


'''simple docstring'''



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

import numpy as np
import torch

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





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class   UpperCAmelCase_    (_UpperCAmelCase    ):





    """simple docstring"""






    lowerCamelCase    :   torch.FloatTensor
    lowerCamelCase    :   Optional[torch.FloatTensor]					=     None







def      UpperCAmelCase__   (      UpperCAmelCase_       :							Tuple ,       UpperCAmelCase_       :							Union[str, Any]=0.999 ,       UpperCAmelCase_       :							Tuple="cosine" ,       )	->						Optional[Any]:
     if alpha_transform_type == "cosine":

          def alpha_bar_fn(UpperCAmelCase_       :							Optional[int]				):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2				) ** 2

     elif alpha_transform_type == "exp":

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

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

     __lowerCamelCase  :      List[str]														=						[]
     for i in range(UpperCAmelCase_				):
          __lowerCamelCase  :      int														=						i / num_diffusion_timesteps
          __lowerCamelCase  :      List[str]														=						(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   UpperCAmelCase_    (_UpperCAmelCase   ,						_UpperCAmelCase    ):





    """simple docstring"""






    @register_to_config
    def __init__(				self     ,	SCREAMING_SNAKE_CASE_ = 10_00     ,	SCREAMING_SNAKE_CASE_ = "fixed_small_log"     ,	SCREAMING_SNAKE_CASE_ = True     ,	SCREAMING_SNAKE_CASE_ = 1.0     ,	SCREAMING_SNAKE_CASE_ = "epsilon"     ,	SCREAMING_SNAKE_CASE_ = "squaredcos_cap_v2"     ,	)							->	List[str]:
         if beta_schedule != "squaredcos_cap_v2":
              raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''      )

         __lowerCamelCase  :      Optional[Any]														=						betas_for_alpha_bar(SCREAMING_SNAKE_CASE_      )

         __lowerCamelCase  :      str														=						1.0 - self.betas
         __lowerCamelCase  :      Union[str, Any]														=						torch.cumprod(self.alphas     ,	dim=0      )
         __lowerCamelCase  :      Optional[Any]														=						torch.tensor(1.0      )

         # standard deviation of the initial noise distribution
         __lowerCamelCase  :      Optional[Any]														=						1.0

         # setable values
         __lowerCamelCase  :      Optional[Any]														=						None
         __lowerCamelCase  :      Optional[int]														=						torch.from_numpy(np.arange(0     ,	SCREAMING_SNAKE_CASE_      )[::-1].copy()      )

         __lowerCamelCase  :      Optional[int]														=						variance_type







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_ = None      )							->	torch.FloatTensor:
         return sample







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_ = None      )							->	Optional[int]:
         __lowerCamelCase  :      Optional[int]														=						num_inference_steps
         __lowerCamelCase  :      Any														=						(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
         __lowerCamelCase  :      str														=						(np.arange(0     ,	SCREAMING_SNAKE_CASE_      ) * step_ratio).round()[::-1].copy().astype(np.intaa      )
         __lowerCamelCase  :      List[str]														=						torch.from_numpy(SCREAMING_SNAKE_CASE_      ).to(SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_=None     ,	SCREAMING_SNAKE_CASE_=None     ,	SCREAMING_SNAKE_CASE_=None      )							->	Dict:
         if prev_timestep is None:
              __lowerCamelCase  :      Dict														=						t - 1

         __lowerCamelCase  :      int														=						self.alphas_cumprod[t]
         __lowerCamelCase  :      str														=						self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
         __lowerCamelCase  :      Optional[int]														=						1 - alpha_prod_t
         __lowerCamelCase  :      Dict														=						1 - alpha_prod_t_prev

         if prev_timestep == t - 1:
              __lowerCamelCase  :      List[str]														=						self.betas[t]
         else:
              __lowerCamelCase  :      List[str]														=						1 - alpha_prod_t / alpha_prod_t_prev

         # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
         # and sample from it to get previous sample
         # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
         __lowerCamelCase  :      List[str]														=						beta_prod_t_prev / beta_prod_t * beta

         if variance_type is None:
              __lowerCamelCase  :      str														=						self.config.variance_type

         # hacks - were probably added for training stability
         if variance_type == "fixed_small_log":
              __lowerCamelCase  :      Optional[Any]														=						torch.log(torch.clamp(SCREAMING_SNAKE_CASE_     ,	min=1E-20      )      )
              __lowerCamelCase  :      List[Any]														=						torch.exp(0.5 * variance      )
         elif variance_type == "learned_range":
              # NOTE difference with DDPM scheduler
              __lowerCamelCase  :      str														=						variance.log()
              __lowerCamelCase  :      Dict														=						beta.log()

              __lowerCamelCase  :      List[str]														=						(predicted_variance + 1) / 2
              __lowerCamelCase  :      str														=						frac * max_log + (1 - frac) * min_log

         return variance







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_ = None     ,	SCREAMING_SNAKE_CASE_=None     ,	SCREAMING_SNAKE_CASE_ = True     ,	)							->	Union[UnCLIPSchedulerOutput, Tuple]:
         __lowerCamelCase  :      List[str]														=						timestep

         if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
              __lowerCamelCase							,			__lowerCamelCase  :      List[Any]														=						torch.split(SCREAMING_SNAKE_CASE_     ,	sample.shape[1]     ,	dim=1      )
         else:
              __lowerCamelCase  :      Optional[int]														=						None

         # 1. compute alphas, betas
         if prev_timestep is None:
              __lowerCamelCase  :      str														=						t - 1

         __lowerCamelCase  :      int														=						self.alphas_cumprod[t]
         __lowerCamelCase  :      Optional[int]														=						self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
         __lowerCamelCase  :      int														=						1 - alpha_prod_t
         __lowerCamelCase  :      List[Any]														=						1 - alpha_prod_t_prev

         if prev_timestep == t - 1:
              __lowerCamelCase  :      Dict														=						self.betas[t]
              __lowerCamelCase  :      List[Any]														=						self.alphas[t]
         else:
              __lowerCamelCase  :      Optional[Any]														=						1 - alpha_prod_t / alpha_prod_t_prev
              __lowerCamelCase  :      Dict														=						1 - beta

         # 2. compute predicted original sample from predicted noise also called
         # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
         if self.config.prediction_type == "epsilon":
              __lowerCamelCase  :      Dict														=						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         elif self.config.prediction_type == "sample":
              __lowerCamelCase  :      Optional[Any]														=						model_output
         else:
              raise ValueError(
                  f'prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`'
                  ' for the UnCLIPScheduler.'      )

         # 3. Clip "predicted x_0"
         if self.config.clip_sample:
              __lowerCamelCase  :      Dict														=						torch.clamp(
                  SCREAMING_SNAKE_CASE_     ,	-self.config.clip_sample_range     ,	self.config.clip_sample_range      )

         # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
         # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
         __lowerCamelCase  :      Any														=						(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
         __lowerCamelCase  :      Optional[int]														=						alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

         # 5. Compute predicted previous sample µ_t
         # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
         __lowerCamelCase  :      Union[str, Any]														=						pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         __lowerCamelCase  :      Dict														=						0
         if t > 0:
              __lowerCamelCase  :      Union[str, Any]														=						randn_tensor(
                  model_output.shape     ,	dtype=model_output.dtype     ,	generator=SCREAMING_SNAKE_CASE_     ,	device=model_output.device      )

              __lowerCamelCase  :      Union[str, Any]														=						self._get_variance(
                  SCREAMING_SNAKE_CASE_     ,	predicted_variance=SCREAMING_SNAKE_CASE_     ,	prev_timestep=SCREAMING_SNAKE_CASE_     ,	)

              if self.variance_type == "fixed_small_log":
                   __lowerCamelCase  :      Optional[Any]														=						variance
              elif self.variance_type == "learned_range":
                   __lowerCamelCase  :      Tuple														=						(0.5 * variance).exp()
              else:
                   raise ValueError(
                       f'variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`'
                       ' for the UnCLIPScheduler.'      )

              __lowerCamelCase  :      Tuple														=						variance * variance_noise

         __lowerCamelCase  :      List[str]														=						pred_prev_sample + variance

         if not return_dict:
              return (pred_prev_sample,)

         return UnCLIPSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_     ,	pred_original_sample=SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	)							->	torch.FloatTensor:
         # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
         __lowerCamelCase  :      str														=						self.alphas_cumprod.to(device=original_samples.device     ,	dtype=original_samples.dtype      )
         __lowerCamelCase  :      Any														=						timesteps.to(original_samples.device      )

         __lowerCamelCase  :      Tuple														=						alphas_cumprod[timesteps] ** 0.5
         __lowerCamelCase  :      List[Any]														=						sqrt_alpha_prod.flatten()
         while len(sqrt_alpha_prod.shape      ) < len(original_samples.shape      ):
              __lowerCamelCase  :      Union[str, Any]														=						sqrt_alpha_prod.unsqueeze(-1      )

         __lowerCamelCase  :      Optional[Any]														=						(1 - alphas_cumprod[timesteps]) ** 0.5
         __lowerCamelCase  :      Tuple														=						sqrt_one_minus_alpha_prod.flatten()
         while len(sqrt_one_minus_alpha_prod.shape      ) < len(original_samples.shape      ):
              __lowerCamelCase  :      str														=						sqrt_one_minus_alpha_prod.unsqueeze(-1      )

         __lowerCamelCase  :      str														=						sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
         return noisy_samples










'''simple docstring'''



from __future__ import annotations

import os
from collections.abc import Mapping

A__						:   Optional[Any]				=    tuple[int, int]





class   UpperCAmelCase_    :





    """simple docstring"""






    def __init__(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	None:
         __lowerCamelCase  :      set[int]														=						vertices
         __lowerCamelCase  :      dict[EdgeT, int]														=						{
             (min(SCREAMING_SNAKE_CASE_      ), max(SCREAMING_SNAKE_CASE_      )): weight for edge, weight in edges.items()
         }







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	None:
         self.vertices.add(edge[0]      )
         self.vertices.add(edge[1]      )
         __lowerCamelCase  :      Union[str, Any]														=						weight







    def  lowercase_							(				self      )							->	Graph:
         __lowerCamelCase  :      Graph														=						Graph({min(self.vertices      )}     ,	{}      )
         __lowerCamelCase  :      EdgeT
         __lowerCamelCase  :      int
         __lowerCamelCase  :      EdgeT
         __lowerCamelCase  :      int

         while len(subgraph.vertices      ) < len(self.vertices      ):
              __lowerCamelCase  :      Any														=						max(self.edges.values()      ) + 1
              for edge, weight in self.edges.items():
                   if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                        if weight < min_weight:
                             __lowerCamelCase  :      Optional[int]														=						edge
                             __lowerCamelCase  :      List[str]														=						weight

              subgraph.add_edge(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )

         return subgraph







def      UpperCAmelCase__   (      UpperCAmelCase_       :							str = "p107_network.txt"				)	->						int:
     __lowerCamelCase  :      str														=						os.path.abspath(os.path.dirname(UpperCAmelCase_				)				)
     __lowerCamelCase  :      str														=						os.path.join(UpperCAmelCase_ ,       UpperCAmelCase_				)
     __lowerCamelCase  :      dict[EdgeT, int]														=						{}
     __lowerCamelCase  :      list[str]
     __lowerCamelCase  :      int
     __lowerCamelCase  :      int

     with open(UpperCAmelCase_				) as f:
          __lowerCamelCase  :      Any														=						f.read().strip().split('\n'				)

     __lowerCamelCase  :      Any														=						[line.split(','				) for line in data]

     for edgea in range(1 ,       len(UpperCAmelCase_				)				):
          for edgea in range(UpperCAmelCase_				):
               if adjaceny_matrix[edgea][edgea] != "-":
                    __lowerCamelCase  :      int														=						int(adjaceny_matrix[edgea][edgea]				)

     __lowerCamelCase  :      Graph														=						Graph(set(range(len(UpperCAmelCase_				)				)				) ,       UpperCAmelCase_				)

     __lowerCamelCase  :      Graph														=						graph.prims_algorithm()

     __lowerCamelCase  :      int														=						sum(graph.edges.values()				)
     __lowerCamelCase  :      int														=						sum(subgraph.edges.values()				)

     return initial_total - optimal_total


if __name__ == "__main__":
      print(f'''{solution() = }''')






