





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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
def     A__					(						SCREAMING_SNAKE_CASE_      :			str							,  SCREAMING_SNAKE_CASE_      :			Optional[Any]=0.9_9_9							,  SCREAMING_SNAKE_CASE_      :			str="cosine"							,  )     ->     List[str]:






   """simple docstring"""







   if alpha_transform_type == "cosine":

      def alpha_bar_fn(SCREAMING_SNAKE_CASE_      :			Union[str, Any]	):
         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(SCREAMING_SNAKE_CASE_      :			Optional[Any]	):
         return math.exp(t * -1_2.0	)

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

   _UpperCAmelCase											=      []
   for i in range(SCREAMING_SNAKE_CASE_	):
      _UpperCAmelCase											=      i / num_diffusion_timesteps
      _UpperCAmelCase											=      (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						(       A__  ,   A__						):
     __A  :     Dict            =      [e.name for e in KarrasDiffusionSchedulers]
     __A  :     int            =      2





     @register_to_config
     def __init__(    self							,       _UpperCamelCase = 1000							,       _UpperCamelCase = 0.00085							,       _UpperCamelCase = 0.012							,       _UpperCamelCase = "linear"							,       _UpperCamelCase = None							,       _UpperCamelCase = "epsilon"							,       _UpperCamelCase = "linspace"							,       _UpperCamelCase = 0							,       ):
        if trained_betas is not None:
           _UpperCAmelCase											=      torch.tensor(_UpperCamelCase							,       dtype=torch.floataa				)
        elif beta_schedule == "linear":
           _UpperCAmelCase											=      torch.linspace(_UpperCamelCase							,       _UpperCamelCase							,       _UpperCamelCase							,       dtype=torch.floataa				)
        elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           _UpperCAmelCase											=      (
               torch.linspace(beta_start**0.5							,       beta_end**0.5							,       _UpperCamelCase							,       dtype=torch.floataa				) ** 2
           )
        elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           _UpperCAmelCase											=      betas_for_alpha_bar(_UpperCamelCase				)
        else:
           raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''				)

        _UpperCAmelCase											=      1.0 - self.betas
        _UpperCAmelCase											=      torch.cumprod(self.alphas							,       dim=0				)

        #  set all values
        self.set_timesteps(_UpperCamelCase							,       _UpperCamelCase							,       _UpperCamelCase				)





     def 		UpperCamelCase(    self							,       _UpperCamelCase							,       _UpperCamelCase=None				):
        if schedule_timesteps is None:
           _UpperCAmelCase											=      self.timesteps

        _UpperCAmelCase											=      (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											=      1 if len(_UpperCamelCase				) > 1 else 0
        else:
           _UpperCAmelCase											=      timestep.cpu().item() if torch.is_tensor(_UpperCamelCase				) else timestep
           _UpperCAmelCase											=      self._index_counter[timestep_int]

        return indices[pos].item()





     @property
     def 		UpperCamelCase(    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 		UpperCamelCase(    self							,       _UpperCamelCase							,       _UpperCamelCase							,       ):
        _UpperCAmelCase											=      self.index_for_timestep(_UpperCamelCase				)

        if self.state_in_first_order:
           _UpperCAmelCase											=      self.sigmas[step_index]
        else:
           _UpperCAmelCase											=      self.sigmas_interpol[step_index - 1]

        _UpperCAmelCase											=      sample / ((sigma**2 + 1) ** 0.5)
        return sample





     def 		UpperCamelCase(    self							,       _UpperCamelCase							,       _UpperCamelCase = None							,       _UpperCamelCase = None							,       ):
        _UpperCAmelCase											=      num_inference_steps

        _UpperCAmelCase											=      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											=      np.linspace(0							,       num_train_timesteps - 1							,       _UpperCamelCase							,       dtype=_UpperCamelCase				)[::-1].copy()
        elif self.config.timestep_spacing == "leading":
           _UpperCAmelCase											=      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											=      (np.arange(0							,       _UpperCamelCase				) * step_ratio).round()[::-1].copy().astype(_UpperCamelCase				)
           timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
           _UpperCAmelCase											=      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											=      (np.arange(_UpperCamelCase							,       0							,       -step_ratio				)).round().copy().astype(_UpperCamelCase				)
           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											=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
        _UpperCAmelCase											=      torch.from_numpy(np.log(_UpperCamelCase				)				).to(_UpperCamelCase				)

        _UpperCAmelCase											=      np.interp(_UpperCamelCase							,       np.arange(0							,       len(_UpperCamelCase				)				)							,       _UpperCamelCase				)
        _UpperCAmelCase											=      np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)
        _UpperCAmelCase											=      torch.from_numpy(_UpperCamelCase				).to(device=_UpperCamelCase				)

        # compute up and down sigmas
        _UpperCAmelCase											=      sigmas.roll(-1				)
        _UpperCAmelCase											=      0.0
        _UpperCAmelCase											=      (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
        _UpperCAmelCase											=      (sigmas_next**2 - sigmas_up**2) ** 0.5
        _UpperCAmelCase											=      0.0

        # compute interpolated sigmas
        _UpperCAmelCase											=      sigmas.log().lerp(sigmas_down.log()							,       0.5				).exp()
        _UpperCAmelCase											=      0.0

        # set sigmas
        _UpperCAmelCase											=      torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2				), sigmas[-1:]]				)
        _UpperCAmelCase											=      torch.cat(
            [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2				), sigmas_interpol[-1:]]				)
        _UpperCAmelCase											=      torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2				), sigmas_up[-1:]]				)
        _UpperCAmelCase											=      torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2				), sigmas_down[-1:]]				)

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

        _UpperCAmelCase											=      self.sigma_to_t(_UpperCamelCase				).to(_UpperCamelCase							,       dtype=timesteps.dtype				)
        _UpperCAmelCase											=      torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])							,       dim=-1				).flatten()

        _UpperCAmelCase											=      torch.cat([timesteps[:1], interleaved_timesteps]				)

        _UpperCAmelCase											=      None

        # for exp beta schedules, such as the one for `pipeline_shap_e.py`
        # we need an index counter
        _UpperCAmelCase											=      defaultdict(_UpperCamelCase				)





     def 		UpperCamelCase(    self							,       _UpperCamelCase				):
        # get log sigma
        _UpperCAmelCase											=      sigma.log()

        # get distribution
        _UpperCAmelCase											=      log_sigma - self.log_sigmas[:, None]

        # get sigmas range
        _UpperCAmelCase											=      dists.ge(0				).cumsum(dim=0				).argmax(dim=0				).clamp(max=self.log_sigmas.shape[0] - 2				)
        _UpperCAmelCase											=      low_idx + 1

        _UpperCAmelCase											=      self.log_sigmas[low_idx]
        _UpperCAmelCase											=      self.log_sigmas[high_idx]

        # interpolate sigmas
        _UpperCAmelCase											=      (low - log_sigma) / (low - high)
        _UpperCAmelCase											=      w.clamp(0							,       1				)

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





     @property
     def 		UpperCamelCase(    self				):
        return self.sample is None





     def 		UpperCamelCase(    self							,       _UpperCamelCase							,       _UpperCamelCase							,       _UpperCamelCase							,       _UpperCamelCase = None							,       _UpperCamelCase = True							,       ):
        _UpperCAmelCase											=      self.index_for_timestep(_UpperCamelCase				)

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

        if self.state_in_first_order:
           _UpperCAmelCase											=      self.sigmas[step_index]
           _UpperCAmelCase											=      self.sigmas_interpol[step_index]
           _UpperCAmelCase											=      self.sigmas_up[step_index]
           _UpperCAmelCase											=      self.sigmas_down[step_index - 1]
        else:
           # 2nd order / KPDM2's method
           _UpperCAmelCase											=      self.sigmas[step_index - 1]
           _UpperCAmelCase											=      self.sigmas_interpol[step_index - 1]
           _UpperCAmelCase											=      self.sigmas_up[step_index - 1]
           _UpperCAmelCase											=      self.sigmas_down[step_index - 1]

        # 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											=      0
        _UpperCAmelCase											=      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

        _UpperCAmelCase											=      model_output.device
        _UpperCAmelCase											=      randn_tensor(model_output.shape							,       dtype=model_output.dtype							,       device=_UpperCamelCase							,       generator=_UpperCamelCase				)

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
           _UpperCAmelCase											=      sigma_hat if self.state_in_first_order else sigma_interpol
           _UpperCAmelCase											=      sample - sigma_input * model_output
        elif self.config.prediction_type == "v_prediction":
           _UpperCAmelCase											=      sigma_hat if self.state_in_first_order else sigma_interpol
           _UpperCAmelCase											=      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
               sample / (sigma_input**2 + 1)
           )
        elif self.config.prediction_type == "sample":
           raise NotImplementedError('''prediction_type not implemented yet: sample'''				)
        else:
           raise ValueError(
               f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''				)

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

           # store for 2nd order step
           _UpperCAmelCase											=      sample
           _UpperCAmelCase											=      dt
           _UpperCAmelCase											=      sample + derivative * dt
        else:
           # DPM-Solver-2
           # 2. Convert to an ODE derivative for 2nd order
           _UpperCAmelCase											=      (sample - pred_original_sample) / sigma_interpol
           # 3. delta timestep
           _UpperCAmelCase											=      sigma_down - sigma_hat

           _UpperCAmelCase											=      self.sample
           _UpperCAmelCase											=      None

           _UpperCAmelCase											=      sample + derivative * dt
           _UpperCAmelCase											=      prev_sample + noise * sigma_up

        if not return_dict:
           return (prev_sample,)

        return SchedulerOutput(prev_sample=_UpperCamelCase				)





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

        _UpperCAmelCase											=      [self.index_for_timestep(_UpperCamelCase							,       _UpperCamelCase				) for t in timesteps]

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

        _UpperCAmelCase											=      original_samples + noise * sigma
        return noisy_samples





     def __len__(    self				):
        return self.config.num_train_timesteps






def     A__					(						SCREAMING_SNAKE_CASE_      :			Optional[int]							,  SCREAMING_SNAKE_CASE_      :			str	)     ->     List[str]:






   """simple docstring"""







   print('''\nVertex Distance'''	)
   for i in range(SCREAMING_SNAKE_CASE_	):
      if dist[i] != float('''inf'''	):
         print(SCREAMING_SNAKE_CASE_							,  '''\t'''							,  int(dist[i]	)							,  end='''\t'''	)
      else:
         print(SCREAMING_SNAKE_CASE_							,  '''\t'''							,  '''INF'''							,  end='''\t'''	)
      print()
def     A__					(						SCREAMING_SNAKE_CASE_      :			Any							,  SCREAMING_SNAKE_CASE_      :			Optional[Any]							,  SCREAMING_SNAKE_CASE_      :			str	)     ->     Any:






   """simple docstring"""







   _UpperCAmelCase											=      float('''inf'''	)
   _UpperCAmelCase											=      -1
   for i in range(SCREAMING_SNAKE_CASE_	):
      if (not vset[i]) and mdist[i] < min_val:
         _UpperCAmelCase											=      i
         _UpperCAmelCase											=      mdist[i]
   return min_ind
def     A__					(						SCREAMING_SNAKE_CASE_      :			str							,  SCREAMING_SNAKE_CASE_      :			Dict							,  SCREAMING_SNAKE_CASE_      :			int	)     ->     Any:






   """simple docstring"""







   _UpperCAmelCase											=      [float('''inf'''	) for _ in range(SCREAMING_SNAKE_CASE_	)]
   _UpperCAmelCase											=      [False for _ in range(SCREAMING_SNAKE_CASE_	)]
   _UpperCAmelCase											=      0.0

   for _ in range(v - 1	):
      _UpperCAmelCase											=      min_dist(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	)
      _UpperCAmelCase											=      True

      for i in range(SCREAMING_SNAKE_CASE_	):
         if (
             (not vset[i])
             and graph[u][i] != float('''inf'''	)
             and mdist[u] + graph[u][i] < mdist[i]
         ):
            _UpperCAmelCase											=      mdist[u] + graph[u][i]

   print_dist(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
   UpperCAmelCase_											=  int(input("Enter number of vertices: ").strip())
   UpperCAmelCase_											=  int(input("Enter number of edges: ").strip())

   UpperCAmelCase_											=  [[float("inf") for i in range(V)] for j in range(V)]

   for i in range(V):
      UpperCAmelCase_											=  0.0

   for i in range(E):
      print("\nEdge ", i + 1)
      UpperCAmelCase_											=  int(input("Enter source:").strip())
      UpperCAmelCase_											=  int(input("Enter destination:").strip())
      UpperCAmelCase_											=  float(input("Enter weight:").strip())
      UpperCAmelCase_											=  weight

   UpperCAmelCase_											=  int(input("\nEnter shortest path source:").strip())
   dijkstra(graph, V, gsrc)