






'''simple docstring'''







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

import numpy as np
import torch
from scipy import integrate

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






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 					a__    (			lowerCamelCase						):
     '''simple docstring'''







     _snake_case             =  42
     _snake_case             =  None







def 						_UpperCamelCase							(     snake_case__							,			snake_case__=0.999							,			snake_case__="cosine"							,			):
      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(snake_case__							):
                  return math.exp(t * -12.0							)

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

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






class 					a__    (			lowerCamelCase ,						lowerCamelCase						):
     '''simple docstring'''







     _snake_case             =  [e.name for e in KarrasDiffusionSchedulers]
     _snake_case             =  1






     @register_to_config
     def __init__(self    :	str				,				lowercase__    :	int = 1000				,				lowercase__    :	float = 0.00_01				,				lowercase__    :	float = 0.02				,				lowercase__    :	str = "linear"				,				lowercase__    :	Optional[Union[np.ndarray, List[float]]] = None				,				lowercase__    :	Optional[bool] = False				,				lowercase__    :	str = "epsilon"				,				lowercase__    :	str = "linspace"				,				lowercase__    :	int = 0				,				)  ->       Union[str, Any]:
           if trained_betas is not None:
                 __A		   =      torch.tensor(lowercase__				,				dtype=torch.floataa					)
           elif beta_schedule == "linear":
                 __A		   =      torch.linspace(lowercase__				,				lowercase__				,				lowercase__				,				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				,				lowercase__				,				dtype=torch.floataa					) ** 2
                 )
           elif beta_schedule == "squaredcos_cap_v2":
                 # Glide cosine schedule
                 __A		   =      betas_for_alpha_bar(lowercase__					)
           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		   =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
           __A		   =      np.concatenate([sigmas[::-1], [0.0]]					).astype(np.floataa					)
           __A		   =      torch.from_numpy(lowercase__					)

           # setable values
           __A		   =      None
           __A		   =      use_karras_sigmas
           self.set_timesteps(lowercase__				,				lowercase__					)
           __A		   =      []
           __A		   =      False






     @property
     def     _UpperCamelCase   (self    :	Optional[Any]					)  ->       Optional[int]:
           # 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     _UpperCamelCase   (self    :	int				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	Union[float, torch.FloatTensor]					)  ->       torch.FloatTensor:
           if isinstance(lowercase__				,				torch.Tensor					):
                 __A		   =      timestep.to(self.timesteps.device					)
           __A		   =      (self.timesteps == timestep).nonzero().item()
           __A		   =      self.sigmas[step_index]
           __A		   =      sample / ((sigma**2 + 1) ** 0.5)
           __A		   =      True
           return sample






     def     _UpperCamelCase   (self    :	Dict				,				lowercase__    :	Any				,				lowercase__    :	str				,				lowercase__    :	Union[str, Any]					)  ->       Any:

           def lms_derivative(lowercase__    :	Optional[Any]					):
                 __A		   =      1.0
                 for k in range(lowercase__					):
                       if current_order == k:
                             continue
                       prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
                 return prod

           __A		   =      integrate.quad(lowercase__				,				self.sigmas[t]				,				self.sigmas[t + 1]				,				epsrel=1e-4					)[0]

           return integrated_coeff






     def     _UpperCamelCase   (self    :	Any				,				lowercase__    :	int				,				lowercase__    :	Union[str, torch.device] = None					)  ->       Union[str, Any]:
           __A		   =      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		   =      np.linspace(0				,				self.config.num_train_timesteps - 1				,				lowercase__				,				dtype=lowercase__					)[
                     ::-1
                 ].copy()
           elif self.config.timestep_spacing == "leading":
                 __A		   =      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		   =      (np.arange(0				,				lowercase__					) * step_ratio).round()[::-1].copy().astype(lowercase__					)
                 timesteps += self.config.steps_offset
           elif self.config.timestep_spacing == "trailing":
                 __A		   =      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		   =      (np.arange(self.config.num_train_timesteps				,				0				,				-step_ratio					)).round().copy().astype(lowercase__					)
                 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		   =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
           __A		   =      np.log(lowercase__					)
           __A		   =      np.interp(lowercase__				,				np.arange(0				,				len(lowercase__					)					)				,				lowercase__					)

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

           __A		   =      np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)

           __A		   =      torch.from_numpy(lowercase__					).to(device=lowercase__					)
           if str(lowercase__					).startswith("mps"					):
                 # mps does not support float64
                 __A		   =      torch.from_numpy(lowercase__					).to(lowercase__				,				dtype=torch.floataa					)
           else:
                 __A		   =      torch.from_numpy(lowercase__					).to(device=lowercase__					)

           __A		   =      []






     def     _UpperCamelCase   (self    :	str				,				lowercase__    :	str				,				lowercase__    :	List[Any]					)  ->       Dict:
           # get log sigma
           __A		   =      np.log(lowercase__					)

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

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

           __A		   =      log_sigmas[low_idx]
           __A		   =      log_sigmas[high_idx]

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

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






     def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	torch.FloatTensor					)  ->       torch.FloatTensor:
           __A		   =      in_sigmas[-1].item()
           __A		   =      in_sigmas[0].item()

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






     def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	Union[float, torch.FloatTensor]				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	int = 4				,				lowercase__    :	bool = True				,				)  ->       Union[LMSDiscreteSchedulerOutput, Tuple]:
           if not self.is_scale_input_called:
                 warnings.warn(
                     "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                     "See `StableDiffusionPipeline` for a usage example."					)

           if isinstance(lowercase__				,				torch.Tensor					):
                 __A		   =      timestep.to(self.timesteps.device					)
           __A		   =      (self.timesteps == timestep).nonzero().item()
           __A		   =      self.sigmas[step_index]

           # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
           if self.config.prediction_type == "epsilon":
                 __A		   =      sample - sigma * model_output
           elif self.config.prediction_type == "v_prediction":
                 # * c_out + input * c_skip
                 __A		   =      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
           elif self.config.prediction_type == "sample":
                 __A		   =      model_output
           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		   =      (sample - pred_original_sample) / sigma
           self.derivatives.append(lowercase__					)
           if len(self.derivatives					) > order:
                 self.derivatives.pop(0					)

           # 3. Compute linear multistep coefficients
           __A		   =      min(step_index + 1				,				lowercase__					)
           __A		   =      [self.get_lms_coefficient(lowercase__				,				lowercase__				,				lowercase__					) for curr_order in range(lowercase__					)]

           # 4. Compute previous sample based on the derivatives path
           __A		   =      sample + sum(
               coeff * derivative for coeff, derivative in zip(lowercase__				,				reversed(self.derivatives					)					)					)

           if not return_dict:
                 return (prev_sample,)

           return LMSDiscreteSchedulerOutput(prev_sample=lowercase__				,				pred_original_sample=lowercase__					)






     def     _UpperCamelCase   (self    :	int				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	torch.FloatTensor				,				lowercase__    :	torch.FloatTensor				,				)  ->       torch.FloatTensor:
           # Make sure sigmas and timesteps have the same device and dtype as original_samples
           __A		   =      self.sigmas.to(device=original_samples.device				,				dtype=original_samples.dtype					)
           if original_samples.device.type == "mps" and torch.is_floating_point(lowercase__					):
                 # mps does not support float64
                 __A		   =      self.timesteps.to(original_samples.device				,				dtype=torch.floataa					)
                 __A		   =      timesteps.to(original_samples.device				,				dtype=torch.floataa					)
           else:
                 __A		   =      self.timesteps.to(original_samples.device					)
                 __A		   =      timesteps.to(original_samples.device					)

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

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

           __A		   =      original_samples + noise * sigma
           return noisy_samples






     def __len__(self    :	Tuple					)  ->       Optional[int]:
           return self.config.num_train_timesteps










'''simple docstring'''







from __future__ import annotations

from queue import Queue






class 					a__    :
     '''simple docstring'''







     def __init__(self    :	Any					)  ->       None:
           __A		   =      {}






     def     _UpperCamelCase   (self    :	Optional[int]					)  ->       None:
           for i in self.vertices:
                 print(lowercase__				,				" : "				,				" -> ".join([str(lowercase__					) for j in self.vertices[i]]					)					)






     def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	int				,				lowercase__    :	int					)  ->       None:
           if from_vertex in self.vertices:
                 self.vertices[from_vertex].append(lowercase__					)
           else:
                 __A		   =      [to_vertex]






     def     _UpperCamelCase   (self    :	Optional[int]				,				lowercase__    :	int					)  ->       set[int]:
           __A		   =      set()

           # create a first in first out queue to store all the vertices for BFS
           __A		   =      Queue()

           # mark the source node as visited and enqueue it
           visited.add(lowercase__					)
           queue.put(lowercase__					)

           while not queue.empty():
                 __A		   =      queue.get()

                 # loop through all adjacent vertex and enqueue it if not yet visited
                 for adjacent_vertex in self.vertices[vertex]:
                       if adjacent_vertex not in visited:
                             queue.put(lowercase__					)
                             visited.add(lowercase__					)
           return visited


if __name__ == "__main__":
       from doctest import testmod

       testmod(verbose=True)

       __A      :       Dict      =	Graph()
       g.add_edge(0, 1)
       g.add_edge(0, 2)
       g.add_edge(1, 2)
       g.add_edge(2, 0)
       g.add_edge(2, 3)
       g.add_edge(3, 3)

       g.print_graph()
       # 0  :  1 -> 2
       # 1  :  2
       # 2  :  0 -> 3
       # 3  :  3

       assert sorted(g.bfs(2)) == [0, 1, 2, 3]


