docstr: Find a good permutation for some matrix (which may be concatenated matrices that require the same permutation)
code: def find_permutation_for_matrix_group(cls, matrix_group):
      """Find a good permutation for some matrix (which may be concatenated matrices that require the same permutation)"""
  
      if cls.__verbosity > 1:
          print(
              f"Searching for a good permutation for this sibling group of shape {matrix_group.shape}"
          )
  
      permutation_found = False
      num_channels = matrix_group.shape[1]
      group_permutation = [c for c in range(num_channels)]
  
      # automatic check for skipping the permutation search process
      original_magnitude = (torch.abs(matrix_group)).sum(
          dtype=torch.float64
      )
      pruned_magnitude = sum_after_2_to_4(
          matrix_group.cpu().detach().numpy()
      )
      diff_ratio = (
          abs(original_magnitude - pruned_magnitude)
          / original_magnitude
      )
      epsilon = 1e-3
  
      if cls.__verbosity > 1:
          print(
              "\n[search_for_good_permutation] Original element abs sum: {:}, Pruned element abs sum: {:}, Diff ratio: {:}".format(
                  original_magnitude, pruned_magnitude, diff_ratio
              )
          )
  
      start_time_accelerated_search_for_good_permutation = (
          time.perf_counter()
      )
      if diff_ratio < epsilon:
          if cls.__verbosity > 2:
              print(
                  "[search_for_good_permutation] Original element abs sum is almost same as the pruned element abs sum, further permutation search will not help, skipping!"
              )
  
      else:
          if cls.__verbosity > 2:
              print(
                  "[search_for_good_permutation] Original element abs sum is different from the pruned element abs sum, further permutation search will help, continue with the permutation search!"
              )
  
          # call the permutation search CUDA kernels as ASP extension.
          # users can provide prefer search strategy by providing a valid 'search_options' as a dictionary,
          # or users can implement their customized 'accelerated_search_for_good_permutation' function.
          search_options = {}
          # No.1 Strategy: Exhaustive Search
          search_options["strategy"] = "exhaustive"
          search_options["stripe_group_size"] = 8
          search_options["escape_attempts"] = 100
          # No.2 Strategy: Progressive Channel Swap Search
          # search_options['strategy'] = 'progressive channel swap'
          # search_options['progressive_search_time_limit'] = 10
          # search_options['improvement_threshold'] = 1e-9
  
          # permutation search time is too long for matrix_group with large channel num
          # change from Exhaustive Search to Progressive Channel Swap Search based on input matrix_group size
          if num_channels > 2048:
              search_options = {}
              search_options["strategy"] = "progressive channel swap"
              search_options["progressive_search_time_limit"] = 120
              search_options["improvement_threshold"] = 1e-9
  
          if cls.__verbosity > 1:
              print(
                  f"[search_for_good_permutation] search options: {search_options}"
              )
  
          group_permutation = accelerated_search_for_good_permutation(
              matrix_group,
              options=search_options,
              verbosity=cls.__verbosity,
          )
          permutation_found = True
  
      if cls.__verbosity > 1:
          duration_accelerated_search_for_good_permutation = (
              time.perf_counter()
              - start_time_accelerated_search_for_good_permutation
          )
          permuted_magnitude = sum_after_2_to_4(
              matrix_group.cpu().detach().numpy()[:, group_permutation]
          )
          print(
              "[search_for_good_permutation] Take {:.4f} seconds to finish accelerated_search_for_good_permutation function and with final magnitude {:}.".format(
                  duration_accelerated_search_for_good_permutation,
                  permuted_magnitude,
              )
          )
  
      return group_permutation, permutation_found
  
imports: import os
  import torch
  import json
  import string
  import time
  import numpy
  import sys
  import builtins
  import io
label_desc: Use image node_id 13 for calling the Permutation obj's underlying member method code with example usage: obj.find_permutation_for_matrix_group(cls, matrix_group) and returns: group_permutation,  permutation_found