28 February 2013   9:41:11.738 AM
 
ROMBERG_PRB
  FORTRAN90 version
  Test the ROMBERG library.
 
TEST01
  TRAPEZOID carries out an iterative procedure to estimate
  an integral using the composite trapezoid rule.
 
       N     Integral         Error
             estimate
 
       2     23.0982         14.9448    
       3     12.4305         4.27709    
       5     9.25451         1.10115    
       9     8.43059        0.277230    
      17     8.22279        0.694282E-01
      33     8.17073        0.173646E-01
      65     8.15771        0.434162E-02
     129     8.15445        0.108543E-02
     257     8.15364        0.271360E-03
     513     8.15343        0.678402E-04
    1025     8.15338        0.169601E-04
    2049     8.15337        0.424002E-05
 
TEST02
  TRAPEZOID_REFINE carries out an iterative procedure
  to estimate an integral using the composite 
  trapezoid rule.
 
     M       N     Integral         Error
                   estimate
 
     1       2     23.0982         14.9448    
     2       3     12.4305         4.27709    
     3       5     9.25451         1.10115    
     4       9     8.43059        0.277230    
     5      17     8.22279        0.694282E-01
     6      33     8.17073        0.173646E-01
     7      65     8.15771        0.434162E-02
     8     129     8.15445        0.108543E-02
     9     257     8.15364        0.271360E-03
    10     513     8.15343        0.678402E-04
    11    1025     8.15338        0.169601E-04
    12    2049     8.15337        0.424002E-05
 
TEST03
  TRAPEZOID_TOL estimates an integral by refining a
  trapezoid estimate until a tolerance is met. 
 
       TOL            Integral        Error        M
                      estimate
 
     1.00000         8.43059        0.277230       4
    0.100000         8.17073        0.173646E-01   6
    0.100000E-01     8.15445        0.108543E-02   8
    0.100000E-02     8.15364        0.271360E-03   9
    0.100000E-03     8.15338        0.169601E-04  11
    0.100000E-04     8.15337        0.106000E-05  13
    0.100000E-05     8.15336        0.265001E-06  14
    0.100000E-06     8.15336        0.165626E-07  16
 
TEST04
  ROMBERG_TRAP estimates an integral by Romberg
  extrapolation from trapezoid estimates. 
 
       TOL            Integral        Error      M
                      estimate
 
     1.00000         8.19586        0.424980E-01   3
    0.100000         8.19586        0.424980E-01   3
    0.100000E-01     8.15595        0.259078E-02   4
    0.100000E-02     8.15353        0.161035E-03   5
    0.100000E-03     8.15337        0.100517E-04   6
    0.100000E-04     8.15336        0.628028E-06   7
    0.100000E-05     8.15336        0.392486E-07   8
    0.100000E-06     8.15336        0.392486E-07   8
 
ROMBERG_PRB
  Normal end of execution.
 
28 February 2013   9:41:11.744 AM