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   lowerCAmelCase    (       _a      ):
     _SCREAMING_SNAKE_CASE  :  torch.FloatTensor
     _SCREAMING_SNAKE_CASE  :  Optional[torch.FloatTensor]		=None


def 				UpperCamelCase					(     lowerCAmelCase_							,       lowerCAmelCase_=0.999							,       lowerCAmelCase_="cosine"							,       )		->    List[Any]:




       '''simple docstring'''






       if alpha_transform_type == "cosine":

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

       elif alpha_transform_type == "exp":

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

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

       _A=						[]
       for i in range(lowerCAmelCase_ ):
              _A=						i / num_diffusion_timesteps
              _A=						(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    (       _a      ,		_a      ):
     _SCREAMING_SNAKE_CASE  :  int		=[e.name for e in KarrasDiffusionSchedulers]
     _SCREAMING_SNAKE_CASE  :  List[Any]		=1



     @register_to_config
     def __init__(       self					,   lowerCAmelCase__ = 1000					,   lowerCAmelCase__ = 0.0001					,   lowerCAmelCase__ = 0.02					,   lowerCAmelCase__ = "linear"					,   lowerCAmelCase__ = None					,   lowerCAmelCase__ = "epsilon"					,   lowerCAmelCase__ = "linear"					,   lowerCAmelCase__ = False					,   lowerCAmelCase__ = "linspace"					,   lowerCAmelCase__ = 0					,   ):
            if trained_betas is not None:
                   _A=						torch.tensor(lowerCAmelCase__					,   dtype=torch.floataa							)
            elif beta_schedule == "linear":
                   _A=						torch.linspace(lowerCAmelCase__					,   lowerCAmelCase__					,   lowerCAmelCase__					,   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					,   lowerCAmelCase__					,   dtype=torch.floataa							) ** 2
                   )
            elif beta_schedule == "squaredcos_cap_v2":
                   # Glide cosine schedule
                   _A=						betas_for_alpha_bar(lowerCAmelCase__							)
            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(lowerCAmelCase__							)

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



     @property
     def       a__	(       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       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__							):
            if isinstance(lowerCAmelCase__					,   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       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__ = None							):
            _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					,   lowerCAmelCase__					,   dtype=lowerCAmelCase__							)[
                       ::-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					,   lowerCAmelCase__							) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__							)
                   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(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'."							)

            _A=						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
            _A=						np.log(lowerCAmelCase__							)

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

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



     def       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__							):
            # get log sigma
            _A=						np.log(lowerCAmelCase__							)

            # 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(lowerCAmelCase__					,   0					,   1							)

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



     def       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__							):
            _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					,   lowerCAmelCase__							)
            _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       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__					,   lowerCAmelCase__					,   lowerCAmelCase__ = 0.0					,   lowerCAmelCase__ = 0.0					,   lowerCAmelCase__ = float('inf'							)					,   lowerCAmelCase__ = 1.0					,   lowerCAmelCase__ = None					,   lowerCAmelCase__ = True					,   ):

            if (
                isinstance(lowerCAmelCase__					,   lowerCAmelCase__							)
                or isinstance(lowerCAmelCase__					,   torch.IntTensor							)
                or isinstance(lowerCAmelCase__					,   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(lowerCAmelCase__					,   torch.Tensor							):
                   _A=						timestep.to(self.timesteps.device							)

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

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

            _A=						randn_tensor(
                model_output.shape					,   dtype=model_output.dtype					,   device=model_output.device					,   generator=lowerCAmelCase__							)

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

            if gamma > 0:
                   _A=						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=						model_output
            elif self.config.prediction_type == "epsilon":
                   _A=						sample - sigma_hat * 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))
            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_hat

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

            _A=						sample + derivative * dt

            if not return_dict:
                   return (prev_sample,)

            return EulerDiscreteSchedulerOutput(prev_sample=lowerCAmelCase__					,   pred_original_sample=lowerCAmelCase__							)



     def       a__	(       self					,   lowerCAmelCase__					,   lowerCAmelCase__					,   lowerCAmelCase__					,   ):
            # 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(lowerCAmelCase__							):
                   # 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							):
            return self.config.num_train_timesteps
import heapq

def 				UpperCamelCase					(     lowerCAmelCase_							,       lowerCAmelCase_							,       lowerCAmelCase_ )		->    Dict:




       '''simple docstring'''






       _A=						[(0, start)]  # cost from start node,end node
       _A=						set()
       while heap:
              ((_A),      (_A))=						heapq.heappop(lowerCAmelCase_ )
              if u in visited:
                     continue
              visited.add(lowerCAmelCase_ )
              if u == end:
                     return cost
              for v, c in graph[u]:
                     if v in visited:
                            continue
                     _A=						cost + c
                     heapq.heappush(lowerCAmelCase_							,       (next_item, v) )
       return -1


UpperCAmelCase_    		=				{
    '''A''': [['''B''', 2], ['''C''', 5]],
    '''B''': [['''A''', 2], ['''D''', 3], ['''E''', 1], ['''F''', 1]],
    '''C''': [['''A''', 5], ['''F''', 3]],
    '''D''': [['''B''', 3]],
    '''E''': [['''B''', 4], ['''F''', 3]],
    '''F''': [['''C''', 3], ['''E''', 3]],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''F''', 3]],
    '''F''': [],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}

UpperCAmelCase_    		=				dijkstra(G, '''E''', '''C''')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 3 --> F == 3

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
      import doctest

      doctest.testmod()