



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  _snake_case	(    _UpperCamelCase):
				UpperCamelCase__ :    torch.FloatTensor
				UpperCamelCase__ :    torch.FloatTensor



def __lowerCAmelCase       (   SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_=0.999  ,     SCREAMING_SNAKE_CASE_="cosine"  ,     ):

			if alpha_transform_type == "cosine":

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

			elif alpha_transform_type == "exp":

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

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

			lowercase__         = []
			for i in range(lowercase_     ):
						lowercase__         = i / num_diffusion_timesteps
						lowercase__         = (i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(lowercase_     ) / alpha_bar_fn(lowercase_     )  ,     lowercase_     )     )
			return torch.tensor(lowercase_  ,     dtype=torch.floataa     )




class  _snake_case	(    _UpperCamelCase			,		_UpperCamelCase):
				UpperCamelCase__ :    Union[str, Any]   						=1




				@register_to_config
				def __init__(  self    :  Optional[Any],    __lowercase    :  int = 1000,    __lowercase    :  float = 0.0001,    __lowercase    :  float = 0.02,    __lowercase    :  str = "linear",    __lowercase    :  float = 0.0,    __lowercase    :  Optional[np.ndarray] = None,    __lowercase    :  bool = True,    ):
							if trained_betas is not None:
										lowercase__         = torch.from_numpy(__a  )
							elif beta_schedule == "linear":
										lowercase__         = torch.linspace(__a,    __a,    __a,    dtype=torch.floataa  )
							elif beta_schedule == "scaled_linear":
										# this schedule is very specific to the latent diffusion model.
										lowercase__         = (
										    torch.linspace(beta_start**0.5,    beta_end**0.5,    __a,    dtype=torch.floataa  ) ** 2
										)
							elif beta_schedule == "squaredcos_cap_v2":
										# Glide cosine schedule
										lowercase__         = betas_for_alpha_bar(__a  )
							elif beta_schedule == "sigmoid":
										# GeoDiff sigmoid schedule
										lowercase__         = torch.linspace(-6,    6,    __a  )
										lowercase__         = torch.sigmoid(__a  ) * (beta_end - beta_start) + beta_start
							else:
										raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''  )

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

							lowercase__         = torch.tensor(1.0  )

							# standard deviation of the initial noise distribution
							lowercase__         = 1.0

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

							lowercase__         = eta




				def 							A__					(  self    :  str,    __lowercase    :  torch.FloatTensor,    __lowercase    :  Optional[int] = None  ):
							return sample




				def 							A__					(  self    :  int,    __lowercase    :  int,    __lowercase    :  int = 10,    __lowercase    :  int = 10,    __lowercase    :  Union[str, torch.device] = None,    ):
							lowercase__         = min(self.config.num_train_timesteps,    __a  )
							lowercase__         = num_inference_steps

							lowercase__         = []

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

							lowercase__         = num_inference_steps
							while t >= 1:
										lowercase__         = t - 1
										timesteps.append(__a  )

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

							lowercase__         = np.array(__a  ) * (self.config.num_train_timesteps // self.num_inference_steps)
							lowercase__         = torch.from_numpy(__a  ).to(__a  )




				def 							A__					(  self    :  Optional[int],    __lowercase    :  Dict  ):
							lowercase__         = t - self.config.num_train_timesteps // self.num_inference_steps

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

							return variance




				def 							A__					(  self    :  str,    __lowercase    :  torch.FloatTensor,    __lowercase    :  int,    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor,    __lowercase    :  Optional[torch.Generator] = None,    __lowercase    :  bool = True,    ):
							lowercase__         = timestep
							lowercase__         = timestep - self.config.num_train_timesteps // self.num_inference_steps

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

							# 3. Clip "predicted x_0"
							if self.config.clip_sample:
										lowercase__         = 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
							lowercase__         = model_output.device
							lowercase__         = randn_tensor(model_output.shape,    generator=__a,    device=__a,    dtype=model_output.dtype  )
							lowercase__         = self.eta * self._get_variance(__a  ) ** 0.5

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

							# 6. compute "direction pointing to x_t" of formula (12)
							# from https://arxiv.org/pdf/2010.02502.pdf
							lowercase__         = (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
							lowercase__         = 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
							lowercase__         = (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
							lowercase__         = 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 							A__					(  self    :  str,    __lowercase    :  Tuple,    __lowercase    :  List[str],    __lowercase    :  Dict=None  ):
							lowercase__         = self.config.num_train_timesteps // self.num_inference_steps

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

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

							return sample




				def 							A__					(  self    :  Tuple,    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.IntTensor,    ):
							raise NotImplementedError("Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."  )




				def __len__(  self    :  int  ):
							return self.config.num_train_timesteps











"""simple docstring"""


from __future__ import annotations




def     lowercase__			(    lowercase_						,lowercase_						,lowercase_	)    ->						int:




      """simple docstring"""

      assert n > 1 and a > 0 and greatest_common_divisor(lowercase_						,lowercase_	) == 1
      ((_UpperCamelCase),     (_UpperCamelCase),     (_UpperCamelCase))					:		int  =				extended_gcd(lowercase_						,lowercase_	)  # Implemented below
      _UpperCamelCase					:		Any  =				(b * s) % n
      return x




def     lowercase__			(    lowercase_						,lowercase_	)    ->						int:




      """simple docstring"""

      ((_UpperCamelCase),     (_UpperCamelCase))					:		List[Any]  =				extended_euclid(lowercase_						,lowercase_	)  # Implemented below
      if b < 0:
            _UpperCamelCase					:		Any  =				(b % n + n) % n
      return b




def     lowercase__			(    lowercase_						,lowercase_						,lowercase_	)    ->						int:




      """simple docstring"""

      _UpperCamelCase					:		Union[str, Any]  =				invert_modulo(lowercase_						,lowercase_	)
      _UpperCamelCase					:		Any  =				(b * s) % n
      return x




def     lowercase__			(    lowercase_						,lowercase_	)    ->						tuple[int, int, int]:




      """simple docstring"""

      assert a >= 0 and b >= 0

      if b == 0:
            _UpperCamelCase,     _UpperCamelCase,     _UpperCamelCase					:		str  =				a, 1, 0
      else:
            ((_UpperCamelCase),     (_UpperCamelCase),     (_UpperCamelCase))					:		str  =				extended_gcd(lowercase_						,a % b	)
            _UpperCamelCase					:		Dict  =				q
            _UpperCamelCase					:		Tuple  =				p - q * (a // b)

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

      return (d, x, y)




def     lowercase__			(    lowercase_						,lowercase_	)    ->						tuple[int, int]:




      """simple docstring"""

      if b == 0:
            return (1, 0)
      ((_UpperCamelCase),     (_UpperCamelCase))					:		Optional[Any]  =				extended_euclid(lowercase_						,a % b	)
      _UpperCamelCase					:		Dict  =				a // b
      return (y, x - k * y)




def     lowercase__			(    lowercase_						,lowercase_	)    ->						int:




      """simple docstring"""

      if a < b:
            _UpperCamelCase,     _UpperCamelCase					:		List[Any]  =				b, a

      while a % b != 0:
            _UpperCamelCase,     _UpperCamelCase					:		List[Any]  =				b, a % b

      return b


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

  testmod(name="modular_division", verbose=True)
  testmod(name="modular_division2", verbose=True)
  testmod(name="invert_modulo", verbose=True)
  testmod(name="extended_gcd", verbose=True)
  testmod(name="extended_euclid", verbose=True)
  testmod(name="greatest_common_divisor", verbose=True)
