




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 	__lowerCAmelCase			(			__magic_name__				):
							UpperCamelCase__        =						42
							UpperCamelCase__        =						42







def 	__A	(			__lowerCamelCase							,    __lowerCamelCase=0.999							,    __lowerCamelCase="cosine"							,    )   -> List[Any]:
					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

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

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

					a		       =							[]
					for i in range(__lowerCamelCase					):
										a		       =							i / num_diffusion_timesteps
										a		       =							(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 	__lowerCAmelCase			(			__magic_name__   , __magic_name__				):
							UpperCamelCase__        =						1
							@register_to_config
							def __init__(		self		:Any	,   __magic_name__		:Optional[Any] = 1000	,   __magic_name__		:str = 0.0001	,   __magic_name__		:str = 0.02	,   __magic_name__		:str = "linear"	,   __magic_name__		:Any = 0.0	,   __magic_name__		:str = None	,   __magic_name__		:Optional[int] = True	,   ):







												'''simple docstring'''







												if trained_betas is not None:
																	a		       =							torch.from_numpy(__magic_name__       )
												elif beta_schedule == "linear":
																	a		       =							torch.linspace(__magic_name__	,   __magic_name__	,   __magic_name__	,   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	,   __magic_name__	,   dtype=torch.floataa       ) ** 2
																	)
												elif beta_schedule == "squaredcos_cap_v2":
																	# Glide cosine schedule
																	a		       =							betas_for_alpha_bar(__magic_name__       )
												elif beta_schedule == "sigmoid":
																	# GeoDiff sigmoid schedule
																	a		       =							torch.linspace(-6	,   6	,   __magic_name__       )
																	a		       =							torch.sigmoid(__magic_name__       ) * (beta_end - beta_start) + beta_start
												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       )
												a		       =							torch.tensor(1.0       )

												a		       =							torch.tensor(1.0       )

												# standard deviation of the initial noise distribution
												a		       =							1.0

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

												a		       =							eta
							def    lowerCamelCase__							(		self		:List[Any]	,   __magic_name__		:Dict	,   __magic_name__		:int = None       ):







												'''simple docstring'''







												return sample
							def    lowerCamelCase__							(		self		:Optional[Any]	,   __magic_name__		:Tuple	,   __magic_name__		:Optional[int] = 10	,   __magic_name__		:List[Any] = 10	,   __magic_name__		:List[Any] = None	,   ):







												'''simple docstring'''







												a		       =							min(self.config.num_train_timesteps	,   __magic_name__       )
												a		       =							num_inference_steps

												a		       =							[]

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

												a		       =							num_inference_steps
												while t >= 1:
																	a		       =							t - 1
																	timesteps.append(__magic_name__       )

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

												a		       =							np.array(__magic_name__       ) * (self.config.num_train_timesteps // self.num_inference_steps)
												a		       =							torch.from_numpy(__magic_name__       ).to(__magic_name__       )
							def    lowerCamelCase__							(		self		:Dict	,   __magic_name__		:Tuple       ):







												'''simple docstring'''







												a		       =							t - self.config.num_train_timesteps // self.num_inference_steps

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

												return variance
							def    lowerCamelCase__							(		self		:int	,   __magic_name__		:Tuple	,   __magic_name__		:List[Any]	,   __magic_name__		:Dict	,   __magic_name__		:Optional[Any]	,   __magic_name__		:List[Any]	,   __magic_name__		:Union[str, Any] = None	,   __magic_name__		:Optional[int] = True	,   ):







												'''simple docstring'''







												a		       =							timestep
												a		       =							timestep - self.config.num_train_timesteps // self.num_inference_steps

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

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

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

												# 6. compute "direction pointing to x_t" of formula (12)
												# from https://arxiv.org/pdf/2010.02502.pdf
												a		       =							(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		       =							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		       =							(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		       =							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=__magic_name__	,   pred_original_sample=__magic_name__       )
							def    lowerCamelCase__							(		self		:Dict	,   __magic_name__		:Optional[Any]	,   __magic_name__		:Optional[Any]	,   __magic_name__		:Optional[Any]=None       ):







												'''simple docstring'''







												a		       =							self.config.num_train_timesteps // self.num_inference_steps

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

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

												return sample
							def    lowerCamelCase__							(		self		:List[str]	,   __magic_name__		:Dict	,   __magic_name__		:Any	,   __magic_name__		:Optional[Any]	,   ):







												'''simple docstring'''







												raise NotImplementedError("""Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."""       )





							def __len__(		self		:Union[str, Any]       ):







												'''simple docstring'''







												return self.config.num_train_timesteps







from itertools import combinations, product





def 	__A	(			__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)   -> bool:
	if xa == ya == 0 or xa == ya == 0:
		return False
	a		       =							xa * xa + ya * ya
	a		       =							xa * xa + ya * ya
	a		       =							(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
	return (
	    a_square + b_square == c_square
	    or a_square + c_square == b_square
	    or b_square + c_square == a_square
	)





def 	__A	(			__lowerCamelCase = 50					)   -> int:
	return sum(
	    1
	    for pta, pta in combinations(product(range(limit + 1					)							,    repeat=2					)							,    2					)
	    if is_right(*__lowerCamelCase							,    *__lowerCamelCase					)					)


if __name__ == "__main__":
		print(F'{solution() = }')

