15-May-2025 18:38:35

permutation_distance_test():
  MATLAB/Octave version 6.4.0
  Test permutation_distance()
  Graphics saved as "permutation_distance_histogram.png"

permutation_distance_stats_test():
  Test permutation_distance_stats().
  Using N = 1000 sample permutations.
  Permutation order is M
  Compute mean and variance of Ulam permutation distance.

   M   Mean   Predicted Variance

   1  0  -1  0
   2  0.522  -0.0330087  0.249766
   3  1.008  0.0159841  0.348284
   4  1.575  0.0849801  0.420796
   5  2.241  0.234994  0.509428
   6  2.879  0.272523  0.56092
   7  3.496  0.235519  0.626611
   8  4.232  0.346365  0.706883
   9  4.961  0.41566  0.748227
  10  5.586  0.312944  0.825429
  11  6.391  0.447085  0.868988
  12  7.152  0.500645  0.851748
  13  7.858  0.464425  0.938775
  14  8.686  0.580404  0.932336
  15  9.401  0.53321  1.01922
  16  10.189  0.573043  1.15443
  17  10.991  0.621535  1.15608
  18  11.725  0.573357  1.14452
  19  12.552  0.63776  1.14644
  20  13.352  0.660078  1.12322
  21  14.252  0.802364  1.24574
  22  15.052  0.811381  1.23453
  23  15.823  0.778627  1.331
  24  16.575  0.717481  1.41179
  25  17.453  0.808358  1.39719
  26  18.279  0.829789  1.40657
  27  19.191  0.952507  1.41994
  28  19.949  0.881861  1.42983
  29  20.717  0.820186  1.35827
  30  21.519  0.796715  1.48913
  31  22.384  0.846346  1.41396
  32  23.202  0.835691  1.61481
  33  23.993  0.78953  1.66862
  34  24.899  0.87878  1.65045
  35  25.83  0.994645  1.61872
  36  26.63  0.950853  1.67077
  37  27.474  0.957129  1.679
  38  28.338  0.98469  1.73749
  39  29.201  1.00859  1.63824
  40  30.04  1.00175  1.73013
  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

     1   2   3   4   5   6   7   8   9  10
     1   2   5   6   7  10   3   8   4   9

  Permutation P2

     1   2   3   4   5   6   7   8   9  10
     7  10   5   9   1   3   4   2   8   6

  Permutation P3

     1   2   3   4   5   6   7   8   9  10
     5   2  10   3   4   6   8   1   7   9

  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) = 5
  K(P1,P2) = 6
  K(P2,P3) = 6
  K(P1,P2) + K(P2,P3) = 12

permutation_distance_test():
  Normal end of execution.

15-May-2025 18:39:20