






"""simple docstring"""

from __future__ import annotations

def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase )		->					tuple[float, float]:

		"""simple docstring"""







		assert (
		    c % greatest_common_divisor(__UpperCamelCase   , __UpperCamelCase ) == 0
		)  # greatest_common_divisor(a,b) function implemented below
		((lowerCAmelCase_)       ,			(lowerCAmelCase_)       ,			(lowerCAmelCase_))     :							Union[str, Any]             =    extended_gcd(__UpperCamelCase   , __UpperCamelCase )  # extended_gcd(a,b) function implemented below
		lowerCAmelCase_     :							Any             =    c / d
		return (r * x, r * y)

def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase = 2 )		->					None:

		"""simple docstring"""







		((lowerCAmelCase_)       ,			(lowerCAmelCase_))     :							List[str]             =    diophantine(__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase )  # Initial value
		lowerCAmelCase_     :							List[str]             =    greatest_common_divisor(__UpperCamelCase   , __UpperCamelCase )
		lowerCAmelCase_     :							Tuple             =    a // d
		lowerCAmelCase_     :							Union[str, Any]             =    b // d

		for i in range(__UpperCamelCase ):
				lowerCAmelCase_     :							List[Any]             =    xa + i * q
				lowerCAmelCase_     :							Optional[int]             =    ya - i * p
				print(__UpperCamelCase   , __UpperCamelCase )

def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase )		->					int:

		"""simple docstring"""







		if a < b:
				lowerCAmelCase_       ,			lowerCAmelCase_     :							Union[str, Any]             =    b, a

		while a % b != 0:
				lowerCAmelCase_       ,			lowerCAmelCase_     :							Union[str, Any]             =    b, a % b

		return b

def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase )		->					tuple[int, int, int]:

		"""simple docstring"""







		assert a >= 0 and b >= 0

		if b == 0:
				lowerCAmelCase_       ,			lowerCAmelCase_       ,			lowerCAmelCase_     :							List[Any]             =    a, 1, 0
		else:
				((lowerCAmelCase_)       ,			(lowerCAmelCase_)       ,			(lowerCAmelCase_))     :							Any             =    extended_gcd(__UpperCamelCase   , a % b )
				lowerCAmelCase_     :							Optional[Any]             =    q
				lowerCAmelCase_     :							Tuple             =    p - q * (a // b)

		assert a % d == 0 and b % d == 0
		assert d == a * x + b * y

		return (d, x, y)


if __name__ == "__main__":
					from doctest import testmod

					testmod(name="""diophantine""", verbose=True)
					testmod(name="""diophantine_all_soln""", verbose=True)
					testmod(name="""extended_gcd""", verbose=True)
					testmod(name="""greatest_common_divisor""", verbose=True)








"""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
class 	__lowerCamelCase       (				A__    ):





		'''simple docstring'''






		a_			:       torch.FloatTensor
		a_			:       torch.FloatTensor







def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase=0.9_99   , __UpperCamelCase="cosine"   , )		->					Any:

		"""simple docstring"""







		if alpha_transform_type == "cosine":

				def alpha_bar_fn(__UpperCamelCase ):
						return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2 ) ** 2

		elif alpha_transform_type == "exp":

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

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

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



class 	__lowerCamelCase       (				A__				,							A__    ):





		'''simple docstring'''






		a_			:       Tuple      =							1





		@register_to_config
		def __init__(     self							:			Optional[int]		,    a_							:			int = 10_00		,    a_							:			float = 0.0001		,    a_							:			float = 0.02		,    a_							:			str = "linear"		,    a_							:			float = 0.0		,    a_							:			Optional[np.ndarray] = None		,    a_							:			bool = True		,    ):
				if trained_betas is not None:
						lowerCAmelCase_     :							Tuple             =    torch.from_numpy(a_			)
				elif beta_schedule == "linear":
						lowerCAmelCase_     :							int             =    torch.linspace(a_		,    a_		,    a_		,    dtype=torch.floataa			)
				elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						lowerCAmelCase_     :							Optional[Any]             =    (
						    torch.linspace(beta_start**0.5		,    beta_end**0.5		,    a_		,    dtype=torch.floataa			) ** 2
						)
				elif beta_schedule == "squaredcos_cap_v2":
						# Glide cosine schedule
						lowerCAmelCase_     :							Tuple             =    betas_for_alpha_bar(a_			)
				elif beta_schedule == "sigmoid":
						# GeoDiff sigmoid schedule
						lowerCAmelCase_     :							List[str]             =    torch.linspace(-6		,    6		,    a_			)
						lowerCAmelCase_     :							int             =    torch.sigmoid(a_			) * (beta_end - beta_start) + beta_start
				else:
						raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''			)

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

				lowerCAmelCase_     :							int             =    torch.tensor(1.0			)

				# standard deviation of the initial noise distribution
				lowerCAmelCase_     :							List[str]             =    1.0

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

				lowerCAmelCase_     :							int             =    eta





		def      lowerCamelCase (     self							:			Optional[Any]		,    a_							:			torch.FloatTensor		,    a_							:			Optional[int] = None			):
				return sample





		def      lowerCamelCase (     self							:			Dict		,    a_							:			int		,    a_							:			int = 10		,    a_							:			int = 10		,    a_							:			Union[str, torch.device] = None		,    ):
				lowerCAmelCase_     :							Union[str, Any]             =    min(self.config.num_train_timesteps		,    a_			)
				lowerCAmelCase_     :							Dict             =    num_inference_steps

				lowerCAmelCase_     :							List[str]             =    []

				lowerCAmelCase_     :							Dict             =    {}
				for j in range(0		,    num_inference_steps - jump_length		,    a_			):
						lowerCAmelCase_     :							Dict             =    jump_n_sample - 1

				lowerCAmelCase_     :							List[Any]             =    num_inference_steps
				while t >= 1:
						lowerCAmelCase_     :							int             =    t - 1
						timesteps.append(a_			)

						if jumps.get(a_		,    0			) > 0:
								lowerCAmelCase_     :							Optional[int]             =    jumps[t] - 1
								for _ in range(a_			):
										lowerCAmelCase_     :							Any             =    t + 1
										timesteps.append(a_			)

				lowerCAmelCase_     :							List[Any]             =    np.array(a_			) * (self.config.num_train_timesteps // self.num_inference_steps)
				lowerCAmelCase_     :							int             =    torch.from_numpy(a_			).to(a_			)





		def      lowerCamelCase (     self							:			Optional[int]		,    a_							:			Optional[Any]			):
				lowerCAmelCase_     :							Optional[Any]             =    t - self.config.num_train_timesteps // self.num_inference_steps

				lowerCAmelCase_     :							List[Any]             =    self.alphas_cumprod[t]
				lowerCAmelCase_     :							Dict             =    self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
				lowerCAmelCase_     :							List[str]             =    1 - alpha_prod_t
				lowerCAmelCase_     :							str             =    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]
				lowerCAmelCase_     :							Dict             =    (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

				return variance





		def      lowerCamelCase (     self							:			Optional[Any]		,    a_							:			torch.FloatTensor		,    a_							:			int		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			Optional[torch.Generator] = None		,    a_							:			bool = True		,    ):
				lowerCAmelCase_     :							Any             =    timestep
				lowerCAmelCase_     :							str             =    timestep - self.config.num_train_timesteps // self.num_inference_steps

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

				# 3. Clip "predicted x_0"
				if self.config.clip_sample:
						lowerCAmelCase_     :							Optional[int]             =    torch.clamp(a_		,    -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
				lowerCAmelCase_     :							Optional[Any]             =    model_output.device
				lowerCAmelCase_     :							List[str]             =    randn_tensor(model_output.shape		,    generator=a_		,    device=a_		,    dtype=model_output.dtype			)
				lowerCAmelCase_     :							List[Any]             =    self.eta * self._get_variance(a_			) ** 0.5

				lowerCAmelCase_     :							Optional[int]             =    0
				if t > 0 and self.eta > 0:
						lowerCAmelCase_     :							Optional[int]             =    std_dev_t * noise

				# 6. compute "direction pointing to x_t" of formula (12)
				# from https://arxiv.org/pdf/2010.02502.pdf
				lowerCAmelCase_     :							Union[str, Any]             =    (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
				lowerCAmelCase_     :							Dict             =    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
				lowerCAmelCase_     :							Union[str, 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
				lowerCAmelCase_     :							Tuple             =    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=a_		,    pred_original_sample=a_			)





		def      lowerCamelCase (     self							:			Dict		,    a_							:			Any		,    a_							:			Dict		,    a_							:			Optional[int]=None			):
				lowerCAmelCase_     :							Dict             =    self.config.num_train_timesteps // self.num_inference_steps

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

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

				return sample





		def      lowerCamelCase (     self							:			Any		,    a_							:			torch.FloatTensor		,    a_							:			torch.FloatTensor		,    a_							:			torch.IntTensor		,    ):
				raise NotImplementedError("Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."			)





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