






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
class      UpperCamelCase_							(				UpperCamelCase       ):
						lowercase									=  42
						lowercase									=  42






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase=0.9_9_9    ,	UpperCAmelCase="cosine"    ,	)     ->		str:







							"""simple docstring"""





							if alpha_transform_type == "cosine":

														def alpha_bar_fn(UpperCAmelCase     ):
																					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(UpperCAmelCase     ):
																					return math.exp(t * -1_2.0     )

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

							_a  :    Tuple			=						[]
							for i in range(_SCREAMING_SNAKE_CASE     ):
														_a  :    Dict			=						i / num_diffusion_timesteps
														_a  :    List[Any]			=						(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_							(				UpperCamelCase ,       UpperCamelCase       ):
						lowercase									=  1




						@register_to_config
						def __init__(    self		,	lowercase = 1_000		,	lowercase = 0.0001		,	lowercase = 0.02		,	lowercase = "linear"		,	lowercase = 0.0		,	lowercase = None		,	lowercase = True		,	)			->						int:
													if trained_betas is not None:
																				_a  :    Tuple			=						torch.from_numpy(_lowerCamelCase       )
													elif beta_schedule == "linear":
																				_a  :    int			=						torch.linspace(_lowerCamelCase		,	_lowerCamelCase		,	_lowerCamelCase		,	dtype=torch.floataa       )
													elif beta_schedule == "scaled_linear":
																				# this schedule is very specific to the latent diffusion model.
																				_a  :    str			=						(
																				    torch.linspace(beta_start**0.5		,	beta_end**0.5		,	_lowerCamelCase		,	dtype=torch.floataa       ) ** 2
																				)
													elif beta_schedule == "squaredcos_cap_v2":
																				# Glide cosine schedule
																				_a  :    List[str]			=						betas_for_alpha_bar(_lowerCamelCase       )
													elif beta_schedule == "sigmoid":
																				# GeoDiff sigmoid schedule
																				_a  :    str			=						torch.linspace(-6		,	6		,	_lowerCamelCase       )
																				_a  :    List[str]			=						torch.sigmoid(_lowerCamelCase       ) * (beta_end - beta_start) + beta_start
													else:
																				raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'       )

													_a  :    Dict			=						1.0 - self.betas
													_a  :    Any			=						torch.cumprod(self.alphas		,	dim=0       )
													_a  :    Optional[int]			=						torch.tensor(1.0       )

													_a  :    Any			=						torch.tensor(1.0       )

													# standard deviation of the initial noise distribution
													_a  :    str			=						1.0

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

													_a  :    List[Any]			=						eta




						def      snake_case__(    self		,	lowercase		,	lowercase = None       )			->						Tuple:
													return sample




						def      snake_case__(    self		,	lowercase		,	lowercase = 10		,	lowercase = 10		,	lowercase = None		,	)			->						Union[str, Any]:
													_a  :    List[Any]			=						min(self.config.num_train_timesteps		,	_lowerCamelCase       )
													_a  :    List[str]			=						num_inference_steps

													_a  :    Any			=						[]

													_a  :    List[Any]			=						{}
													for j in range(0		,	num_inference_steps - jump_length		,	_lowerCamelCase       ):
																				_a  :    Optional[int]			=						jump_n_sample - 1

													_a  :    Dict			=						num_inference_steps
													while t >= 1:
																				_a  :    Union[str, Any]			=						t - 1
																				timesteps.append(_lowerCamelCase       )

																				if jumps.get(_lowerCamelCase		,	0       ) > 0:
																											_a  :    str			=						jumps[t] - 1
																											for _ in range(_lowerCamelCase       ):
																																		_a  :    Any			=						t + 1
																																		timesteps.append(_lowerCamelCase       )

													_a  :    int			=						np.array(_lowerCamelCase       ) * (self.config.num_train_timesteps // self.num_inference_steps)
													_a  :    Optional[Any]			=						torch.from_numpy(_lowerCamelCase       ).to(_lowerCamelCase       )




						def      snake_case__(    self		,	lowercase       )			->						Tuple:
													_a  :    Dict			=						t - self.config.num_train_timesteps // self.num_inference_steps

													_a  :    int			=						self.alphas_cumprod[t]
													_a  :    Optional[int]			=						self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
													_a  :    List[str]			=						1 - alpha_prod_t
													_a  :    Optional[Any]			=						1 - 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
													# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
													# without eta.
													# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
													_a  :    Optional[int]			=						(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

													return variance




						def      snake_case__(    self		,	lowercase		,	lowercase		,	lowercase		,	lowercase		,	lowercase		,	lowercase = None		,	lowercase = True		,	)			->						Any:
													_a  :    str			=						timestep
													_a  :    Dict			=						timestep - self.config.num_train_timesteps // self.num_inference_steps

													# 1. compute alphas, betas
													_a  :    List[str]			=						self.alphas_cumprod[t]
													_a  :    Optional[Any]			=						self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
													_a  :    str			=						1 - alpha_prod_t

													# 2. compute predicted original sample from predicted noise also called
													# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
													_a  :    int			=						(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

													# 3. Clip "predicted x_0"
													if self.config.clip_sample:
																				_a  :    Union[str, Any]			=						torch.clamp(_lowerCamelCase		,	-1		,	1       )

													# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
													# substitute formula (7) in the algorithm coming from DDPM paper
													# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
													# DDIM schedule gives the same results as DDPM with eta = 1.0
													# Noise is being reused in 7. and 8., but no impact on quality has
													# been observed.

													# 5. Add noise
													_a  :    Optional[int]			=						model_output.device
													_a  :    Any			=						randn_tensor(model_output.shape		,	generator=_lowerCamelCase		,	device=_lowerCamelCase		,	dtype=model_output.dtype       )
													_a  :    List[str]			=						self.eta * self._get_variance(_lowerCamelCase       ) ** 0.5

													_a  :    int			=						0
													if t > 0 and self.eta > 0:
																				_a  :    str			=						std_dev_t * noise

													# 6. compute "direction pointing to x_t" of formula (12)
													# from https://arxiv.org/pdf/2010.02502.pdf
													_a  :    int			=						(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

													# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													_a  :    Union[str, Any]			=						alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

													# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
													_a  :    Optional[Any]			=						(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

													# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
													_a  :    List[Any]			=						mask * prev_known_part + (1.0 - mask) * prev_unknown_part

													if not return_dict:
																				return (
																				    pred_prev_sample,
																				    pred_original_sample,
																				)

													return RePaintSchedulerOutput(prev_sample=_lowerCamelCase		,	pred_original_sample=_lowerCamelCase       )




						def      snake_case__(    self		,	lowercase		,	lowercase		,	lowercase=None       )			->						Optional[int]:
													_a  :    Union[str, Any]			=						self.config.num_train_timesteps // self.num_inference_steps

													for i in range(_lowerCamelCase       ):
																				_a  :    Union[str, Any]			=						self.betas[timestep + i]
																				if sample.device.type == "mps":
																											# randn does not work reproducibly on mps
																											_a  :    Dict			=						randn_tensor(sample.shape		,	dtype=sample.dtype		,	generator=_lowerCamelCase       )
																											_a  :    Any			=						noise.to(sample.device       )
																				else:
																											_a  :    Union[str, Any]			=						randn_tensor(sample.shape		,	generator=_lowerCamelCase		,	device=sample.device		,	dtype=sample.dtype       )

																				# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
																				_a  :    int			=						(1 - beta) ** 0.5 * sample + beta**0.5 * noise

													return sample




						def      snake_case__(    self		,	lowercase		,	lowercase		,	lowercase		,	)			->						Any:
													raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'''       )







						def __len__(    self       )			->						Any:
													return self.config.num_train_timesteps

def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      Dict:

							"""simple docstring"""






							if power < 0:
														return -1
							base %= mod
							_UpperCAmelCase  :			Optional[Any]	       =		1

							while power > 0:
														if power & 1:
																					_UpperCAmelCase  :			Optional[Any]	       =		(result * base) % mod
														_UpperCAmelCase  :			List[str]	       =		power >> 1
														_UpperCAmelCase  :			Optional[int]	       =		(base * base) % mod

							return result




def 		lowerCAmelCase_     (     )   ->      List[str]:

							"""simple docstring"""






							print(modular_exponential(3      ,	2_0_0      ,	1_3  )  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				main()




