
'''simple docstring'''



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 (_lowerCamelCase):





       """simple docstring"""




       SCREAMING_SNAKE_CASE					=     42
       SCREAMING_SNAKE_CASE					=     None






def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_=0.999			,					SCREAMING_SNAKE_CASE_="cosine"			,					)   ->   Tuple:




   """simple docstring"""
   if alpha_transform_type == "cosine":

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

   elif alpha_transform_type == "exp":

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

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

   _SCREAMING_SNAKE_CASE          = []
   for i in range(SCREAMING_SNAKE_CASE_  ):
      _SCREAMING_SNAKE_CASE          = i / num_diffusion_timesteps
      _SCREAMING_SNAKE_CASE          = (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       _a (_lowerCamelCase     ,    _lowerCamelCase):





       """simple docstring"""




       SCREAMING_SNAKE_CASE					=     [e.name for e in KarrasDiffusionSchedulers]
       SCREAMING_SNAKE_CASE					=     1






       @register_to_config
       def __init__(							self				,							A__ = 10_00				,							A__ = 0.0001				,							A__ = 0.02				,							A__ = "linear"				,							A__ = None				,							A__ = False				,							A__ = "epsilon"				,							A__ = "linspace"				,							A__ = 0				,							)			->	Optional[Any]:
          if trained_betas is not None:
             _SCREAMING_SNAKE_CASE          = torch.tensor(A__				,							dtype=torch.floataa					)
          elif beta_schedule == "linear":
             _SCREAMING_SNAKE_CASE          = torch.linspace(A__				,							A__				,							A__				,							dtype=torch.floataa					)
          elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             _SCREAMING_SNAKE_CASE          = (
                 torch.linspace(beta_start**0.5				,							beta_end**0.5				,							A__				,							dtype=torch.floataa					) ** 2
             )
          elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             _SCREAMING_SNAKE_CASE          = betas_for_alpha_bar(A__					)
          else:
             raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"					)

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

          _SCREAMING_SNAKE_CASE          = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
          _SCREAMING_SNAKE_CASE          = np.concatenate([sigmas[::-1], [0.0]]					).astype(np.floataa					)
          _SCREAMING_SNAKE_CASE          = torch.from_numpy(A__					)

          # setable values
          _SCREAMING_SNAKE_CASE          = None
          _SCREAMING_SNAKE_CASE          = use_karras_sigmas
          self.set_timesteps(A__				,							A__					)
          _SCREAMING_SNAKE_CASE          = []
          _SCREAMING_SNAKE_CASE          = False






       @property
       def 				UpperCamelCase (							self					)			->	str:
          # 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				,							A__				,							A__					)			->	torch.FloatTensor:
          if isinstance(A__				,							torch.Tensor					):
             _SCREAMING_SNAKE_CASE          = timestep.to(self.timesteps.device					)
          _SCREAMING_SNAKE_CASE          = (self.timesteps == timestep).nonzero().item()
          _SCREAMING_SNAKE_CASE          = self.sigmas[step_index]
          _SCREAMING_SNAKE_CASE          = sample / ((sigma**2 + 1) ** 0.5)
          _SCREAMING_SNAKE_CASE          = True
          return sample






       def 				UpperCamelCase (							self				,							A__				,							A__				,							A__					)			->	Optional[int]:

          def lms_derivative(A__					):
             _SCREAMING_SNAKE_CASE          = 1.0
             for k in range(A__					):
                if current_order == k:
                   continue
                prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
             return prod

          _SCREAMING_SNAKE_CASE          = integrate.quad(A__				,							self.sigmas[t]				,							self.sigmas[t + 1]				,							epsrel=1E-4					)[0]

          return integrated_coeff






       def 				UpperCamelCase (							self				,							A__				,							A__ = None					)			->	List[Any]:
          _SCREAMING_SNAKE_CASE          = 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":
             _SCREAMING_SNAKE_CASE          = np.linspace(0				,							self.config.num_train_timesteps - 1				,							A__				,							dtype=A__					)[
                 ::-1
             ].copy()
          elif self.config.timestep_spacing == "leading":
             _SCREAMING_SNAKE_CASE          = 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
             _SCREAMING_SNAKE_CASE          = (np.arange(0				,							A__					) * step_ratio).round()[::-1].copy().astype(A__					)
             timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
             _SCREAMING_SNAKE_CASE          = 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
             _SCREAMING_SNAKE_CASE          = (np.arange(self.config.num_train_timesteps				,							0				,							-step_ratio					)).round().copy().astype(A__					)
             timesteps -= 1
          else:
             raise ValueError(
                 F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."					)

          _SCREAMING_SNAKE_CASE          = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
          _SCREAMING_SNAKE_CASE          = np.log(A__					)
          _SCREAMING_SNAKE_CASE          = np.interp(A__				,							np.arange(0				,							len(A__					)					)				,							A__					)

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

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

          _SCREAMING_SNAKE_CASE          = torch.from_numpy(A__					).to(device=A__					)
          if str(A__					).startswith("""mps"""					):
             # mps does not support float64
             _SCREAMING_SNAKE_CASE          = torch.from_numpy(A__					).to(A__				,							dtype=torch.floataa					)
          else:
             _SCREAMING_SNAKE_CASE          = torch.from_numpy(A__					).to(device=A__					)

          _SCREAMING_SNAKE_CASE          = []






       def 				UpperCamelCase (							self				,							A__				,							A__					)			->	Dict:
          # get log sigma
          _SCREAMING_SNAKE_CASE          = np.log(A__					)

          # get distribution
          _SCREAMING_SNAKE_CASE          = log_sigma - log_sigmas[:, np.newaxis]

          # get sigmas range
          _SCREAMING_SNAKE_CASE          = np.cumsum((dists >= 0)				,							axis=0					).argmax(axis=0					).clip(max=log_sigmas.shape[0] - 2					)
          _SCREAMING_SNAKE_CASE          = low_idx + 1

          _SCREAMING_SNAKE_CASE          = log_sigmas[low_idx]
          _SCREAMING_SNAKE_CASE          = log_sigmas[high_idx]

          # interpolate sigmas
          _SCREAMING_SNAKE_CASE          = (low - log_sigma) / (low - high)
          _SCREAMING_SNAKE_CASE          = np.clip(A__				,							0				,							1					)

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






       def 				UpperCamelCase (							self				,							A__					)			->	torch.FloatTensor:
          _SCREAMING_SNAKE_CASE          = in_sigmas[-1].item()
          _SCREAMING_SNAKE_CASE          = in_sigmas[0].item()

          _SCREAMING_SNAKE_CASE          = 7.0  # 7.0 is the value used in the paper
          _SCREAMING_SNAKE_CASE          = np.linspace(0				,							1				,							self.num_inference_steps					)
          _SCREAMING_SNAKE_CASE          = sigma_min ** (1 / rho)
          _SCREAMING_SNAKE_CASE          = sigma_max ** (1 / rho)
          _SCREAMING_SNAKE_CASE          = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas






       def 				UpperCamelCase (							self				,							A__				,							A__				,							A__				,							A__ = 4				,							A__ = True				,							)			->	Union[LMSDiscreteSchedulerOutput, Tuple]:
          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(A__				,							torch.Tensor					):
             _SCREAMING_SNAKE_CASE          = timestep.to(self.timesteps.device					)
          _SCREAMING_SNAKE_CASE          = (self.timesteps == timestep).nonzero().item()
          _SCREAMING_SNAKE_CASE          = self.sigmas[step_index]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
             _SCREAMING_SNAKE_CASE          = sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
             # * c_out + input * c_skip
             _SCREAMING_SNAKE_CASE          = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          elif self.config.prediction_type == "sample":
             _SCREAMING_SNAKE_CASE          = 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
          _SCREAMING_SNAKE_CASE          = (sample - pred_original_sample) / sigma
          self.derivatives.append(A__					)
          if len(self.derivatives					) > order:
             self.derivatives.pop(0					)

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

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

          if not return_dict:
             return (prev_sample,)

          return LMSDiscreteSchedulerOutput(prev_sample=A__				,							pred_original_sample=A__					)






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

          _SCREAMING_SNAKE_CASE          = [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

          _SCREAMING_SNAKE_CASE          = original_samples + noise * sigma
          return noisy_samples






       def __len__(							self					)			->	List[Any]:
          return self.config.num_train_timesteps








'''simple docstring'''



UpperCamelCase__					:						Tuple											=     [
    ["ab-e1", "ac-e3", "ad-e5", "bc-e4", "bd-e2", "be-e6", "bh-e12", "cd-e2", "ce-e4",
     "de-e1", "df-e8", "dg-e5", "dh-e10", "ef-e3", "eg-e2", "fg-e6", "gh-e6", "hi-e3"],
    ["ab-e1", "ac-e3", "ad-e5", "bc-e4", "bd-e2", "be-e6", "cd-e2", "de-e1", "df-e8",
     "ef-e3", "eg-e2", "fg-e6"],
    ["ab-e1", "ac-e3", "bc-e4", "bd-e2", "de-e1", "df-e8", "dg-e5", "ef-e3", "eg-e2",
     "eh-e12", "fg-e6", "fh-e10", "gh-e6"],
    ["ab-e1", "ac-e3", "bc-e4", "bd-e2", "bh-e12", "cd-e2", "df-e8", "dh-e10"],
    ["ab-e1", "ac-e3", "ad-e5", "bc-e4", "bd-e2", "cd-e2", "ce-e4", "de-e1", "df-e8",
     "dg-e5", "ef-e3", "eg-e2", "fg-e6"]
]
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   List[str]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = set()
   for row in edge_array:
      for item in row:
         distinct_edge.add(item[0]  )
   return list(SCREAMING_SNAKE_CASE_  )
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )   ->   List[str]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = ["""0"""] * len(SCREAMING_SNAKE_CASE_  )
   for i, row in enumerate(SCREAMING_SNAKE_CASE_  ):
      for item in row:
         if distinct_edge in item[0]:
            _SCREAMING_SNAKE_CASE          = """1"""
            break
   return "".join(SCREAMING_SNAKE_CASE_  )
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   Union[str, Any]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = get_distinct_edge(SCREAMING_SNAKE_CASE_  )
   _SCREAMING_SNAKE_CASE          = {}

   for item in distinct_edge:
      _SCREAMING_SNAKE_CASE          = get_bitcode(SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
      # print('bit',bit)
      # bt=''.join(bit)
      _SCREAMING_SNAKE_CASE          = bit.count("""1"""  )
      _SCREAMING_SNAKE_CASE          = [s, bit]
   # Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
   _SCREAMING_SNAKE_CASE          = [
       [k, v[0], v[1]]
       for k, v in sorted(frequency_table.items()			,					key=lambda SCREAMING_SNAKE_CASE_  : v[1][0]			,					reverse=SCREAMING_SNAKE_CASE_  )
   ]
   return sorted_frequency_table
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   List[str]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = {}
   for _, item in enumerate(SCREAMING_SNAKE_CASE_  ):
      nodes.setdefault(item[2]			,					[]  ).append(item[0]  )
   return nodes
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = {}
   for key, value in nodes.items():
      _SCREAMING_SNAKE_CASE          = value
   return cluster
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   str:




   """simple docstring"""
   return [i * 1_00 / len(SCREAMING_SNAKE_CASE_  ) for i in cluster]
def       lowerCAmelCase_		( )   ->   None:




   """simple docstring"""
   print("""\nNodes\n"""  )
   for key, value in nodes.items():
      print(SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
   print("""\nSupport\n"""  )
   print(SCREAMING_SNAKE_CASE_  )
   print("""\n Cluster \n"""  )
   for key, value in sorted(cluster.items()			,					reverse=SCREAMING_SNAKE_CASE_  ):
      print(SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
   print("""\n Graph\n"""  )
   for key, value in graph.items():
      print(SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
   print("""\n Edge List of Frequent subgraphs \n"""  )
   for edge_list in freq_subgraph_edge_list:
      print(SCREAMING_SNAKE_CASE_  )
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )   ->   Optional[int]:




   """simple docstring"""
   for i in cluster[ca]:
      _SCREAMING_SNAKE_CASE          = 0
      _SCREAMING_SNAKE_CASE          = ca + 1
      while ca < max(cluster.keys()  ):
         for j in cluster[ca]:
            if int(SCREAMING_SNAKE_CASE_			,					2  ) & int(SCREAMING_SNAKE_CASE_			,					2  ) == int(SCREAMING_SNAKE_CASE_			,					2  ):
               if tuple(nodes[i]  ) in graph:
                  graph[tuple(nodes[i]  )].append(nodes[j]  )
               else:
                  _SCREAMING_SNAKE_CASE          = [nodes[j]]
               count += 1
         if count == 0:
            _SCREAMING_SNAKE_CASE          = ca + 1
         else:
            break
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )   ->   Optional[int]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = cluster[max(cluster.keys()  )]
   _SCREAMING_SNAKE_CASE          = """Header"""
   _SCREAMING_SNAKE_CASE          = {}
   for i in x:
      if (["Header"],) in graph:
         graph[(["Header"],)].append(x[i]  )
      else:
         _SCREAMING_SNAKE_CASE          = [x[i]]
   for i in x:
      _SCREAMING_SNAKE_CASE          = [["""Header"""]]
   _SCREAMING_SNAKE_CASE          = 1
   while i < max(SCREAMING_SNAKE_CASE_  ) - 1:
      create_edge(SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
      _SCREAMING_SNAKE_CASE          = i + 1
   return graph
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_=None  )   ->   List[Any]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = (path or []) + [start]
   if start == end:
      paths.append(SCREAMING_SNAKE_CASE_  )
   for node in graph[start]:
      if tuple(SCREAMING_SNAKE_CASE_  ) not in path:
         my_dfs(SCREAMING_SNAKE_CASE_			,					tuple(SCREAMING_SNAKE_CASE_  )			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_			,					SCREAMING_SNAKE_CASE_  )   ->   int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = int(s / 1_00 * (len(SCREAMING_SNAKE_CASE_  ) - 1)  )
   for i in cluster[k]:
      my_dfs(SCREAMING_SNAKE_CASE_			,					tuple(cluster[k][i]  )			,					(["""Header"""],)  )
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   Optional[Any]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE          = []
   for edges in paths:
      _SCREAMING_SNAKE_CASE          = []
      for j in range(len(SCREAMING_SNAKE_CASE_  ) - 1  ):
         _SCREAMING_SNAKE_CASE          = list(edges[j]  )
         for e in temp:
            _SCREAMING_SNAKE_CASE          = (e[0], e[1])
            el.append(SCREAMING_SNAKE_CASE_  )
      freq_sub_el.append(SCREAMING_SNAKE_CASE_  )
   return freq_sub_el
def       lowerCAmelCase_		( SCREAMING_SNAKE_CASE_  )   ->   Any:




   """simple docstring"""
   for i in range(len(SCREAMING_SNAKE_CASE_  )  ):
      for j in range(len(edge_array[i]  )  ):
         _SCREAMING_SNAKE_CASE          = edge_array[i][j].split("""-"""  )
         _SCREAMING_SNAKE_CASE          = t


if __name__ == "__main__":
     preprocess(edge_array)
     UpperCamelCase__					:						List[Any]											=     get_frequency_table(edge_array)
     UpperCamelCase__					:						List[Any]											=     get_nodes(frequency_table)
     UpperCamelCase__					:						List[str]											=     get_cluster(nodes)
     UpperCamelCase__					:						List[Any]											=     get_support(cluster)
     UpperCamelCase__					:						Union[str, Any]											=     construct_graph(cluster, nodes)
     find_freq_subgraph_given_support(60, cluster, graph)
     UpperCamelCase__					:						list											=     []
     UpperCamelCase__					:						int											=     freq_subgraphs_edge_list(paths)
     print_all()






