07-Jan-2022 21:39:51

hankel_spd_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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 :    0.814724             0             0             0             0  
      2 :   0.0975404      0.905792             0             0             0  
      3 :     1.01872      0.278498      0.126987             0             0  
      4 :    0.431591       1.20268      0.546882      0.913376             0  
      5 :     1.38878      0.782296       8.92528      0.957507      0.632359  

  The Hankel matrix H = L * L':

  Col:       1             2             3             4             5       
  Row
      1 :    0.663775     0.0794685      0.829973      0.351628       1.13147  
      2 :   0.0794685      0.829973      0.351628       1.13147      0.844059  
      3 :    0.829973      0.351628       1.13147      0.844059       2.76604  
      4 :    0.351628       1.13147      0.844059       2.76604       7.29587  
      5 :     1.13147      0.844059       2.76604       7.29587       83.5181  

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.

07-Jan-2022 21:39:51