



from __future__ import annotations

from collections import deque
from queue import Queue
from timeit import timeit

__snake_case		:Any 						=	{
    '''A''': ['''B''', '''C'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F'''],
    '''D''': ['''B'''],
    '''E''': ['''B''', '''F'''],
    '''F''': ['''C''', '''E'''],
}





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase							):
    __a					=							{start}
    __a					=							[start]
    __a					=							Queue()
    queue.put(_UpperCAmelCase							)
    while not queue.empty():
        __a					=							queue.get()
        for w in graph[v]:
            if w not in explored:
                explored.add(_UpperCAmelCase							)
                result.append(_UpperCAmelCase							)
                queue.put(_UpperCAmelCase							)
    return result





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase							):
    __a					=							{start}
    __a					=							[start]
    __a					=							deque([start]							)
    while queue:
        __a					=							queue.popleft()
        for child in graph[v]:
            if child not in visited:
                visited.add(_UpperCAmelCase							)
                result.append(_UpperCAmelCase							)
                queue.append(_UpperCAmelCase							)
    return result





def 	__snake_case      (     _UpperCAmelCase							):
    __a					=							f'from __main__ import G, {name}'
    __a					=							10000
    __a					=							timeit(f'{name}(G, \'A\')'  ,					setup=_UpperCAmelCase  ,					number=_UpperCAmelCase							)
    print(f'{name:<35} finished {number} runs in {res:.5f} seconds'							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 benchmark_function('''breadth_first_search''')
 benchmark_function('''breadth_first_search_with_deque''')
 # breadth_first_search                finished 10000 runs in 0.20999 seconds
 # breadth_first_search_with_deque     finished 10000 runs in 0.01421 seconds










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			(      __UpperCAmelCase       ):
       UpperCamelCase__    :       torch.FloatTensor
       UpperCamelCase__    :       Optional[torch.FloatTensor]		   =		None





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase=0.9_99  ,					_UpperCAmelCase="cosine"  ,					):
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(_UpperCAmelCase							):
            return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2							) ** 2

    elif alpha_transform_type == "exp":

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

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

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

class        _A			(      __UpperCAmelCase ,__UpperCAmelCase       ):
       UpperCamelCase__    :       List[Any]		   =		[e.name for e in KarrasDiffusionSchedulers]
       UpperCamelCase__    :       Optional[Any]		   =		1



       @register_to_config
       def __init__(						self				:	Tuple	,						__SCREAMING_SNAKE_CASE				:	int = 1_000	,						__SCREAMING_SNAKE_CASE				:	float = 0.00_01	,						__SCREAMING_SNAKE_CASE				:	float = 0.02	,						__SCREAMING_SNAKE_CASE				:	str = "linear"	,						__SCREAMING_SNAKE_CASE				:	Optional[Union[np.ndarray, List[float]]] = None	,						__SCREAMING_SNAKE_CASE				:	Optional[bool] = False	,						__SCREAMING_SNAKE_CASE				:	str = "epsilon"	,						__SCREAMING_SNAKE_CASE				:	str = "linspace"	,						__SCREAMING_SNAKE_CASE				:	int = 0	,						):


           '''simple docstring'''

           if trained_betas is not None:
               __a					=							torch.tensor(__SCREAMING_SNAKE_CASE	,						dtype=torch.floataa)
           elif beta_schedule == "linear":
               __a					=							torch.linspace(__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE	,						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	,						__SCREAMING_SNAKE_CASE	,						dtype=torch.floataa) ** 2
               )
           elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               __a					=							betas_for_alpha_bar(__SCREAMING_SNAKE_CASE)
           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(__SCREAMING_SNAKE_CASE)

           # setable values
           __a					=							None
           __a					=							use_karras_sigmas
           self.set_timesteps(__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE)
           __a					=							[]
           __a					=							False



       @property
       def 						_lowerCamelCase     (						self				:	Tuple):


           '''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				:	Any	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	Union[float, torch.FloatTensor]):


           '''simple docstring'''

           if isinstance(__SCREAMING_SNAKE_CASE	,						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 						_lowerCamelCase     (						self				:	Union[str, Any]	,						__SCREAMING_SNAKE_CASE				:	str	,						__SCREAMING_SNAKE_CASE				:	int	,						__SCREAMING_SNAKE_CASE				:	Optional[int]):


           '''simple docstring'''

           def lms_derivative(__SCREAMING_SNAKE_CASE				:	str):
               __a					=							1.0
               for k in range(__SCREAMING_SNAKE_CASE):
                   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(__SCREAMING_SNAKE_CASE	,						self.sigmas[t]	,						self.sigmas[t + 1]	,						epsrel=1E-4)[0]

           return integrated_coeff



       def 						_lowerCamelCase     (						self				:	int	,						__SCREAMING_SNAKE_CASE				:	int	,						__SCREAMING_SNAKE_CASE				:	Union[str, torch.device] = None):


           '''simple docstring'''

           __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	,						__SCREAMING_SNAKE_CASE	,						dtype=__SCREAMING_SNAKE_CASE)[
                   ::-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	,						__SCREAMING_SNAKE_CASE) * step_ratio).round()[::-1].copy().astype(__SCREAMING_SNAKE_CASE)
               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(__SCREAMING_SNAKE_CASE)
               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(__SCREAMING_SNAKE_CASE)
           __a					=							np.interp(__SCREAMING_SNAKE_CASE	,						np.arange(0	,						len(__SCREAMING_SNAKE_CASE))	,						__SCREAMING_SNAKE_CASE)

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

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

           __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)
           if str(__SCREAMING_SNAKE_CASE).startswith('''mps'''):
               # mps does not support float64
               __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(__SCREAMING_SNAKE_CASE	,						dtype=torch.floataa)
           else:
               __a					=							torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)

           __a					=							[]



       def 						_lowerCamelCase     (						self				:	Optional[int]	,						__SCREAMING_SNAKE_CASE				:	Dict	,						__SCREAMING_SNAKE_CASE				:	Any):


           '''simple docstring'''

           __a					=							np.log(__SCREAMING_SNAKE_CASE)

           # 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(__SCREAMING_SNAKE_CASE	,						0	,						1)

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



       def 						_lowerCamelCase     (						self				:	Optional[Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor):


           '''simple docstring'''

           __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 						_lowerCamelCase     (						self				:	Union[str, Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	Union[float, torch.FloatTensor]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	int = 4	,						__SCREAMING_SNAKE_CASE				:	bool = True	,						):


           '''simple docstring'''

           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(__SCREAMING_SNAKE_CASE	,						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(__SCREAMING_SNAKE_CASE)
           if len(self.derivatives) > order:
               self.derivatives.pop(0)

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

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

           if not return_dict:
               return (prev_sample,)

           return LMSDiscreteSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE	,						pred_original_sample=__SCREAMING_SNAKE_CASE)



       def 						_lowerCamelCase     (						self				:	Optional[Any]	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						__SCREAMING_SNAKE_CASE				:	torch.FloatTensor	,						):


           '''simple docstring'''

           __a					=							self.sigmas.to(device=original_samples.device	,						dtype=original_samples.dtype)
           if original_samples.device.type == "mps" and torch.is_floating_point(__SCREAMING_SNAKE_CASE):
               # 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				:	List[str]):


           '''simple docstring'''

           return self.config.num_train_timesteps





