
'''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			(					__UpperCAmelCase      ):
		a				:       torch.FloatTensor
		a				:       torch.FloatTensor



def       _a		(						_SCREAMING_SNAKE_CASE		: Union[str, Any]						,      _SCREAMING_SNAKE_CASE		: List[Any]=0.999						,      _SCREAMING_SNAKE_CASE		: Optional[Any]="cosine"						,      ):
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(_SCREAMING_SNAKE_CASE		: Union[str, Any]	):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2	) ** 2

						elif alpha_transform_type == "exp":

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

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

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




class       lowerCAmelCase			(					__UpperCAmelCase		,  __UpperCAmelCase      ):
		a				:       Any							=       1




		@register_to_config
		def __init__(					self       ,    UpperCamelCase = 1_000       ,    UpperCamelCase = 0.00_01       ,    UpperCamelCase = 0.02       ,    UpperCamelCase = "linear"       ,    UpperCamelCase = 0.0       ,    UpperCamelCase = None       ,    UpperCamelCase = True       ,    ):
								if trained_betas is not None:
														_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   )
								elif beta_schedule == "linear":
														_SCREAMING_SNAKE_CASE					=			torch.linspace(UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    dtype=torch.floataa   )
								elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														_SCREAMING_SNAKE_CASE					=			(
														    torch.linspace(beta_start**0.5       ,    beta_end**0.5       ,    UpperCamelCase       ,    dtype=torch.floataa   ) ** 2
														)
								elif beta_schedule == "squaredcos_cap_v2":
														# Glide cosine schedule
														_SCREAMING_SNAKE_CASE					=			betas_for_alpha_bar(UpperCamelCase   )
								elif beta_schedule == "sigmoid":
														# GeoDiff sigmoid schedule
														_SCREAMING_SNAKE_CASE					=			torch.linspace(-6       ,    6       ,    UpperCamelCase   )
														_SCREAMING_SNAKE_CASE					=			torch.sigmoid(UpperCamelCase   ) * (beta_end - beta_start) + beta_start
								else:
														raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'   )

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

								_SCREAMING_SNAKE_CASE					=			torch.tensor(1.0   )

								# standard deviation of the initial noise distribution
								_SCREAMING_SNAKE_CASE					=			1.0

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

								_SCREAMING_SNAKE_CASE					=			eta




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase = None   ):
								return sample




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase = 10       ,    UpperCamelCase = 10       ,    UpperCamelCase = None       ,    ):
								_SCREAMING_SNAKE_CASE					=			min(self.config.num_train_timesteps       ,    UpperCamelCase   )
								_SCREAMING_SNAKE_CASE					=			num_inference_steps

								_SCREAMING_SNAKE_CASE					=			[]

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

								_SCREAMING_SNAKE_CASE					=			num_inference_steps
								while t >= 1:
														_SCREAMING_SNAKE_CASE					=			t - 1
														timesteps.append(UpperCamelCase   )

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

								_SCREAMING_SNAKE_CASE					=			np.array(UpperCamelCase   ) * (self.config.num_train_timesteps // self.num_inference_steps)
								_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   ).to(UpperCamelCase   )




		def      lowercase							(					self       ,    UpperCamelCase   ):
								_SCREAMING_SNAKE_CASE					=			t - self.config.num_train_timesteps // self.num_inference_steps

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

								return variance




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase = None       ,    UpperCamelCase = True       ,    ):
								_SCREAMING_SNAKE_CASE					=			timestep
								_SCREAMING_SNAKE_CASE					=			timestep - self.config.num_train_timesteps // self.num_inference_steps

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

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

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

								# 6. compute "direction pointing to x_t" of formula (12)
								# from https://arxiv.org/pdf/2010.02502.pdf
								_SCREAMING_SNAKE_CASE					=			(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
								_SCREAMING_SNAKE_CASE					=			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
								_SCREAMING_SNAKE_CASE					=			(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
								_SCREAMING_SNAKE_CASE					=			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      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase=None   ):
								_SCREAMING_SNAKE_CASE					=			self.config.num_train_timesteps // self.num_inference_steps

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

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

								return sample




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    ):
								raise NotImplementedError("Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."   )




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

'''simple docstring'''







class       lowerCAmelCase			:




		def __init__(					self       ,    UpperCamelCase=None   ):
								_SCREAMING_SNAKE_CASE					=			data
								_SCREAMING_SNAKE_CASE					=			None




		def __repr__(					self   ):
								_SCREAMING_SNAKE_CASE					=			""
								_SCREAMING_SNAKE_CASE					=			self
								while temp:
														string_rep += F'<{temp.data}> ---> '
														_SCREAMING_SNAKE_CASE					=			temp.next
								string_rep += "<END>"
								return string_rep



def       _a		(						_SCREAMING_SNAKE_CASE		: Any	):

						# if elements_list is empty
						if not elements_list:
												raise Exception("The Elements List is empty"	)

						# Set first element as Head
						_SCREAMING_SNAKE_CASE					=			Node(elements_list[0]	)
						_SCREAMING_SNAKE_CASE					=			head
						# Loop through elements from position 1
						for data in elements_list[1:]:
												_SCREAMING_SNAKE_CASE					=			Node(_SCREAMING_SNAKE_CASE	)
												_SCREAMING_SNAKE_CASE					=			current.next
						return head


_snake_case					: List[Any]     			=					[1, 3, 5, 32, 44, 12, 43]
print(F"List: {list_data}")
print("""Creating Linked List from List.""")
_snake_case					: List[Any]     			=					make_linked_list(list_data)
print("""Linked List:""")




print(linked_list)