

"""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 			_snake_case     (						UpperCamelCase       ):
						__snake_case 			=     42
						__snake_case 			=     42





def 				__UpperCamelCase   (    a__: Union[str, Any] ,	a__: Tuple=0.9_99 ,	a__: List[Any]="cosine" ,	)				->			int:




					"""simple docstring"""



					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(a__: Optional[Any]			):
															return math.exp(t * -12.0			)

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

					__lowercase												=			[]
					for i in range(a__			):
										__lowercase												=			i / num_diffusion_timesteps
										__lowercase												=			(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 			_snake_case     (						UpperCamelCase						,			UpperCamelCase       ):
						__snake_case 			=     1







						@register_to_config
						def __init__(self     ,							UpperCAmelCase_ = 1_0_0_0     ,							UpperCAmelCase_ = 0.0_0_0_1     ,							UpperCAmelCase_ = 0.0_2     ,							UpperCAmelCase_ = "linear"     ,							UpperCAmelCase_ = 0.0     ,							UpperCAmelCase_ = None     ,							UpperCAmelCase_ = True     ,							)			->						Any:
											if trained_betas is not None:
																__lowercase												=			torch.from_numpy(UpperCAmelCase_							)
											elif beta_schedule == "linear":
																__lowercase												=			torch.linspace(UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							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     ,							UpperCAmelCase_     ,							dtype=torch.floataa							) ** 2
																)
											elif beta_schedule == "squaredcos_cap_v2":
																# Glide cosine schedule
																__lowercase												=			betas_for_alpha_bar(UpperCAmelCase_							)
											elif beta_schedule == "sigmoid":
																# GeoDiff sigmoid schedule
																__lowercase												=			torch.linspace(-6     ,							6     ,							UpperCAmelCase_							)
																__lowercase												=			torch.sigmoid(UpperCAmelCase_							) * (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     ,							UpperCAmelCase_							)[::-1].copy()							)

											__lowercase												=			eta







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = None							)			->						torch.FloatTensor:
											return sample







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = 1_0     ,							UpperCAmelCase_ = 1_0     ,							UpperCAmelCase_ = None     ,							)			->						int:
											__lowercase												=			min(self.config.num_train_timesteps     ,							UpperCAmelCase_							)
											__lowercase												=			num_inference_steps

											__lowercase												=			[]

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

											__lowercase												=			num_inference_steps
											while t >= 1:
																__lowercase												=			t - 1
																timesteps.append(UpperCAmelCase_							)

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

											__lowercase												=			np.array(UpperCAmelCase_							) * (self.config.num_train_timesteps // self.num_inference_steps)
											__lowercase												=			torch.from_numpy(UpperCAmelCase_							).to(UpperCAmelCase_							)







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_							)			->						str:
											__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        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_ = None     ,							UpperCAmelCase_ = True     ,							)			->						Union[RePaintSchedulerOutput, Tuple]:
											__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(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
											__lowercase												=			model_output.device
											__lowercase												=			randn_tensor(model_output.shape     ,							generator=UpperCAmelCase_     ,							device=UpperCAmelCase_     ,							dtype=model_output.dtype							)
											__lowercase												=			self.eta * self._get_variance(UpperCAmelCase_							) ** 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=UpperCAmelCase_     ,							pred_original_sample=UpperCAmelCase_							)







						def        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_=None							)			->						Tuple:
											__lowercase												=			self.config.num_train_timesteps // self.num_inference_steps

											for i in range(UpperCAmelCase_							):
																__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=UpperCAmelCase_							)
																					__lowercase												=			noise.to(sample.device							)
																else:
																					__lowercase												=			randn_tensor(sample.shape     ,							generator=UpperCAmelCase_     ,							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        _UpperCamelCase    (self     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							UpperCAmelCase_     ,							)			->						torch.FloatTensor:
											raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'''							)







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





"""simple docstring"""

def 				__UpperCamelCase   (    a__: int ,	a__: int = 10_00			)				->			str:




					"""simple docstring"""



					if (not isinstance(a__ ,	a__			)) or (digit_position <= 0):
										raise ValueError('''Digit position must be a positive integer'''			)
					elif (not isinstance(a__ ,	a__			)) or (precision < 0):
										raise ValueError('''Precision must be a nonnegative integer'''			)

					# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
					# accurate
					__lowercase												=			(
					    4 * _subsum(a__ ,	1 ,	a__			)
					    - 2 * _subsum(a__ ,	4 ,	a__			)
					    - _subsum(a__ ,	5 ,	a__			)
					    - _subsum(a__ ,	6 ,	a__			)
					)

					# return the first hex digit of the fractional part of the result
					return hex(int((sum_result % 1) * 16			)			)[2:]





def 				__UpperCamelCase   (    a__: int ,	a__: int ,	a__: int			)				->			float:




					"""simple docstring"""



					__lowercase												=			0.0
					for sum_index in range(digit_pos_to_extract + precision			):
										__lowercase												=			8 * sum_index + denominator_addend
										if sum_index < digit_pos_to_extract:
															# if the exponential term is an integer and we mod it by the denominator
															# before dividing, only the integer part of the sum will change;
															# the fractional part will not
															__lowercase												=			pow(
															    16 ,	digit_pos_to_extract - 1 - sum_index ,	a__			)
										else:
															__lowercase												=			pow(16 ,	digit_pos_to_extract - 1 - sum_index			)
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()


