08-Oct-2025 12:18:01

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  0.488  -0.11486  0.250106
   3  1.015  0.0299442  0.34512
   4  1.553  0.0453884  0.411603
   5  2.221  0.201604  0.486646
   6  2.87  0.258215  0.56967
   7  3.57  0.348889  0.5997
   8  4.228  0.34042  0.684701
   9  4.913  0.346058  0.762193
  10  5.612  0.349932  0.818274
  11  6.436  0.509855  0.886791
  12  7.108  0.440167  0.909245
  13  7.923  0.552565  0.925997
  14  8.737  0.648683  0.990822
  15  9.426  0.566358  1.03756
  16  10.217  0.609808  1.03294
  17  10.941  0.556436  1.05257
  18  11.789  0.656023  1.16965
  19  12.575  0.667249  1.14152
  20  13.402  0.723748  1.23363
  21  14.094  0.602395  1.24441
  22  15.002  0.748483  1.27527
  23  15.761  0.701025  1.30919
  24  16.637  0.794696  1.3666
  25  17.438  0.789766  1.25942
  26  18.263  0.810046  1.55138
  27  19.09  0.828421  1.48939
  28  19.967  0.90389  1.43134
  29  20.712  0.814088  1.43649
  30  21.59  0.883008  1.45736
  31  22.415  0.883896  1.56634
  32  23.181  0.81033  1.50975
  33  24.073  0.885849  1.74542
  34  24.955  0.945996  1.69667
  35  25.8  0.95874  1.73974
  36  26.537  0.839815  1.73036
  37  27.465  0.946412  1.64042
  38  28.229  0.855194  1.60817
  39  29.255  1.07258  1.63761
  40  30.059  1.02422  1.80132
  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
    10   6   1   8   5   9   7   4   3   2

  Permutation P2

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

  Permutation P3

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

  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) = 6
  K(P1,P2) = 6
  K(P2,P3) = 7
  K(P1,P2) + K(P2,P3) = 13

permutation_distance_test():
  Normal end of execution.

08-Oct-2025 12:18:41