
"""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     lowercase(_lowercase       ):
     __snake_case:	torch.FloatTensor
     __snake_case:	Optional[torch.FloatTensor]						=     None




def     __magic_name__		(					UpperCamelCase     :		List[Any]							,		UpperCamelCase     :		Union[str, Any]=0.999							,		UpperCamelCase     :		Any="cosine"							,		)     ->						List[str]:
    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     :		Dict     ):
            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     lowercase(_lowercase    ,						_lowercase       ):



     @register_to_config
     def __init__(							self     ,				__SCREAMING_SNAKE_CASE = 1_0_0_0     ,				__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"     ,				)		->     Optional[Any]:







         """simple docstring"""



         if beta_schedule != "squaredcos_cap_v2":
             raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''   )

         a__		=			betas_for_alpha_bar(__SCREAMING_SNAKE_CASE   )

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

         # standard deviation of the initial noise distribution
         a__		=			1.0

         # setable values
         a__		=			None
         a__		=			torch.from_numpy(np.arange(0     ,				__SCREAMING_SNAKE_CASE   )[::-1].copy()   )

         a__		=			variance_type



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE = None   )		->     torch.FloatTensor:







         """simple docstring"""



         return sample



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE = None   )		->     Tuple:







         """simple docstring"""



         a__		=			num_inference_steps
         a__		=			(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
         a__		=			(np.arange(0     ,				__SCREAMING_SNAKE_CASE   ) * step_ratio).round()[::-1].copy().astype(np.intaa   )
         a__		=			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   )		->     Tuple:







         """simple docstring"""



         if prev_timestep is None:
             a__		=			t - 1

         a__		=			self.alphas_cumprod[t]
         a__		=			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
         a__		=			1 - alpha_prod_t
         a__		=			1 - alpha_prod_t_prev

         if prev_timestep == t - 1:
             a__		=			self.betas[t]
         else:
             a__		=			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
         a__		=			beta_prod_t_prev / beta_prod_t * beta

         if variance_type is None:
             a__		=			self.config.variance_type

         # hacks - were probably added for training stability
         if variance_type == "fixed_small_log":
             a__		=			torch.log(torch.clamp(__SCREAMING_SNAKE_CASE     ,				min=1e-20   )   )
             a__		=			torch.exp(0.5 * variance   )
         elif variance_type == "learned_range":
             # NOTE difference with DDPM scheduler
             a__		=			variance.log()
             a__		=			beta.log()

             a__		=			(predicted_variance + 1) / 2
             a__		=			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]:







         """simple docstring"""



         a__		=			timestep

         if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
             a__	,     a__		=			torch.split(__SCREAMING_SNAKE_CASE     ,				sample.shape[1]     ,				dim=1   )
         else:
             a__		=			None

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

         a__		=			self.alphas_cumprod[t]
         a__		=			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
         a__		=			1 - alpha_prod_t
         a__		=			1 - alpha_prod_t_prev

         if prev_timestep == t - 1:
             a__		=			self.betas[t]
             a__		=			self.alphas[t]
         else:
             a__		=			1 - alpha_prod_t / alpha_prod_t_prev
             a__		=			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":
             a__		=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         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 `sample`'
                 ' for the UnCLIPScheduler.'   )

         # 3. Clip "predicted x_0"
         if self.config.clip_sample:
             a__		=			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
         a__		=			(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
         a__		=			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
         a__		=			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         a__		=			0
         if t > 0:
             a__		=			randn_tensor(
                 model_output.shape     ,				dtype=model_output.dtype     ,				generator=__SCREAMING_SNAKE_CASE     ,				device=model_output.device   )

             a__		=			self._get_variance(
                 __SCREAMING_SNAKE_CASE     ,				predicted_variance=__SCREAMING_SNAKE_CASE     ,				prev_timestep=__SCREAMING_SNAKE_CASE     ,				)

             if self.variance_type == "fixed_small_log":
                 a__		=			variance
             elif self.variance_type == "learned_range":
                 a__		=			(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.'   )

             a__		=			variance * variance_noise

         a__		=			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:







         """simple docstring"""



         a__		=			self.alphas_cumprod.to(device=original_samples.device     ,				dtype=original_samples.dtype   )
         a__		=			timesteps.to(original_samples.device   )

         a__		=			alphas_cumprod[timesteps] ** 0.5
         a__		=			sqrt_alpha_prod.flatten()
         while len(sqrt_alpha_prod.shape   ) < len(original_samples.shape   ):
             a__		=			sqrt_alpha_prod.unsqueeze(-1   )

         a__		=			(1 - alphas_cumprod[timesteps]) ** 0.5
         a__		=			sqrt_one_minus_alpha_prod.flatten()
         while len(sqrt_one_minus_alpha_prod.shape   ) < len(original_samples.shape   ):
             a__		=			sqrt_one_minus_alpha_prod.unsqueeze(-1   )

         a__		=			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     lowercase:



     def __init__(							self     ,				__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE   )		->     None:







         """simple docstring"""



         a__		=			vertices
         a__		=			{
             (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:







         """simple docstring"""



         self.vertices.add(edge[0]   )
         self.vertices.add(edge[1]   )
         a__		=			weight




     def 			lowercase__  (							self   )		->     Graph:







         """simple docstring"""



         a__		=			Graph({min(self.vertices   )}     ,				{}   )
         a__		=			42
         a__		=			42
         a__		=			42
         a__		=			42

         while len(subgraph.vertices   ) < len(self.vertices   ):
             a__		=			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:
                         a__		=			edge
                         a__		=			weight

             subgraph.add_edge(__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE   )

         return subgraph




def     __magic_name__		(					UpperCamelCase     :		str = "p107_network.txt"     )     ->						int:
    a__		=			os.path.abspath(os.path.dirname(UpperCamelCase     )     )
    a__		=			os.path.join(UpperCamelCase							,		UpperCamelCase     )
    a__		=			{}
    a__		=			42
    a__		=			42
    a__		=			42

    with open(UpperCamelCase     ) as f:
        a__		=			f.read().strip().split('\n'     )

    a__		=			[line.split(','     ) for line in data]

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

    a__		=			Graph(set(range(len(UpperCamelCase     )     )     )							,		UpperCamelCase     )

    a__		=			graph.prims_algorithm()

    a__		=			sum(graph.edges.values()     )
    a__		=			sum(subgraph.edges.values()     )

    return initial_total - optimal_total


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


