


'''simple docstring'''


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def  __lowerCAmelCase (__lowerCAmelCase      , __lowerCAmelCase=0.9_9_9      , __lowerCAmelCase="cosine"      , ):

		'''simple docstring'''





		if alpha_transform_type == "cosine":

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

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

		_UpperCAmelCase		:       List[Any]								=      []
		for i in range(lowerCamelCase_   ):
				_UpperCAmelCase		:       List[Any]								=      i / num_diffusion_timesteps
				_UpperCAmelCase		:       Union[str, Any]								=      (i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(lowerCamelCase_   ) / alpha_bar_fn(lowerCamelCase_   )      , lowerCamelCase_   )   )
		return torch.tensor(lowerCamelCase_      , dtype=torch.floataa   )






class 	lowerCAmelCase__			(			lowerCAmelCase__    ,       lowerCAmelCase__	):
			lowerCAmelCase :	str          =     [e.name for e in KarrasDiffusionSchedulers]
			lowerCAmelCase :	Dict          =     2




			@register_to_config
			def __init__(		self  :     Dict	,  lowerCamelCase__  :     List[Any] = 10_00	,  lowerCamelCase__  :     Any = 0.0_0_0_8_5	,  lowerCamelCase__  :     Any = 0.0_1_2	,  lowerCamelCase__  :     int = "linear"	,  lowerCamelCase__  :     Union[str, Any] = None	,  lowerCamelCase__  :     Optional[Any] = "epsilon"	,  lowerCamelCase__  :     List[str] = False	,  lowerCamelCase__  :     List[Any] = False	,  lowerCamelCase__  :     str = 1.0	,  lowerCamelCase__  :     Tuple = "linspace"	,  lowerCamelCase__  :     List[str] = 0	,  )   ->List[Any]:



					'''simple docstring'''







					if trained_betas is not None:
							_UpperCAmelCase		:       Optional[int]								=      torch.tensor(_lowerCamelCase	,  dtype=torch.floataa )
					elif beta_schedule == "linear":
							_UpperCAmelCase		:       Dict								=      torch.linspace(_lowerCamelCase	,  _lowerCamelCase	,  _lowerCamelCase	,  dtype=torch.floataa )
					elif beta_schedule == "scaled_linear":
							# this schedule is very specific to the latent diffusion model.
							_UpperCAmelCase		:       Optional[Any]								=      (
							    torch.linspace(beta_start**0.5	,  beta_end**0.5	,  _lowerCamelCase	,  dtype=torch.floataa ) ** 2
							)
					elif beta_schedule == "squaredcos_cap_v2":
							# Glide cosine schedule
							_UpperCAmelCase		:       Optional[Any]								=      betas_for_alpha_bar(_lowerCamelCase	,  alpha_transform_type="cosine" )
					elif beta_schedule == "exp":
							_UpperCAmelCase		:       str								=      betas_for_alpha_bar(_lowerCamelCase	,  alpha_transform_type="exp" )
					else:
							raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}""" )

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

					#  set all values
					self.set_timesteps(_lowerCamelCase	,  _lowerCamelCase	,  _lowerCamelCase )
					_UpperCAmelCase		:       Dict								=      use_karras_sigmas




			def 							lowerCAmelCase__    (		self  :     Optional[int]	,  lowerCamelCase__  :     List[Any]	,  lowerCamelCase__  :     Optional[Any]=None )   ->Optional[int]:



					'''simple docstring'''







					if schedule_timesteps is None:
							_UpperCAmelCase		:       Any								=      self.timesteps

					_UpperCAmelCase		:       int								=      (schedule_timesteps == timestep).nonzero()

					# The sigma index that is taken for the **very** first `step`
					# is always the second index (or the last index if there is only 1)
					# This way we can ensure we don't accidentally skip a sigma in
					# case we start in the middle of the denoising schedule (e.g. for image-to-image)
					if len(self._index_counter ) == 0:
							_UpperCAmelCase		:       Union[str, Any]								=      1 if len(_lowerCamelCase ) > 1 else 0
					else:
							_UpperCAmelCase		:       Tuple								=      timestep.cpu().item() if torch.is_tensor(_lowerCamelCase ) else timestep
							_UpperCAmelCase		:       int								=      self._index_counter[timestep_int]

					return indices[pos].item()




			@property
			def 							lowerCAmelCase__    (		self  :     List[Any] )   ->Optional[int]:



					'''simple docstring'''







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

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




			def 							lowerCAmelCase__    (		self  :     List[str]	,  lowerCamelCase__  :     Tuple	,  lowerCamelCase__  :     List[Any]	,  )   ->torch.FloatTensor:



					'''simple docstring'''







					_UpperCAmelCase		:       Any								=      self.index_for_timestep(_lowerCamelCase )

					_UpperCAmelCase		:       Tuple								=      self.sigmas[step_index]
					_UpperCAmelCase		:       Dict								=      sample / ((sigma**2 + 1) ** 0.5)
					return sample




			def 							lowerCAmelCase__    (		self  :     Optional[int]	,  lowerCamelCase__  :     Any	,  lowerCamelCase__  :     int = None	,  lowerCamelCase__  :     Dict = None	,  )   ->Optional[int]:



					'''simple docstring'''







					_UpperCAmelCase		:       Union[str, Any]								=      num_inference_steps

					_UpperCAmelCase		:       List[str]								=      num_train_timesteps or self.config.num_train_timesteps

					# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
					if self.config.timestep_spacing == "linspace":
							_UpperCAmelCase		:       str								=      np.linspace(0	,  num_train_timesteps - 1	,  _lowerCamelCase	,  dtype=_lowerCamelCase )[::-1].copy()
					elif self.config.timestep_spacing == "leading":
							_UpperCAmelCase		:       int								=      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
							_UpperCAmelCase		:       Tuple								=      (np.arange(0	,  _lowerCamelCase ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase )
							timesteps += self.config.steps_offset
					elif self.config.timestep_spacing == "trailing":
							_UpperCAmelCase		:       Dict								=      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
							_UpperCAmelCase		:       int								=      (np.arange(_lowerCamelCase	,  0	,  -step_ratio )).round().copy().astype(_lowerCamelCase )
							timesteps -= 1
					else:
							raise ValueError(
							    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'.""" )

					_UpperCAmelCase		:       Dict								=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
					_UpperCAmelCase		:       List[Any]								=      np.log(_lowerCamelCase )
					_UpperCAmelCase		:       int								=      np.interp(_lowerCamelCase	,  np.arange(0	,  len(_lowerCamelCase ) )	,  _lowerCamelCase )

					if self.config.use_karras_sigmas:
							_UpperCAmelCase		:       Dict								=      self._convert_to_karras(in_sigmas=_lowerCamelCase	,  num_inference_steps=self.num_inference_steps )
							_UpperCAmelCase		:       Tuple								=      np.array([self._sigma_to_t(_lowerCamelCase	,  _lowerCamelCase ) for sigma in sigmas] )

					_UpperCAmelCase		:       int								=      np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
					_UpperCAmelCase		:       Optional[Any]								=      torch.from_numpy(_lowerCamelCase ).to(device=_lowerCamelCase )
					_UpperCAmelCase		:       List[Any]								=      torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2 ), sigmas[-1:]] )

					_UpperCAmelCase		:       str								=      torch.from_numpy(_lowerCamelCase )
					_UpperCAmelCase		:       Any								=      torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2 )] )

					if str(_lowerCamelCase ).startswith("mps" ):
							# mps does not support float64
							_UpperCAmelCase		:       Optional[int]								=      timesteps.to(_lowerCamelCase	,  dtype=torch.floataa )
					else:
							_UpperCAmelCase		:       List[str]								=      timesteps.to(device=_lowerCamelCase )

					# empty dt and derivative
					_UpperCAmelCase		:       Union[str, Any]								=      None
					_UpperCAmelCase		:       List[str]								=      None

					# for exp beta schedules, such as the one for `pipeline_shap_e.py`
					# we need an index counter
					_UpperCAmelCase		:       List[Any]								=      defaultdict(_lowerCamelCase )




			def 							lowerCAmelCase__    (		self  :     List[Any]	,  lowerCamelCase__  :     List[Any]	,  lowerCamelCase__  :     List[Any] )   ->str:



					'''simple docstring'''







					_UpperCAmelCase		:       List[Any]								=      np.log(_lowerCamelCase )

					# get distribution
					_UpperCAmelCase		:       Optional[Any]								=      log_sigma - log_sigmas[:, np.newaxis]

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

					_UpperCAmelCase		:       Optional[Any]								=      log_sigmas[low_idx]
					_UpperCAmelCase		:       str								=      log_sigmas[high_idx]

					# interpolate sigmas
					_UpperCAmelCase		:       Optional[Any]								=      (low - log_sigma) / (low - high)
					_UpperCAmelCase		:       Optional[int]								=      np.clip(_lowerCamelCase	,  0	,  1 )

					# transform interpolation to time range
					_UpperCAmelCase		:       int								=      (1 - w) * low_idx + w * high_idx
					_UpperCAmelCase		:       Optional[int]								=      t.reshape(sigma.shape )
					return t




			def 							lowerCAmelCase__    (		self  :     Any	,  lowerCamelCase__  :     str	,  lowerCamelCase__  :     Dict )   ->torch.FloatTensor:



					'''simple docstring'''







					_UpperCAmelCase		:       List[Any]								=      in_sigmas[-1].item()
					_UpperCAmelCase		:       List[str]								=      in_sigmas[0].item()

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




			@property
			def 							lowerCAmelCase__    (		self  :     Tuple )   ->Any:



					'''simple docstring'''







					return self.dt is None




			def 							lowerCAmelCase__    (		self  :     int	,  lowerCamelCase__  :     Union[str, Any]	,  lowerCamelCase__  :     Tuple	,  lowerCamelCase__  :     Optional[int]	,  lowerCamelCase__  :     List[str] = True	,  )   ->Union[SchedulerOutput, Tuple]:



					'''simple docstring'''







					_UpperCAmelCase		:       Dict								=      self.index_for_timestep(_lowerCamelCase )

					# advance index counter by 1
					_UpperCAmelCase		:       Optional[int]								=      timestep.cpu().item() if torch.is_tensor(_lowerCamelCase ) else timestep
					self._index_counter[timestep_int] += 1

					if self.state_in_first_order:
							_UpperCAmelCase		:       List[Any]								=      self.sigmas[step_index]
							_UpperCAmelCase		:       int								=      self.sigmas[step_index + 1]
					else:
							# 2nd order / Heun's method
							_UpperCAmelCase		:       List[str]								=      self.sigmas[step_index - 1]
							_UpperCAmelCase		:       Tuple								=      self.sigmas[step_index]

					# currently only gamma=0 is supported. This usually works best anyways.
					# We can support gamma in the future but then need to scale the timestep before
					# passing it to the model which requires a change in API
					_UpperCAmelCase		:       List[Any]								=      0
					_UpperCAmelCase		:       List[Any]								=      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

					# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
					if self.config.prediction_type == "epsilon":
							_UpperCAmelCase		:       Optional[int]								=      sigma_hat if self.state_in_first_order else sigma_next
							_UpperCAmelCase		:       int								=      sample - sigma_input * model_output
					elif self.config.prediction_type == "v_prediction":
							_UpperCAmelCase		:       Dict								=      sigma_hat if self.state_in_first_order else sigma_next
							_UpperCAmelCase		:       Optional[int]								=      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
							    sample / (sigma_input**2 + 1)
							)
					elif self.config.prediction_type == "sample":
							_UpperCAmelCase		:       Any								=      model_output
					else:
							raise ValueError(
							    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`""" )

					if self.config.clip_sample:
							_UpperCAmelCase		:       Any								=      pred_original_sample.clamp(
							    -self.config.clip_sample_range	,  self.config.clip_sample_range )

					if self.state_in_first_order:
							# 2. Convert to an ODE derivative for 1st order
							_UpperCAmelCase		:       int								=      (sample - pred_original_sample) / sigma_hat
							# 3. delta timestep
							_UpperCAmelCase		:       Dict								=      sigma_next - sigma_hat

							# store for 2nd order step
							_UpperCAmelCase		:       Tuple								=      derivative
							_UpperCAmelCase		:       List[Any]								=      dt
							_UpperCAmelCase		:       Optional[Any]								=      sample
					else:
							# 2. 2nd order / Heun's method
							_UpperCAmelCase		:       Optional[Any]								=      (sample - pred_original_sample) / sigma_next
							_UpperCAmelCase		:       List[Any]								=      (self.prev_derivative + derivative) / 2

							# 3. take prev timestep & sample
							_UpperCAmelCase		:       Dict								=      self.dt
							_UpperCAmelCase		:       int								=      self.sample

							# free dt and derivative
							# Note, this puts the scheduler in "first order mode"
							_UpperCAmelCase		:       Union[str, Any]								=      None
							_UpperCAmelCase		:       Optional[Any]								=      None
							_UpperCAmelCase		:       str								=      None

					_UpperCAmelCase		:       Optional[Any]								=      sample + derivative * dt

					if not return_dict:
							return (prev_sample,)

					return SchedulerOutput(prev_sample=_lowerCamelCase )




			def 							lowerCAmelCase__    (		self  :     List[Any]	,  lowerCamelCase__  :     str	,  lowerCamelCase__  :     Optional[int]	,  lowerCamelCase__  :     int	,  )   ->torch.FloatTensor:



					'''simple docstring'''







					_UpperCAmelCase		:       Dict								=      self.sigmas.to(device=original_samples.device	,  dtype=original_samples.dtype )
					if original_samples.device.type == "mps" and torch.is_floating_point(_lowerCamelCase ):
							# mps does not support float64
							_UpperCAmelCase		:       List[Any]								=      self.timesteps.to(original_samples.device	,  dtype=torch.floataa )
							_UpperCAmelCase		:       Union[str, Any]								=      timesteps.to(original_samples.device	,  dtype=torch.floataa )
					else:
							_UpperCAmelCase		:       Dict								=      self.timesteps.to(original_samples.device )
							_UpperCAmelCase		:       int								=      timesteps.to(original_samples.device )

					_UpperCAmelCase		:       int								=      [self.index_for_timestep(_lowerCamelCase	,  _lowerCamelCase ) for t in timesteps]

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

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






			def __len__(		self  :     Any )   ->Dict:



					'''simple docstring'''







					return self.config.num_train_timesteps







'''simple docstring'''


def  __lowerCAmelCase (__lowerCAmelCase   ):  # noqa: E741
		_UpperCAmelCase		:       List[str]								=      len(__lowerCAmelCase   )
		_UpperCAmelCase		:       str								=      0
		_UpperCAmelCase		:       List[str]								=      [0] * n
		_UpperCAmelCase		:       int								=      [False] * n
		_UpperCAmelCase		:       Dict								=      [False] * n

		def dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   ):
				if parent == root:
						out_edge_count += 1
				_UpperCAmelCase		:       List[Any]								=      True
				_UpperCAmelCase		:       str								=      at

				for to in l[at]:
						if to == parent:
								pass
						elif not visited[to]:
								_UpperCAmelCase		:       List[str]								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   )
								_UpperCAmelCase		:       Tuple								=      min(low[at]      , low[to]   )

								# AP found via bridge
								if at < low[to]:
										_UpperCAmelCase		:       Dict								=      True
								# AP found via cycle
								if at == low[to]:
										_UpperCAmelCase		:       Dict								=      True
						else:
								_UpperCAmelCase		:       Optional[int]								=      min(low[at]      , __lowerCAmelCase   )
				return out_edge_count

		for i in range(__lowerCAmelCase   ):
				if not visited[i]:
						_UpperCAmelCase		:       str								=      0
						_UpperCAmelCase		:       Tuple								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , -1      , __lowerCAmelCase   )
						_UpperCAmelCase		:       Optional[int]								=      out_edge_count > 1

		for x in range(len(__lowerCAmelCase   )   ):
				if is_art[x] is True:
						print(__lowerCAmelCase   )


# Adjacency list of graph
lowerCamelCase__    	=     {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}





compute_ap(data)



