






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 					__SCREAMING_SNAKE_CASE(		a_		):
							_UpperCAmelCase	      =    42
							_UpperCAmelCase	      =    42


def        a_	( _A ,				_A=0.999 ,				_A="cosine" ,				)     ->     Optional[Any]:







				"""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}'''					)

				snake_case__													=       []
				for i in range(_A					):
								snake_case__													=       i / num_diffusion_timesteps
								snake_case__													=       (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(		a_      ,					a_		):
							_UpperCAmelCase	      =    1
							@register_to_config
							def __init__(       self: Optional[int]    ,		UpperCamelCase: int = 10_00    ,		UpperCamelCase: float = 0.0_001    ,		UpperCamelCase: float = 0.02    ,		UpperCamelCase: str = "linear"    ,		UpperCamelCase: float = 0.0    ,		UpperCamelCase: Optional[np.ndarray] = None    ,		UpperCamelCase: bool = True    ,		)						->						int:
											if trained_betas is not None:
															snake_case__													=       torch.from_numpy(UpperCamelCase  )
											elif beta_schedule == "linear":
															snake_case__													=       torch.linspace(UpperCamelCase    ,		UpperCamelCase    ,		UpperCamelCase    ,		dtype=torch.floataa  )
											elif beta_schedule == "scaled_linear":
															# this schedule is very specific to the latent diffusion model.
															snake_case__													=       (
															    torch.linspace(beta_start**0.5    ,		beta_end**0.5    ,		UpperCamelCase    ,		dtype=torch.floataa  ) ** 2
															)
											elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															snake_case__													=       betas_for_alpha_bar(UpperCamelCase  )
											elif beta_schedule == "sigmoid":
															# GeoDiff sigmoid schedule
															snake_case__													=       torch.linspace(-6    ,		6    ,		UpperCamelCase  )
															snake_case__													=       torch.sigmoid(UpperCamelCase  ) * (beta_end - beta_start) + beta_start
											else:
															raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''  )

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

											snake_case__													=       torch.tensor(1.0  )

											# standard deviation of the initial noise distribution
											snake_case__													=       1.0

											# setable values
											snake_case__													=       None
											snake_case__													=       torch.from_numpy(np.arange(0    ,		UpperCamelCase  )[::-1].copy()  )

											snake_case__													=       eta
							def lowerCAmelCase_	(       self: str    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: Optional[int] = None  )						->						torch.FloatTensor:
											return sample
							def lowerCAmelCase_	(       self: Optional[int]    ,		UpperCamelCase: int    ,		UpperCamelCase: int = 10    ,		UpperCamelCase: int = 10    ,		UpperCamelCase: Union[str, torch.device] = None    ,		)						->						Union[str, Any]:
											snake_case__													=       min(self.config.num_train_timesteps    ,		UpperCamelCase  )
											snake_case__													=       num_inference_steps

											snake_case__													=       []

											snake_case__													=       {}
											for j in range(0    ,		num_inference_steps - jump_length    ,		UpperCamelCase  ):
															snake_case__													=       jump_n_sample - 1

											snake_case__													=       num_inference_steps
											while t >= 1:
															snake_case__													=       t - 1
															timesteps.append(UpperCamelCase  )

															if jumps.get(UpperCamelCase    ,		0  ) > 0:
																			snake_case__													=       jumps[t] - 1
																			for _ in range(UpperCamelCase  ):
																							snake_case__													=       t + 1
																							timesteps.append(UpperCamelCase  )

											snake_case__													=       np.array(UpperCamelCase  ) * (self.config.num_train_timesteps // self.num_inference_steps)
											snake_case__													=       torch.from_numpy(UpperCamelCase  ).to(UpperCamelCase  )
							def lowerCAmelCase_	(       self: Any    ,		UpperCamelCase: Optional[Any]  )						->						str:
											snake_case__													=       t - self.config.num_train_timesteps // self.num_inference_steps

											snake_case__													=       self.alphas_cumprod[t]
											snake_case__													=       self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
											snake_case__													=       1 - alpha_prod_t
											snake_case__													=       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]
											snake_case__													=       (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

											return variance
							def lowerCAmelCase_	(       self: Tuple    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: int    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: Optional[torch.Generator] = None    ,		UpperCamelCase: bool = True    ,		)						->						Union[RePaintSchedulerOutput, Tuple]:
											snake_case__													=       timestep
											snake_case__													=       timestep - self.config.num_train_timesteps // self.num_inference_steps

											# 1. compute alphas, betas
											snake_case__													=       self.alphas_cumprod[t]
											snake_case__													=       self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
											snake_case__													=       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
											snake_case__													=       (sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

											# 3. Clip "predicted x_0"
											if self.config.clip_sample:
															snake_case__													=       torch.clamp(UpperCamelCase    ,		-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
											snake_case__													=       model_output.device
											snake_case__													=       randn_tensor(model_output.shape    ,		generator=UpperCamelCase    ,		device=UpperCamelCase    ,		dtype=model_output.dtype  )
											snake_case__													=       self.eta * self._get_variance(UpperCamelCase  ) ** 0.5

											snake_case__													=       0
											if t > 0 and self.eta > 0:
															snake_case__													=       std_dev_t * noise

											# 6. compute "direction pointing to x_t" of formula (12)
											# from https://arxiv.org/pdf/2010.02502.pdf
											snake_case__													=       (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
											snake_case__													=       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
											snake_case__													=       (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
											snake_case__													=       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=UpperCamelCase    ,		pred_original_sample=UpperCamelCase  )
							def lowerCAmelCase_	(       self: List[Any]    ,		UpperCamelCase: Optional[int]    ,		UpperCamelCase: Any    ,		UpperCamelCase: Any=None  )						->						str:
											snake_case__													=       self.config.num_train_timesteps // self.num_inference_steps

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

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

											return sample
							def lowerCAmelCase_	(       self: Dict    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: torch.FloatTensor    ,		UpperCamelCase: torch.IntTensor    ,		)						->						torch.FloatTensor:
											raise NotImplementedError('Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'  )


							def __len__(       self: Union[str, Any]  )						->						Tuple:
											return self.config.num_train_timesteps












def        a_	( _A ,				_A					)     ->     Union[str, Any]:







				"""simple docstring"""
				snake_case__													=       1
				while b > 0:
								if b & 1:
												res *= a

								a *= a
								b >>= 1

				return res
def        a_	( _A ,				_A ,				_A					)     ->     Dict:







				"""simple docstring"""
				snake_case__													=       1
				while b > 0:
								if b & 1:
												snake_case__													=       ((res % c) * (a % c)) % c

								a *= a
								b >>= 1

				return res




