04 March 2022 10:51:07 AM

QR_SOLVE_TEST
  C++ version
  Test the QR_SOLVE library.
  QR_SOLVE needs the R8LIB library.
  This test also needs the TEST_LS library.

NORMAL_SOLVE_TEST
  NORMAL_SOLVE is a function with a simple interface which
  solves a linear system A*x = b in the least squares sense.
  Compare a tabulated solution X1 to the NORMAL_SOLVE result X2.

  NORMAL_SOLVE cannot be applied when N < M,
  or if the matrix does not have full column rank.

  Number of problems = 6

  Index     M     N     ||B||         ||X1 - X2||   ||X1||       ||X2||        ||R1||        ||R2||

      1     5     3       6.20484   2.86071e-08       5.46115       5.46115       1.07544       1.07544
      2     6     3       537.569   5.41634e-05       194.819       194.819       5.22193       5.22193
      3     5     3       40.3733  ------------        10.844  ------------   5.47723e-07  ------------
      4     3     5        232.11  ------------        7.4162  ------------             0  ------------
      5    10    10             1  ------------   1.53439e+07  ------------   1.50702e-10  ------------
      6    10    10             1   4.71436e-16             1             1    4.7364e-16    2.2197e-16

QR_SOLVE_TEST
  QR_SOLVE is a function with a simple interface which
  solves a linear system A*x = b in the least squares sense.
  Compare a tabulated solution X1 to the QR_SOLVE result X2.

  Number of problems = 6

  Index     M     N     ||B||         ||X1 - X2||   ||X1||       ||X2||        ||R1||        ||R2||

      1     5     3       6.20484   2.86071e-08       5.46115       5.46115       1.07544       1.07544
      2     6     3       537.569   5.41634e-05       194.819       194.819       5.22193       5.22193
      3     5     3       40.3733       40.7616        10.844       42.1794   5.47723e-07   6.39488e-14
      4     3     5        232.11       10.3682        7.4162       12.7475             0   8.93845e-14
      5    10    10             1       2182.02   1.53439e+07   1.53417e+07   1.50702e-10   1.03352e-09
      6    10    10             1   6.52846e-16             1             1    4.7364e-16   3.90883e-16

SVD_SOLVE_TEST
  SVD_SOLVE is a function with a simple interface which
  solves a linear system A*x = b in the least squares sense.
  Compare a tabulated solution X1 to the SVD_SOLVE result X2.

  Number of problems = 6

  Index     M     N     ||B||         ||X1 - X2||   ||X1||       ||X2||        ||R1||        ||R2||

      1     5     3       6.20484   2.86071e-08       5.46115       5.46115       1.07544       1.07544
      2     6     3       537.569   5.41634e-05       194.819       194.819       5.22193       5.22193
      3     5     3       40.3733   5.09175e-08        10.844        10.844   5.47723e-07   4.28172e-14
      4     3     5        232.11   1.14813e-13        7.4162        7.4162             0   1.31642e-13
      5    10    10             1       1730.72   1.53439e+07   1.53422e+07   1.50702e-10   7.09956e-10
      6    10    10             1   5.64913e-16             1             1    4.7364e-16   5.54561e-16

DQRLS_TEST
  DQRLS solves a linear system A*x = b in the least squares sense.

  Coefficient matrix A:

  Col:          0             1             2       
  Row

    0:            1             1             1  
    1:            1             2             4  
    2:            1             3             9  
    3:            1             4            16  
    4:            1             5            25  

  Right hand side b:

         0:              1
         1:            2.3
         2:            4.6
         3:            3.1
         4:            1.2

  Error code = 0
  Estimated matrix rank = 3

  Least squares solution x:

         0:          -3.02
         1:        4.49143
         2:      -0.728571

  Residuals A*x-b

         0:       0.257143
         1:      -0.748571
         2:       0.702857
         3:      -0.188571
         4:     -0.0228571

QR_SOLVE_TEST
  Normal end of execution.

04 March 2022 10:51:07 AM