SCREAMING_SNAKE_CASE				=	timestep.to(self.timesteps.device			)
									SCREAMING_SNAKE_CASE				=	(self.timesteps == timestep).nonzero().item()
									SCREAMING_SNAKE_CASE				=	self.sigmas[step_index]

									SCREAMING_SNAKE_CASE				=	sample / ((sigma**2 + 1) ** 0.5)

									SCREAMING_SNAKE_CASE				=	True
									return sample


				def 							A					(				self		,	lowercase__		,	lowercase__ = None			)    ->    Optional[Any]:
									"""simple docstring"""







									SCREAMING_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":
														SCREAMING_SNAKE_CASE				=	np.linspace(0		,	self.config.num_train_timesteps - 1		,	lowercase__		,	dtype=lowercase__			)[
														    ::-1
														].copy()
									elif self.config.timestep_spacing == "leading":
														SCREAMING_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
														SCREAMING_SNAKE_CASE				=	(np.arange(0		,	lowercase__			) * step_ratio).round()[::-1].copy().astype(lowercase__			)
														timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
														SCREAMING_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
														SCREAMING_SNAKE_CASE				=	(np.arange(self.config.num_train_timesteps		,	0		,	-step_ratio			)).round().copy().astype(lowercase__			)
														timesteps -= 1
									else:
														raise ValueError(
														    f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''			)

									SCREAMING_SNAKE_CASE				=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
									SCREAMING_SNAKE_CASE				=	np.log(lowercase__			)

									if self.config.interpolation_type == "linear":
														SCREAMING_SNAKE_CASE				=	np.interp(lowercase__		,	np.arange(0		,	len(lowercase__			)			)		,	lowercase__			)
									elif self.config.interpolation_type == "log_linear":
														SCREAMING_SNAKE_CASE				=	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:
														SCREAMING_SNAKE_CASE				=	self._convert_to_karras(in_sigmas=lowercase__		,	num_inference_steps=self.num_inference_steps			)
														SCREAMING_SNAKE_CASE				=	np.array([self._sigma_to_t(lowercase__		,	lowercase__			) for sigma in sigmas]			)

									SCREAMING_SNAKE_CASE				=	np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
									SCREAMING_SNAKE_CASE				=	torch.from_numpy(lowercase__			).to(device=lowercase__			)
									if str(lowercase__			).startswith('mps'			):
														# mps does not support float64
														SCREAMING_SNAKE_CASE				=	torch.from_numpy(lowercase__			).to(lowercase__		,	dtype=torch.floataa			)
									else:
														SCREAMING_SNAKE_CASE				=	torch.from_numpy(lowercase__			).to(device=lowercase__			)


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    Union[str, Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	np.log(lowercase__			)

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

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

									SCREAMING_SNAKE_CASE				=	log_sigmas[low_idx]
									SCREAMING_SNAKE_CASE				=	log_sigmas[high_idx]

									# interpolate sigmas
									SCREAMING_SNAKE_CASE				=	(low - log_sigma) / (low - high)
									SCREAMING_SNAKE_CASE				=	np.clip(lowercase__		,	0		,	1			)

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


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    torch.FloatTensor:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	in_sigmas[-1].item()
									SCREAMING_SNAKE_CASE				=	in_sigmas[0].item()

									SCREAMING_SNAKE_CASE				=	7.0  # 7.0 is the value used in the paper
									SCREAMING_SNAKE_CASE				=	np.linspace(0		,	1		,	lowercase__			)
									SCREAMING_SNAKE_CASE				=	sigma_min ** (1 / rho)
									SCREAMING_SNAKE_CASE				=	sigma_max ** (1 / rho)
									SCREAMING_SNAKE_CASE				=	(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas


				def 							A					(				self		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__ = 0.0		,	lowercase__ = 0.0		,	lowercase__ = float('inf'			)		,	lowercase__ = 1.0		,	lowercase__ = None		,	lowercase__ = True		,	)    ->    Union[EulerDiscreteSchedulerOutput, Tuple]:
									"""simple docstring"""







									if (
									    isinstance(lowercase__		,	lowercase__			)
									    or isinstance(lowercase__		,	torch.IntTensor			)
									    or isinstance(lowercase__		,	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(lowercase__		,	torch.Tensor			):
														SCREAMING_SNAKE_CASE				=	timestep.to(self.timesteps.device			)

									SCREAMING_SNAKE_CASE				=	(self.timesteps == timestep).nonzero().item()
									SCREAMING_SNAKE_CASE				=	self.sigmas[step_index]

									SCREAMING_SNAKE_CASE				=	min(s_churn / (len(self.sigmas			) - 1)		,	2**0.5 - 1			) if s_tmin <= sigma <= s_tmax else 0.0

									SCREAMING_SNAKE_CASE				=	randn_tensor(
									    model_output.shape		,	dtype=model_output.dtype		,	device=model_output.device		,	generator=lowercase__			)

									SCREAMING_SNAKE_CASE				=	noise * s_noise
									SCREAMING_SNAKE_CASE				=	sigma * (gamma + 1)

									if gamma > 0:
														SCREAMING_SNAKE_CASE				=	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":
														SCREAMING_SNAKE_CASE				=	model_output
									elif self.config.prediction_type == "epsilon":
														SCREAMING_SNAKE_CASE				=	sample - sigma_hat * model_output
									elif self.config.prediction_type == "v_prediction":
														# * c_out + input * c_skip
														SCREAMING_SNAKE_CASE				=	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
									SCREAMING_SNAKE_CASE				=	(sample - pred_original_sample) / sigma_hat

									SCREAMING_SNAKE_CASE				=	self.sigmas[step_index + 1] - sigma_hat

									SCREAMING_SNAKE_CASE				=	sample + derivative * dt

									if not return_dict:
														return (prev_sample,)

									return EulerDiscreteSchedulerOutput(prev_sample=lowercase__		,	pred_original_sample=lowercase__			)


				def 							A					(				self		,	lowercase__		,	lowercase__		,	lowercase__		,	)    ->    torch.FloatTensor:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	self.sigmas.to(device=original_samples.device		,	dtype=original_samples.dtype			)
									if original_samples.device.type == "mps" and torch.is_floating_point(lowercase__			):
														# mps does not support float64
														SCREAMING_SNAKE_CASE				=	self.timesteps.to(original_samples.device		,	dtype=torch.floataa			)
														SCREAMING_SNAKE_CASE				=	timesteps.to(original_samples.device		,	dtype=torch.floataa			)
									else:
														SCREAMING_SNAKE_CASE				=	self.timesteps.to(original_samples.device			)
														SCREAMING_SNAKE_CASE				=	timesteps.to(original_samples.device			)

									SCREAMING_SNAKE_CASE				=	[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

									SCREAMING_SNAKE_CASE				=	original_samples + noise * sigma
									return noisy_samples




				def __len__(				self			)    ->    List[Any]:
									"""simple docstring"""







									return self.config.num_train_timesteps








from __future__ import annotations

from collections.abc import Generator

def    lowerCAmelCase__		(			_a				:	int			):
		if not isinstance(_a     ,					_a			) or n < 1:
				raise Exception("Sequence only defined for positive integers"			)

		yield n
		while n != 1:
				if n % 2 == 0:
						n //= 2
				else:
						snake_case_ :							List[str]         =				3 * n + 1
				yield n

def    lowerCAmelCase__		(			):
		snake_case_ :							Optional[int]         =				43
		snake_case_ :							Union[str, Any]         =				tuple(collatz_sequence(_a			)			)
		print(_a			)
		print(F'''Collatz sequence from {n} took {len(_a			)} steps.'''			)


if __name__ == "__main__":
							main()
