





"""simple docstring"""






import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 					__UpperCAmelCase							(						_UpperCamelCase  ):
				__lowerCamelCase				:	torch.FloatTensor
				__lowerCamelCase				:	Optional[torch.FloatTensor]				     =				None






def      lowercase__ (					lowerCAmelCase__   :			int							,			lowerCAmelCase__   :			str=0.999							,			lowerCAmelCase__   :			Union[str, Any]="cosine"							,			)    ->			Dict:



			'''simple docstring'''
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(lowerCAmelCase__   :			List[Any]			):
									return math.cos((t + 0.008) / 1.008 * math.pi / 2			) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(lowerCAmelCase__   :			List[Any]			):
									return math.exp(t * -12.0			)

			else:
						raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"			)

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





class 					__UpperCAmelCase							(						_UpperCamelCase						,  _UpperCamelCase  ):
				@register_to_config
				def __init__(		self    :			Any	, a_    :			int = 10_00	, a_    :			str = "fixed_small_log"	, a_    :			bool = True	, a_    :			Optional[float] = 1.0	, a_    :			str = "epsilon"	, a_    :			str = "squaredcos_cap_v2"	, )	->	Tuple:



							'''simple docstring'''



							if beta_schedule != "squaredcos_cap_v2":
										raise ValueError("UnCLIPScheduler only supports `beta_schedule`: 'squaredcos_cap_v2'"    )

							a__  :	Tuple		 =			betas_for_alpha_bar(a_    )

							a__  :	str		 =			1.0 - self.betas
							a__  :	List[str]		 =			torch.cumprod(self.alphas	, dim=0    )
							a__  :	str		 =			torch.tensor(1.0    )

							# standard deviation of the initial noise distribution
							a__  :	Any		 =			1.0

							# setable values
							a__  :	str		 =			None
							a__  :	List[Any]		 =			torch.from_numpy(np.arange(0	, a_    )[::-1].copy()    )

							a__  :	List[str]		 =			variance_type
				def       UpperCAmelCase      (		self    :			Dict	, a_    :			torch.FloatTensor	, a_    :			Optional[int] = None    )	->	torch.FloatTensor:



							'''simple docstring'''



							return sample
				def       UpperCAmelCase      (		self    :			List[str]	, a_    :			int	, a_    :			Union[str, torch.device] = None    )	->	Optional[Any]:



							'''simple docstring'''



							a__  :	List[Any]		 =			num_inference_steps
							a__  :	List[str]		 =			(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
							a__  :	Tuple		 =			(np.arange(0	, a_    ) * step_ratio).round()[::-1].copy().astype(np.intaa    )
							a__  :	List[str]		 =			torch.from_numpy(a_    ).to(a_    )
				def       UpperCAmelCase      (		self    :			Union[str, Any]	, a_    :			Any	, a_    :			Dict=None	, a_    :			Dict=None	, a_    :			Any=None    )	->	List[str]:



							'''simple docstring'''



							if prev_timestep is None:
										a__  :	Tuple		 =			t - 1

							a__  :	List[str]		 =			self.alphas_cumprod[t]
							a__  :	Dict		 =			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
							a__  :	List[str]		 =			1 - alpha_prod_t
							a__  :	str		 =			1 - alpha_prod_t_prev

							if prev_timestep == t - 1:
										a__  :	Union[str, Any]		 =			self.betas[t]
							else:
										a__  :	Dict		 =			1 - alpha_prod_t / alpha_prod_t_prev

							# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
							# and sample from it to get previous sample
							# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
							a__  :	str		 =			beta_prod_t_prev / beta_prod_t * beta

							if variance_type is None:
										a__  :	Union[str, Any]		 =			self.config.variance_type

							# hacks - were probably added for training stability
							if variance_type == "fixed_small_log":
										a__  :	int		 =			torch.log(torch.clamp(a_	, min=1E-20    )    )
										a__  :	List[Any]		 =			torch.exp(0.5 * variance    )
							elif variance_type == "learned_range":
										# NOTE difference with DDPM scheduler
										a__  :	Union[str, Any]		 =			variance.log()
										a__  :	Optional[int]		 =			beta.log()

										a__  :	Tuple		 =			(predicted_variance + 1) / 2
										a__  :	List[str]		 =			frac * max_log + (1 - frac) * min_log

							return variance
				def       UpperCAmelCase      (		self    :			List[Any]	, a_    :			torch.FloatTensor	, a_    :			int	, a_    :			torch.FloatTensor	, a_    :			Optional[int] = None	, a_    :			List[str]=None	, a_    :			bool = True	, )	->	Union[UnCLIPSchedulerOutput, Tuple]:



							'''simple docstring'''



							a__  :	str		 =			timestep

							if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
										a__ ,	a__  :	Tuple		 =			torch.split(a_	, sample.shape[1]	, dim=1    )
							else:
										a__  :	Any		 =			None

							# 1. compute alphas, betas
							if prev_timestep is None:
										a__  :	Tuple		 =			t - 1

							a__  :	Union[str, Any]		 =			self.alphas_cumprod[t]
							a__  :	Any		 =			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
							a__  :	Any		 =			1 - alpha_prod_t
							a__  :	Any		 =			1 - alpha_prod_t_prev

							if prev_timestep == t - 1:
										a__  :	Any		 =			self.betas[t]
										a__  :	List[str]		 =			self.alphas[t]
							else:
										a__  :	Dict		 =			1 - alpha_prod_t / alpha_prod_t_prev
										a__  :	str		 =			1 - beta

							# 2. compute predicted original sample from predicted noise also called
							# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
							if self.config.prediction_type == "epsilon":
										a__  :	Any		 =			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
							elif self.config.prediction_type == "sample":
										a__  :	Any		 =			model_output
							else:
										raise ValueError(
										    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
										    " for the UnCLIPScheduler."    )

							# 3. Clip "predicted x_0"
							if self.config.clip_sample:
										a__  :	str		 =			torch.clamp(
										    a_	, -self.config.clip_sample_range	, self.config.clip_sample_range    )

							# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
							# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
							a__  :	Optional[int]		 =			(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
							a__  :	str		 =			alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

							# 5. Compute predicted previous sample µ_t
							# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
							a__  :	Optional[Any]		 =			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

							# 6. Add noise
							a__  :	Any		 =			0
							if t > 0:
										a__  :	Dict		 =			randn_tensor(
										    model_output.shape	, dtype=model_output.dtype	, generator=a_	, device=model_output.device    )

										a__  :	str		 =			self._get_variance(
										    a_	, predicted_variance=a_	, prev_timestep=a_	, )

										if self.variance_type == "fixed_small_log":
													a__  :	int		 =			variance
										elif self.variance_type == "learned_range":
													a__  :	Any		 =			(0.5 * variance).exp()
										else:
													raise ValueError(
													    F"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
													    " for the UnCLIPScheduler."    )

										a__  :	Optional[Any]		 =			variance * variance_noise

							a__  :	Optional[int]		 =			pred_prev_sample + variance

							if not return_dict:
										return (pred_prev_sample,)

							return UnCLIPSchedulerOutput(prev_sample=a_	, pred_original_sample=a_    )






				def       UpperCAmelCase      (		self    :			Optional[int]	, a_    :			torch.FloatTensor	, a_    :			torch.FloatTensor	, a_    :			torch.IntTensor	, )	->	torch.FloatTensor:



							'''simple docstring'''



							a__  :	List[str]		 =			self.alphas_cumprod.to(device=original_samples.device	, dtype=original_samples.dtype    )
							a__  :	List[str]		 =			timesteps.to(original_samples.device    )

							a__  :	Optional[Any]		 =			alphas_cumprod[timesteps] ** 0.5
							a__  :	Optional[int]		 =			sqrt_alpha_prod.flatten()
							while len(sqrt_alpha_prod.shape    ) < len(original_samples.shape    ):
										a__  :	List[str]		 =			sqrt_alpha_prod.unsqueeze(-1    )

							a__  :	List[Any]		 =			(1 - alphas_cumprod[timesteps]) ** 0.5
							a__  :	int		 =			sqrt_one_minus_alpha_prod.flatten()
							while len(sqrt_one_minus_alpha_prod.shape    ) < len(original_samples.shape    ):
										a__  :	Union[str, Any]		 =			sqrt_one_minus_alpha_prod.unsqueeze(-1    )

							a__  :	Optional[int]		 =			sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
							return noisy_samples






"""simple docstring"""






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors






def      lowercase__ (					lowerCAmelCase__   :			int			)    ->			int:



			'''simple docstring'''
			a__  :	Tuple		 =			prime_factors(lowerCAmelCase__			)
			if is_square_free(lowerCAmelCase__			):
						return -1 if len(lowerCAmelCase__			) % 2 else 1
			return 0


if __name__ == "__main__":
		import doctest

		doctest.testmod()