01 March 2022 07:27:09 AM

hankel_spd_test
  C++ version
  Test the hankel_spd library.

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:          0             1             2             3             4       
  Row

    0:            1             0             0             0             0  
    1:            1             1             0             0             0  
    2:            2             1             1             0             0  
    3:            3             3             1             1             0  
    4:            6             4             4             1             1  

  The Hankel matrix H = L * L':

  Col:          0             1             2             3             4       
  Row

    0:            1             1             2             3             6  
    1:            1             2             3             6            10  
    2:            2             3             6            10            20  
    3:            3             6            10            20            35  
    4:            6            10            20            35            70  

  The Cholesky factor L:

  Col:          0             1             2             3             4       
  Row

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

  The Hankel matrix H = L * L':

  Col:          0             1             2             3             4       
  Row

    0:            1             4            20            86           418  
    1:            4            20            86           418          1837  
    2:           20            86           418          1837          8785  
    3:           86           418          1837          8785       39122.8  
    4:          418          1837          8785       39122.8        185057  

  The Cholesky factor L:

  Col:          0             1             2             3             4       
  Row

    0:     0.218418             0             0             0             0  
    1:    0.0661187      0.956318             0             0             0  
    2:      4.20713      0.257578      0.829509             0             0  
    3:      2.40134       19.1313      0.109957      0.561695             0  
    4:      84.4911       9.97088       16.9598      0.043829      0.415307  

  The Hankel matrix H = L * L':

  Col:          0             1             2             3             4       
  Row

    0:    0.0477066     0.0144415      0.918915      0.524497       18.4544  
    1:    0.0144415      0.918915      0.524497       18.4544       15.1218  
    2:     0.918915      0.524497       18.4544       15.1218       372.102  
    3:     0.524497       18.4544       15.1218       372.102       395.538  
    4:      18.4544       15.1218       372.102       395.538       7525.98  

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:          0             1             2             3             4       
  Row

    0:            1             0             0             0             0  
    1:            1             1             0             0             0  
    2:            2             1             1             0             0  
    3:            3             3             1             1             0  
    4:            6             4             4             1             1  

  The Hankel matrix H = L * L':

  Col:          0             1             2             3             4       
  Row

    0:            1             1             2             3             6  
    1:            1             2             3             6            10  
    2:            2             3             6            10            20  
    3:            3             6            10            20            35  
    4:            6            10            20            35            70  

  The Cholesky factor L2 of H:

  Col:          0             1             2             3             4       
  Row

    0:            1             0             0             0             0  
    1:            1             1             0             0             0  
    2:            2             1             1             0             0  
    3:            3             3             1             1             0  
    4:            6             4             4             1             1  

  The Hankel matrix H2 = L2 * L2':

  Col:          0             1             2             3             4       
  Row

    0:            1             1             2             3             6  
    1:            1             2             3             6            10  
    2:            2             3             6            10            20  
    3:            3             6            10            20            35  
    4:            6            10            20            35            70  

hankel_spd_test
  Normal end of execution.

01 March 2022 07:27:09 AM