Mon Sep 19 08:49:14 2022

permutation_distance_test():
  Python version: 3.6.9
  Test permutation_distance()
  Graphics saved as "permutation_distance_histogram.png"

permutation_distance_stats_test():
  Test permutation_distance_stats().
  Using N =  10000  sample permutations.
  Permutation order is M
  Compute mean and variance of Ulam permutation distance.

   M   Mean   Predicted Variance

   1  0  -1  0
   2  0.4943  -0.0995706  0.249968
   3  1.0053  0.010593  0.328672
   4  1.5694  0.0749139  0.413984
   5  2.217  0.194919  0.489911
   6  2.8502  0.226707  0.57176
   7  3.5365  0.297617  0.622868
   8  4.2425  0.361966  0.686694
   9  4.9298  0.370431  0.748872
  10  5.6627  0.421986  0.791529
  11  6.406  0.468015  0.846164
  12  7.1597  0.511223  0.879396
  13  7.9172  0.544704  0.944944
  14  8.6581  0.54303  0.993004
  15  9.4355  0.578952  1.03084
  16  10.2369  0.635931  1.04238
  17  11.0043  0.638846  1.11288
  18  11.7918  0.659638  1.15365
  19  12.5926  0.689811  1.15383
  20  13.379  0.694463  1.19056
  21  14.2027  0.739994  1.22561
  22  14.9829  0.72445  1.25901
  23  15.8081  0.75998  1.29247
  24  16.6227  0.776889  1.32714
  25  17.4291  0.778735  1.36297
  26  18.2637  0.81091  1.39236
  27  19.0962  0.83604  1.40795
  28  19.9367  0.866806  1.46749
  29  20.7325  0.839091  1.49814
  30  21.6011  0.896497  1.49378
  31  22.4211  0.891285  1.48917
  32  23.2771  0.926369  1.52412
  33  24.0863  0.901859  1.56605
  34  24.9321  0.918511  1.60969
  35  25.7968  0.95491  1.59651
  36  26.6614  0.988336  1.66375
  37  27.4832  0.968084  1.67872
  38  28.3419  0.989322  1.713
  39  29.2147  1.02482  1.6986
  40  30.0682  1.0351  1.74455
  Graphics saved as "permutation_distance_stats.png"

permutation_distance_ulam():
  permutation_distance_ulam() computes the Ulam metric distance
  between two permutations of (1,...,N).

  Permutation P1

  
   0
   1
   2
   3
   4
   5
   6
   7
   8
   9

  
   5
   6
   0
   7
   2
   4
   9
   8
   3
   1


  Permutation P2

  
   0
   1
   2
   3
   4
   5
   6
   7
   8
   9

  
   2
   9
   5
   7
   0
   1
   6
   3
   4
   8


  Permutation P3

  
   0
   1
   2
   3
   4
   5
   6
   7
   8
   9

  
   8
   3
   0
   6
   1
   2
   9
   4
   5
   7


  K(P1,P1) should be 0.

  K(P1,P1) =  0

  K(P1,P2) should equal K(P2,P1).

  K(P1,P2) =  6
  K(P2,P1) =  6

  K(P1,P3) <= K(P1,P2) + K(P2,P3).

  K(P1,P3) =  7
  K(P1,P2) =  6
  K(P2,P3) =  6
  K(P1,P2) + K(P2,P3) =  12

permutation_distance_test():
  Normal end of execution.
Mon Sep 19 08:50:31 2022