Tue Oct 19 17:05:48 2021

qr_solve_testS
  Python version: 3.6.9
  Test the qr_solve library.

lstsq_solve_test
  Python version: 3.6.9
  The function x=np.linalg.lstsq(A,b)

  solves a linear system A*x = b in the least squares sense.
  Compare a tabulated solution X1 to the LSTSQ result X2.

  Number of problems = 6

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

      1     5     3         6.205     2.861e-08         5.461         5.461         1.075         1.075
      2     6     3         537.6     5.416e-05         194.8         194.8         5.222         5.222
      3     5     3         40.37     5.092e-08         10.84         10.84     5.477e-07      2.93e-14
      4     3     5         232.1     2.485e-14         7.416         7.416             0      8.71e-14
      5    10    10             1          1332     1.534e+07     1.534e+07       1.2e-10     9.331e-10
      6    10    10             1     5.042e-16             1             1     4.773e-16      6.92e-16

lstsq_solve_test
  Normal end of execution.

normal_solve_test
  Python version: 3.6.9
  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
         6.205     2.861e-08
         5.461         5.461
         1.075         1.075
      2     6     3
         537.6     5.416e-05
         194.8         194.8
         5.222         5.222
      3     5     3
         40.37  ------------
         10.84  ------------
     5.477e-07  ------------
      4     3     5
         232.1  ------------
         7.416  ------------
             0  ------------
      5    10    10
             1  ------------
     1.534e+07  ------------
       1.2e-10  ------------
      6    10    10
             1     5.231e-16
             1             1
     4.773e-16     2.017e-16

normal_solve_test
  Normal end of execution.

qr_solve_test
  Python version: 3.6.9
  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
         6.205     2.861e-08
         5.461         5.461
         1.075         1.075
      2     6     3
         537.6     5.416e-05
         194.8         194.8
         5.222         5.222
      3     5     3
         40.37         20.96
         10.84          23.6
     5.477e-07     1.231e-14
      4     3     5
         232.1         10.37
         7.416         12.75
             0     3.553e-14
      5    10    10
             1          2290
     1.534e+07     1.534e+07
       1.2e-10     9.917e-10
      6    10    10
             1      5.93e-16
             1             1
     4.773e-16     3.295e-16

qr_solve_test
  Normal end of execution.

svd_solve_test
  Python version: 3.6.9
  svd_solve is a function with a simple interface which
  solves a linear system A*x = b in the least squares sense
  using the singular value decomposition (SVD).
  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
         6.205     2.861e-08
         5.461         5.461
         1.075         1.075
      2     6     3
         537.6     5.416e-05
         194.8         194.8
         5.222         5.222
      3     5     3
         40.37     5.092e-08
         10.84         10.84
     5.477e-07     7.105e-15
      4     3     5
         232.1     1.026e-13
         7.416         7.416
             0     2.693e-13
      5    10    10
             1          1997
     1.534e+07     1.534e+07
       1.2e-10     1.163e-09
      6    10    10
             1     8.163e-16
             1             1
     4.773e-16     6.186e-16

svd_solve_test
  Normal end of execution.

qr_solve_tests
  Normal end of execution.
Tue Oct 19 17:05:48 2021