
'''simple docstring'''







import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


_snake_case					: Optional[int]     			=					logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class       lowerCAmelCase			(					__UpperCAmelCase      ):
		a				:       torch.FloatTensor
		a				:       Optional[torch.FloatTensor]							=       None



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

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

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(_SCREAMING_SNAKE_CASE		: str	):
																		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				:       Dict							=       [e.name for e in KarrasDiffusionSchedulers]
		a				:       Optional[Any]							=       1




		@register_to_config
		def __init__(					self       ,    UpperCamelCase = 1_000       ,    UpperCamelCase = 0.00_01       ,    UpperCamelCase = 0.02       ,    UpperCamelCase = "linear"       ,    UpperCamelCase = None       ,    UpperCamelCase = "epsilon"       ,    UpperCamelCase = "linear"       ,    UpperCamelCase = False       ,    UpperCamelCase = "linspace"       ,    UpperCamelCase = 0       ,    ):
								if trained_betas is not None:
														_SCREAMING_SNAKE_CASE					=			torch.tensor(UpperCamelCase       ,    dtype=torch.floataa   )
								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   )
								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					=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
								_SCREAMING_SNAKE_CASE					=			np.concatenate([sigmas[::-1], [0.0]]   ).astype(np.floataa   )
								_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   )

								# setable values
								_SCREAMING_SNAKE_CASE					=			None
								_SCREAMING_SNAKE_CASE					=			np.linspace(0       ,    num_train_timesteps - 1       ,    UpperCamelCase       ,    dtype=UpperCamelCase   )[::-1].copy()
								_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   )
								_SCREAMING_SNAKE_CASE					=			False
								_SCREAMING_SNAKE_CASE					=			use_karras_sigmas




		@property
		def      lowercase							(					self   ):
								# standard deviation of the initial noise distribution
								if self.config.timestep_spacing in ["linspace", "trailing"]:
														return self.sigmas.max()

								return (self.sigmas.max() ** 2 + 1) ** 0.5




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase   ):
								if isinstance(UpperCamelCase       ,    torch.Tensor   ):
														_SCREAMING_SNAKE_CASE					=			timestep.to(self.timesteps.device   )
								_SCREAMING_SNAKE_CASE					=			(self.timesteps == timestep).nonzero().item()
								_SCREAMING_SNAKE_CASE					=			self.sigmas[step_index]

								_SCREAMING_SNAKE_CASE					=			sample / ((sigma**2 + 1) ** 0.5)

								_SCREAMING_SNAKE_CASE					=			True
								return sample




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase = None   ):
								_SCREAMING_SNAKE_CASE					=			num_inference_steps

								# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
								if self.config.timestep_spacing == "linspace":
														_SCREAMING_SNAKE_CASE					=			np.linspace(0       ,    self.config.num_train_timesteps - 1       ,    UpperCamelCase       ,    dtype=UpperCamelCase   )[
														    ::-1
														].copy()
								elif self.config.timestep_spacing == "leading":
														_SCREAMING_SNAKE_CASE					=			self.config.num_train_timesteps // self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														_SCREAMING_SNAKE_CASE					=			(np.arange(0       ,    UpperCamelCase   ) * step_ratio).round()[::-1].copy().astype(UpperCamelCase   )
														timesteps += self.config.steps_offset
								elif self.config.timestep_spacing == "trailing":
														_SCREAMING_SNAKE_CASE					=			self.config.num_train_timesteps / self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														_SCREAMING_SNAKE_CASE					=			(np.arange(self.config.num_train_timesteps       ,    0       ,    -step_ratio   )).round().copy().astype(UpperCamelCase   )
														timesteps -= 1
								else:
														raise ValueError(
														    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'   )

								_SCREAMING_SNAKE_CASE					=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
								_SCREAMING_SNAKE_CASE					=			np.log(UpperCamelCase   )

								if self.config.interpolation_type == "linear":
														_SCREAMING_SNAKE_CASE					=			np.interp(UpperCamelCase       ,    np.arange(0       ,    len(UpperCamelCase   )   )       ,    UpperCamelCase   )
								elif self.config.interpolation_type == "log_linear":
														_SCREAMING_SNAKE_CASE					=			torch.linspace(np.log(sigmas[-1]   )       ,    np.log(sigmas[0]   )       ,    num_inference_steps + 1   ).exp()
								else:
														raise ValueError(
														    F'{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'
														    " 'linear' or 'log_linear'"   )

								if self.use_karras_sigmas:
														_SCREAMING_SNAKE_CASE					=			self._convert_to_karras(in_sigmas=UpperCamelCase       ,    num_inference_steps=self.num_inference_steps   )
														_SCREAMING_SNAKE_CASE					=			np.array([self._sigma_to_t(UpperCamelCase       ,    UpperCamelCase   ) for sigma in sigmas]   )

								_SCREAMING_SNAKE_CASE					=			np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
								_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   ).to(device=UpperCamelCase   )
								if str(UpperCamelCase   ).startswith("mps"   ):
														# mps does not support float64
														_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   ).to(UpperCamelCase       ,    dtype=torch.floataa   )
								else:
														_SCREAMING_SNAKE_CASE					=			torch.from_numpy(UpperCamelCase   ).to(device=UpperCamelCase   )




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase   ):
								# get log sigma
								_SCREAMING_SNAKE_CASE					=			np.log(UpperCamelCase   )

								# get distribution
								_SCREAMING_SNAKE_CASE					=			log_sigma - log_sigmas[:, np.newaxis]

								# get sigmas range
								_SCREAMING_SNAKE_CASE					=			np.cumsum((dists >= 0)       ,    axis=0   ).argmax(axis=0   ).clip(max=log_sigmas.shape[0] - 2   )
								_SCREAMING_SNAKE_CASE					=			low_idx + 1

								_SCREAMING_SNAKE_CASE					=			log_sigmas[low_idx]
								_SCREAMING_SNAKE_CASE					=			log_sigmas[high_idx]

								# interpolate sigmas
								_SCREAMING_SNAKE_CASE					=			(low - log_sigma) / (low - high)
								_SCREAMING_SNAKE_CASE					=			np.clip(UpperCamelCase       ,    0       ,    1   )

								# transform interpolation to time range
								_SCREAMING_SNAKE_CASE					=			(1 - w) * low_idx + w * high_idx
								_SCREAMING_SNAKE_CASE					=			t.reshape(sigma.shape   )
								return t




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase   ):
								_SCREAMING_SNAKE_CASE					=			in_sigmas[-1].item()
								_SCREAMING_SNAKE_CASE					=			in_sigmas[0].item()

								_SCREAMING_SNAKE_CASE					=			7.0  # 7.0 is the value used in the paper
								_SCREAMING_SNAKE_CASE					=			np.linspace(0       ,    1       ,    UpperCamelCase   )
								_SCREAMING_SNAKE_CASE					=			sigma_min ** (1 / rho)
								_SCREAMING_SNAKE_CASE					=			sigma_max ** (1 / rho)
								_SCREAMING_SNAKE_CASE					=			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
								return sigmas




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase = 0.0       ,    UpperCamelCase = 0.0       ,    UpperCamelCase = float("inf"   )       ,    UpperCamelCase = 1.0       ,    UpperCamelCase = None       ,    UpperCamelCase = True       ,    ):

								if (
								    isinstance(UpperCamelCase       ,    UpperCamelCase   )
								    or isinstance(UpperCamelCase       ,    torch.IntTensor   )
								    or isinstance(UpperCamelCase       ,    torch.LongTensor   )
								):
														raise ValueError(
														    (
														        "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
														        " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
														        " one of the `scheduler.timesteps` as a timestep."
														    )       ,    )

								if not self.is_scale_input_called:
														logger.warning(
														    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
														    "See `StableDiffusionPipeline` for a usage example."   )

								if isinstance(UpperCamelCase       ,    torch.Tensor   ):
														_SCREAMING_SNAKE_CASE					=			timestep.to(self.timesteps.device   )

								_SCREAMING_SNAKE_CASE					=			(self.timesteps == timestep).nonzero().item()
								_SCREAMING_SNAKE_CASE					=			self.sigmas[step_index]

								_SCREAMING_SNAKE_CASE					=			min(s_churn / (len(self.sigmas   ) - 1)       ,    2**0.5 - 1   ) if s_tmin <= sigma <= s_tmax else 0.0

								_SCREAMING_SNAKE_CASE					=			randn_tensor(
								    model_output.shape       ,    dtype=model_output.dtype       ,    device=model_output.device       ,    generator=UpperCamelCase   )

								_SCREAMING_SNAKE_CASE					=			noise * s_noise
								_SCREAMING_SNAKE_CASE					=			sigma * (gamma + 1)

								if gamma > 0:
														_SCREAMING_SNAKE_CASE					=			sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

								# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
								# NOTE: "original_sample" should not be an expected prediction_type but is left in for
								# backwards compatibility
								if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
														_SCREAMING_SNAKE_CASE					=			model_output
								elif self.config.prediction_type == "epsilon":
														_SCREAMING_SNAKE_CASE					=			sample - sigma_hat * model_output
								elif self.config.prediction_type == "v_prediction":
														# * c_out + input * c_skip
														_SCREAMING_SNAKE_CASE					=			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
								else:
														raise ValueError(
														    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'   )

								# 2. Convert to an ODE derivative
								_SCREAMING_SNAKE_CASE					=			(sample - pred_original_sample) / sigma_hat

								_SCREAMING_SNAKE_CASE					=			self.sigmas[step_index + 1] - sigma_hat

								_SCREAMING_SNAKE_CASE					=			sample + derivative * dt

								if not return_dict:
														return (prev_sample,)

								return EulerDiscreteSchedulerOutput(prev_sample=UpperCamelCase       ,    pred_original_sample=UpperCamelCase   )




		def      lowercase							(					self       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    ):
								# Make sure sigmas and timesteps have the same device and dtype as original_samples
								_SCREAMING_SNAKE_CASE					=			self.sigmas.to(device=original_samples.device       ,    dtype=original_samples.dtype   )
								if original_samples.device.type == "mps" and torch.is_floating_point(UpperCamelCase   ):
														# mps does not support float64
														_SCREAMING_SNAKE_CASE					=			self.timesteps.to(original_samples.device       ,    dtype=torch.floataa   )
														_SCREAMING_SNAKE_CASE					=			timesteps.to(original_samples.device       ,    dtype=torch.floataa   )
								else:
														_SCREAMING_SNAKE_CASE					=			self.timesteps.to(original_samples.device   )
														_SCREAMING_SNAKE_CASE					=			timesteps.to(original_samples.device   )

								_SCREAMING_SNAKE_CASE					=			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

								_SCREAMING_SNAKE_CASE					=			sigmas[step_indices].flatten()
								while len(sigma.shape   ) < len(original_samples.shape   ):
														_SCREAMING_SNAKE_CASE					=			sigma.unsqueeze(-1   )

								_SCREAMING_SNAKE_CASE					=			original_samples + noise * sigma
								return noisy_samples




		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)