"""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


UpperCamelCase     					=     logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class   UpperCAmelCase__				(    lowerCAmelCase_			):


	"""simple docstring"""
	lowerCAmelCase__    :					Tuple						      =							42
	lowerCAmelCase__    :					str						      =							None




def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:Any		,			_SCREAMING_SNAKE_CASE	:Tuple=0.999		,			_SCREAMING_SNAKE_CASE	:Optional[int]="cosine"		,			):
						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

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

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

						a_							:			Any     		=					[]
						for i in range(_SCREAMING_SNAKE_CASE  ):
												a_							:			Optional[int]     		=					i / num_diffusion_timesteps
												a_							:			List[str]     		=					(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   UpperCAmelCase__				(    lowerCAmelCase_,      lowerCAmelCase_			):


	"""simple docstring"""
	lowerCAmelCase__    :					List[str]						      =							[e.name for e in KarrasDiffusionSchedulers]
	lowerCAmelCase__    :					int						      =							1







	@register_to_config
	def __init__(			self       ,     _SCREAMING_SNAKE_CASE = 1_0_0_0       ,     _SCREAMING_SNAKE_CASE = 0.0_0_0_1       ,     _SCREAMING_SNAKE_CASE = 0.0_2       ,     _SCREAMING_SNAKE_CASE = "linear"       ,     _SCREAMING_SNAKE_CASE = None       ,     _SCREAMING_SNAKE_CASE = "epsilon"       ,     _SCREAMING_SNAKE_CASE = "linear"       ,     _SCREAMING_SNAKE_CASE = False       ,     _SCREAMING_SNAKE_CASE = "linspace"       ,     _SCREAMING_SNAKE_CASE = 0       ,     )    ->	Optional[Any]:





							if trained_betas is not None:
													a_							:			Any     		=					torch.tensor(__a       ,     dtype=torch.floataa )
							elif beta_schedule == "linear":
													a_							:			Dict     		=					torch.linspace(__a       ,     __a       ,     __a       ,     dtype=torch.floataa )
							elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													a_							:			Any     		=					(
													    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_							:			int     		=					betas_for_alpha_bar(__a )
							else:
													raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''' )

							a_							:			List[Any]     		=					1.0 - self.betas
							a_							:			int     		=					torch.cumprod(self.alphas       ,     dim=0 )

							a_							:			List[Any]     		=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
							a_							:			List[Any]     		=					np.concatenate([sigmas[::-1], [0.0]] ).astype(np.floataa )
							a_							:			Union[str, Any]     		=					torch.from_numpy(__a )

							# setable values
							a_							:			List[str]     		=					None
							a_							:			List[Any]     		=					np.linspace(0       ,     num_train_timesteps - 1       ,     __a       ,     dtype=__a )[::-1].copy()
							a_							:			Optional[Any]     		=					torch.from_numpy(__a )
							a_							:			Any     		=					False
							a_							:			str     		=					use_karras_sigmas







	@property
	def       A    (			self )    ->	Dict:





							if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

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







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE )    ->	Optional[Any]:





							if isinstance(__a       ,     torch.Tensor ):
													a_							:			Optional[int]     		=					timestep.to(self.timesteps.device )
							a_							:			Optional[Any]     		=					(self.timesteps == timestep).nonzero().item()
							a_							:			List[str]     		=					self.sigmas[step_index]

							a_							:			int     		=					sample / ((sigma**2 + 1) ** 0.5)

							a_							:			Union[str, Any]     		=					True
							return sample







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE = None )    ->	Union[str, Any]:
							a_							:			Dict     		=					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":
													a_							:			Optional[Any]     		=					np.linspace(0       ,     self.config.num_train_timesteps - 1       ,     __a       ,     dtype=__a )[
													    ::-1
													].copy()
							elif self.config.timestep_spacing == "leading":
													a_							:			str     		=					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
													a_							:			int     		=					(np.arange(0       ,     __a ) * step_ratio).round()[::-1].copy().astype(__a )
													timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
													a_							:			Optional[int]     		=					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
													a_							:			str     		=					(np.arange(self.config.num_train_timesteps       ,     0       ,     -step_ratio )).round().copy().astype(__a )
													timesteps -= 1
							else:
													raise ValueError(
													    f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''' )

							a_							:			Tuple     		=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
							a_							:			Tuple     		=					np.log(__a )

							if self.config.interpolation_type == "linear":
													a_							:			Optional[Any]     		=					np.interp(__a       ,     np.arange(0       ,     len(__a ) )       ,     __a )
							elif self.config.interpolation_type == "log_linear":
													a_							:			Optional[Any]     		=					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:
													a_							:			Any     		=					self._convert_to_karras(in_sigmas=__a       ,     num_inference_steps=self.num_inference_steps )
													a_							:			Tuple     		=					np.array([self._sigma_to_t(__a       ,     __a ) for sigma in sigmas] )

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







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE )    ->	Optional[int]:
							a_							:			Any     		=					np.log(__a )

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

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

							a_							:			Tuple     		=					log_sigmas[low_idx]
							a_							:			Any     		=					log_sigmas[high_idx]

							# interpolate sigmas
							a_							:			Dict     		=					(low - log_sigma) / (low - high)
							a_							:			List[Any]     		=					np.clip(__a       ,     0       ,     1 )

							# transform interpolation to time range
							a_							:			Union[str, Any]     		=					(1 - w) * low_idx + w * high_idx
							a_							:			Optional[Any]     		=					t.reshape(sigma.shape )
							return t







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE )    ->	List[Any]:
							a_							:			float     		=					in_sigmas[-1].item()
							a_							:			float     		=					in_sigmas[0].item()

							a_							:			Union[str, Any]     		=					7.0  # 7.0 is the value used in the paper
							a_							:			int     		=					np.linspace(0       ,     1       ,     __a )
							a_							:			int     		=					sigma_min ** (1 / rho)
							a_							:			Optional[Any]     		=					sigma_max ** (1 / rho)
							a_							:			Optional[Any]     		=					(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE = 0.0       ,     _SCREAMING_SNAKE_CASE = 0.0       ,     _SCREAMING_SNAKE_CASE = float("inf" )       ,     _SCREAMING_SNAKE_CASE = 1.0       ,     _SCREAMING_SNAKE_CASE = None       ,     _SCREAMING_SNAKE_CASE = True       ,     )    ->	Any:





							if (
							    isinstance(__a       ,     __a )
							    or isinstance(__a       ,     torch.IntTensor )
							    or isinstance(__a       ,     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(__a       ,     torch.Tensor ):
													a_							:			Optional[int]     		=					timestep.to(self.timesteps.device )

							a_							:			str     		=					(self.timesteps == timestep).nonzero().item()
							a_							:			List[Any]     		=					self.sigmas[step_index]

							a_							:			List[Any]     		=					min(s_churn / (len(self.sigmas ) - 1)       ,     2**0.5 - 1 ) if s_tmin <= sigma <= s_tmax else 0.0

							a_							:			Optional[Any]     		=					randn_tensor(
							    model_output.shape       ,     dtype=model_output.dtype       ,     device=model_output.device       ,     generator=__a )

							a_							:			Optional[Any]     		=					noise * s_noise
							a_							:			int     		=					sigma * (gamma + 1)

							if gamma > 0:
													a_							:			Optional[Any]     		=					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":
													a_							:			Optional[Any]     		=					model_output
							elif self.config.prediction_type == "epsilon":
													a_							:			Tuple     		=					sample - sigma_hat * model_output
							elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													a_							:			List[Any]     		=					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
							a_							:			List[Any]     		=					(sample - pred_original_sample) / sigma_hat

							a_							:			Union[str, Any]     		=					self.sigmas[step_index + 1] - sigma_hat

							a_							:			Tuple     		=					sample + derivative * dt

							if not return_dict:
													return (prev_sample,)

							return EulerDiscreteSchedulerOutput(prev_sample=__a       ,     pred_original_sample=__a )







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE       ,     )    ->	Dict:
							a_							:			Optional[int]     		=					self.sigmas.to(device=original_samples.device       ,     dtype=original_samples.dtype )
							if original_samples.device.type == "mps" and torch.is_floating_point(__a ):
													# mps does not support float64
													a_							:			int     		=					self.timesteps.to(original_samples.device       ,     dtype=torch.floataa )
													a_							:			int     		=					timesteps.to(original_samples.device       ,     dtype=torch.floataa )
							else:
													a_							:			Optional[Any]     		=					self.timesteps.to(original_samples.device )
													a_							:			Any     		=					timesteps.to(original_samples.device )

							a_							:			Tuple     		=					[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

							a_							:			Optional[Any]     		=					original_samples + noise * sigma
							return noisy_samples







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





"""simple docstring"""






from __future__ import annotations

from queue import Queue

def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:int		,			_SCREAMING_SNAKE_CASE	:int  )				-> tuple[int, int]:
						a ^= b
						b ^= a
						a ^= b
						return a, b

def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:int		,			_SCREAMING_SNAKE_CASE	:list[list[int]]  )				-> list[list[int]]:
						a_							:			List[str]     		=					1
						while (1 << j) < max_node:
												for i in range(1		,			max_node + 1  ):
																		a_							:			Union[str, Any]     		=					parent[j - 1][parent[j - 1][i]]
												j += 1
						return parent

def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:int		,			_SCREAMING_SNAKE_CASE	:int		,			_SCREAMING_SNAKE_CASE	:list[int]		,			_SCREAMING_SNAKE_CASE	:list[list[int]]  )				-> int:
						# u must be deeper in the tree than v
						if level[u] < level[v]:
												a_		,					a_							:			Tuple     		=					swap(_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )
						# making depth of u same as depth of v
						for i in range(18		,			-1		,			-1  ):
												if level[u] - (1 << i) >= level[v]:
																		a_							:			Union[str, Any]     		=					parent[i][u]
    # at the same depth if u==v that mean lca is found
						if u == v:
												return u
						# moving both nodes upwards till lca in found
						for i in range(18		,			-1		,			-1  ):
												if parent[i][u] not in [0, parent[i][v]]:
																		a_		,					a_							:			Optional[Any]     		=					parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
						return parent[0][u]

def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:list[int]		,			_SCREAMING_SNAKE_CASE	:list[list[int]]		,			_SCREAMING_SNAKE_CASE	:int		,			_SCREAMING_SNAKE_CASE	:dict[int, list[int]]		,			_SCREAMING_SNAKE_CASE	:int = 1		,			)				-> tuple[list[int], list[list[int]]]:
						a_							:			List[Any]     		=					0
						a_							:			Queue[int]     		=					Queue(maxsize=_SCREAMING_SNAKE_CASE  )
						q.put(_SCREAMING_SNAKE_CASE  )
						while q.qsize() != 0:
												a_							:			List[str]     		=					q.get()
												for v in graph[u]:
																		if level[v] == -1:
																								a_							:			Tuple     		=					level[u] + 1
																								q.put(_SCREAMING_SNAKE_CASE  )
																								a_							:			Optional[int]     		=					u
						return level, parent

def  lowerCAmelCase_      ()				-> None:
						a_							:			List[Any]     		=					13
						# initializing with 0
						a_							:			Dict     		=					[[0 for _ in range(max_node + 10  )] for _ in range(20  )]
						# initializing with -1 which means every node is unvisited
						a_							:			Optional[int]     		=					[-1 for _ in range(max_node + 10  )]
						a_							:			dict[int, list[int]]     		=					{
						    1: [2, 3, 4],
						    2: [5],
						    3: [6, 7],
						    4: [8],
						    5: [9, 10],
						    6: [11],
						    7: [],
						    8: [12, 13],
						    9: [],
						    10: [],
						    11: [],
						    12: [],
						    13: [],
						}
						a_		,					a_							:			Any     		=					breadth_first_search(_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE		,			1  )
						a_							:			Any     		=					create_sparse(_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )
						print("LCA of node 1 and 3 is: "		,			lowest_common_ancestor(1		,			3		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )
						print("LCA of node 5 and 6 is: "		,			lowest_common_ancestor(5		,			6		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )
						print("LCA of node 7 and 11 is: "		,			lowest_common_ancestor(7		,			11		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )
						print("LCA of node 6 and 7 is: "		,			lowest_common_ancestor(6		,			7		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )
						print("LCA of node 4 and 12 is: "		,			lowest_common_ancestor(4		,			12		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )
						print("LCA of node 8 and 8 is: "		,			lowest_common_ancestor(8		,			8		,			_SCREAMING_SNAKE_CASE		,			_SCREAMING_SNAKE_CASE  )  )


if __name__ == "__main__":
				main()




