26-Dec-2022 20:38:54

hankel_spd_test():
  MATLAB/Octave version 4.2.2
  Test hankel_spd().

hankel_spd_cholesky_lower_test01():
  hankel_spd_cholesky_lower() computes a lower Cholesky
  matrix L such that the matrix H = L * L' is a
  symmetric positive definite (SPD) Hankel matrix.

  The Cholesky factor L:

  Col:       1             2             3             4             5       
  Row
      1 :           1             0             0             0             0  
      2 :           1             1             0             0             0  
      3 :           2             1             1             0             0  
      4 :           3             3             1             1             0  
      5 :           6             4             4             1             1  

  The Hankel matrix H = L * L':

  Col:       1             2             3             4             5       
  Row
      1 :           1             1             2             3             6  
      2 :           1             2             3             6            10  
      3 :           2             3             6            10            20  
      4 :           3             6            10            20            35  
      5 :           6            10            20            35            70  

  The Cholesky factor L:

  Col:       1             2             3             4             5       
  Row
      1 :           1             0             0             0             0  
      2 :           4             2             0             0             0  
      3 :          20             3             3             0             0  
      4 :          86            37             2             4             0  
      5 :         418          82.5       59.1667             1             5  

  The Hankel matrix H = L * L':

  Col:       1             2             3             4             5       
  Row
      1 :           1             4            20            86           418  
      2 :           4            20            86           418          1837  
      3 :          20            86           418          1837          8785  
      4 :          86           418          1837          8785       39122.8  
      5 :         418          1837          8785       39122.8        185057  

  The Cholesky factor L:

  Col:       1             2             3             4             5       
  Row
      1 :    0.905466             0             0             0             0  
      2 :    0.942274       0.32724             0             0             0  
      3 :     1.09884      0.851458      0.938649             0             0  
      4 :     1.45123        4.4189      0.271269      0.178527             0  
      5 :     3.10724       8.20177       12.0816      0.701044      0.148746  

  The Hankel matrix H = L * L':

  Col:       1             2             3             4             5       
  Row
      1 :    0.819869      0.853198      0.994967       1.31404        2.8135  
      2 :    0.853198      0.994967       1.31404        2.8135       5.61181  
      3 :    0.994967       1.31404        2.8135       5.61181       21.7382  
      4 :     1.31404        2.8135       5.61181       21.7382       44.1547  
      5 :      2.8135       5.61181       21.7382       44.1547       223.403  

hankel_spd_cholesky_lower_test02():
  hankel_spd_cholesky_lower() computes a lower Cholesky
  matrix L such that the matrix H = L * L' is a
  symmetric positive definite (SPD) Hankel matrix.

  The Cholesky factor L:

  Col:       1             2             3             4             5       
  Row
      1 :           1             0             0             0             0  
      2 :           1             1             0             0             0  
      3 :           2             1             1             0             0  
      4 :           3             3             1             1             0  
      5 :           6             4             4             1             1  

  The Hankel matrix H = L * L':

  Col:       1             2             3             4             5       
  Row
      1 :           1             1             2             3             6  
      2 :           1             2             3             6            10  
      3 :           2             3             6            10            20  
      4 :           3             6            10            20            35  
      5 :           6            10            20            35            70  

  The Cholesky factor L2 of H:

  Col:       1             2             3             4             5       
  Row
      1 :           1             0             0             0             0  
      2 :           1             1             0             0             0  
      3 :           2             1             1             0             0  
      4 :           3             3             1             1             0  
      5 :           6             4             4             1             1  

  The Hankel matrix H2 = L2 * L2':

  Col:       1             2             3             4             5       
  Row
      1 :           1             1             2             3             6  
      2 :           1             2             3             6            10  
      3 :           2             3             6            10            20  
      4 :           3             6            10            20            35  
      5 :           6            10            20            35            70  

hankel_spd_test():
  Normal end of execution.

26-Dec-2022 20:38:54