



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   ( SCREAMING_SNAKE_CASE):







							'''simple docstring'''






							UpperCamelCase__					:   torch.FloatTensor
							UpperCamelCase__					:   torch.FloatTensor




def       A_   (						__a  :					Dict			,		__a  :					Optional[int]=0.9_9_9			,		__a  :					Dict="cosine"			,		):

				"""simple docstring"""
				if alpha_transform_type == "cosine":

								def alpha_bar_fn(__a  :					List[Any]		):
												return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2		) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(__a  :					int		):
												return math.exp(t * -1_2.0		)

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

				a__					   =		[]
				for i in range(__a		):
								a__					   =		i / num_diffusion_timesteps
								a__					   =		(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   ( SCREAMING_SNAKE_CASE      ,SCREAMING_SNAKE_CASE):







							'''simple docstring'''






							UpperCamelCase__					:   Any       =       1


							@register_to_config
							def __init__(				self	,	a_ = 1_000	,	a_ = 0.0_001	,	a_ = 0.02	,	a_ = "linear"	,	a_ = 0.0	,	a_ = None	,	a_ = True	,	):
											if trained_betas is not None:
															a__					   =		torch.from_numpy(a_		)
											elif beta_schedule == "linear":
															a__					   =		torch.linspace(a_	,	a_	,	a_	,	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	,	a_	,	dtype=torch.floataa		) ** 2
															)
											elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															a__					   =		betas_for_alpha_bar(a_		)
											elif beta_schedule == "sigmoid":
															# GeoDiff sigmoid schedule
															a__					   =		torch.linspace(-6	,	6	,	a_		)
															a__					   =		torch.sigmoid(a_		) * (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	,	a_		)[::-1].copy()		)

											a__					   =		eta


							def _a   (				self	,	a_	,	a_ = None		):
											return sample


							def _a   (				self	,	a_	,	a_ = 10	,	a_ = 10	,	a_ = None	,	):
											a__					   =		min(self.config.num_train_timesteps	,	a_		)
											a__					   =		num_inference_steps

											a__					   =		[]

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

											a__					   =		num_inference_steps
											while t >= 1:
															a__					   =		t - 1
															timesteps.append(a_		)

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

											a__					   =		np.array(a_		) * (self.config.num_train_timesteps // self.num_inference_steps)
											a__					   =		torch.from_numpy(a_		).to(a_		)


							def _a   (				self	,	a_		):
											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 _a   (				self	,	a_	,	a_	,	a_	,	a_	,	a_	,	a_ = None	,	a_ = True	,	):
											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(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
											a__					   =		model_output.device
											a__					   =		randn_tensor(model_output.shape	,	generator=a_	,	device=a_	,	dtype=model_output.dtype		)
											a__					   =		self.eta * self._get_variance(a_		) ** 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=a_	,	pred_original_sample=a_		)


							def _a   (				self	,	a_	,	a_	,	a_=None		):
											a__					   =		self.config.num_train_timesteps // self.num_inference_steps

											for i in range(a_		):
															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=a_		)
																			a__					   =		noise.to(sample.device		)
															else:
																			a__					   =		randn_tensor(sample.shape	,	generator=a_	,	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 _a   (				self	,	a_	,	a_	,	a_	,	):
											raise NotImplementedError("""Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."""		)







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






import math
from decimal import Decimal, getcontext

def       A_   (						__a  :					int = 4_000_000		):

				"""simple docstring"""

				try:
								a__					   =		int(__a		)
				except (TypeError, ValueError):
								raise TypeError("""Parameter n must be int or castable to int."""		)
				if n <= 0:
								raise ValueError("""Parameter n must be greater than or equal to one."""		)
				a__					   =		100
				a__					   =		(Decimal(5		) ** Decimal(0.5		) + 1) / Decimal(2		)

				a__					   =		(math.floor(math.log(n * (phi + 2)			,		__a		) - 1		) // 3) * 3 + 2
				a__					   =		Decimal(round(phi ** Decimal(index + 1		)		)		) / (phi + 2)
				a__					   =		num // 2
				return int(__a		)


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

