09 May 2025   9:28:52.081 PM
 
qr_solve_test():
  FORTRAN90 version
  Test qr_solve().
  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     6.205        0.2861E-07     5.461         5.461         1.075         1.075    
      2     6     3     537.6        0.5416E-04     194.8         194.8         5.222         5.222    
      3     5     3     40.37      ------------     10.84      ------------    0.5477E-06  ------------
      4     3     5     232.1      ------------     7.416      ------------     0.000      ------------
      5    10    10     1.000      ------------    0.1534E+08  ------------    0.2261E-09  ------------
      6    10    10     1.000        0.4990E-15     1.000         1.000        0.4988E-15    0.8696E-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     6.205        0.2861E-07     5.461         5.461         1.075         1.075    
      2     6     3     537.6        0.5416E-04     194.8         194.8         5.222         5.222    
      3     5     3     40.37         26.68         10.84         28.80        0.5477E-06    0.4936E-13
      4     3     5     232.1         10.37         7.416         12.75         0.000        0.1097E-12
      5    10    10     1.000         2182.        0.1534E+08    0.1534E+08    0.2261E-09    0.6014E-09
      6    10    10     1.000        0.5752E-15     1.000         1.000        0.4988E-15    0.4190E-15
 
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     6.205        0.2861E-07     5.461         5.461         1.075         1.075    
      2     6     3     537.6        0.5416E-04     194.8         194.8         5.222         5.222    
      3     5     3     40.37        0.5092E-07     10.84         10.84        0.5477E-06    0.4082E-13
      4     3     5     232.1        0.1565E-12     7.416         7.416         0.000        0.1045E-12
      5    10    10     1.000         1731.        0.1534E+08    0.1534E+08    0.2261E-09    0.4856E-09
      6    10    10     1.000        0.1133E-14     1.000         1.000        0.4988E-15    0.1063E-14
 
DQRLS_TEST
  DQRLS solves a linear system A*x = b 
  in the least squares sense.
 
  Coefficient matrix A:
 
  Col          1             2             3      
  Row
 
    1:   1.00000       1.00000       1.00000    
    2:   1.00000       2.00000       4.00000    
    3:   1.00000       3.00000       9.00000    
    4:   1.00000       4.00000       16.0000    
    5:   1.00000       5.00000       25.0000    
 
  Right hand side b:
 
         1:    1.0000000    
         2:    2.3000000    
         3:    4.6000000    
         4:    3.1000000    
         5:    1.2000000    
 
  Error code =   0
  Estimated matrix rank =   3
 
  Least squares solution x:
 
         1:   -3.0200000    
         2:    4.4914286    
         3:  -0.72857143    
 
  Residuals A*x-b
 
         1:   0.25714286    
         2:  -0.74857143    
         3:   0.70285714    
         4:  -0.18857143    
         5:  -0.22857143E-01
 
qr_solve_test():
  Normal end of execution.
 
09 May 2025   9:28:52.082 PM