09 May 2025   9:45:48.660 PM
 
square_integrals_test():
  FORTRAN90 version
  Test the SQUARE_INTEGRALS library.
 
SQUARE01_MONOMIAL_INTEGRAL_TEST
  SQUARE01_MONOMIAL_INTEGRAL returns the exact integral
  of a monomial over the interior of the unit square in 2D.

  Number of sample points used is   4192

  Ex  Ey     MC-Estimate           Exact      Error

   5   7    0.209430E-01    0.208333E-01    0.11E-03
   0   7    0.121322        0.125000        0.37E-02
   7   2    0.421700E-01    0.416667E-01    0.50E-03
   3   7    0.312652E-01    0.312500E-01    0.15E-04
   5   4    0.332888E-01    0.333333E-01    0.45E-04
   2   5    0.549039E-01    0.555556E-01    0.65E-03
   3   0    0.250251        0.250000        0.25E-03
   7   3    0.315343E-01    0.312500E-01    0.28E-03
   4   7    0.250786E-01    0.250000E-01    0.79E-04
   1   1    0.250260        0.250000        0.26E-03
   4   3    0.497986E-01    0.500000E-01    0.20E-03
   4   1    0.100646        0.100000        0.65E-03
   3   0    0.250251        0.250000        0.25E-03
   5   2    0.557444E-01    0.555556E-01    0.19E-03
   3   5    0.413836E-01    0.416667E-01    0.28E-03
   7   1    0.633414E-01    0.625000E-01    0.84E-03
   7   7    0.157928E-01    0.156250E-01    0.17E-03
   1   3    0.122825        0.125000        0.22E-02
   6   6    0.205142E-01    0.204082E-01    0.11E-03
   4   6    0.285549E-01    0.285714E-01    0.17E-04
 
SQUARESYM_MONOMIAL_INTEGRAL_TEST
  SQUARESYM_MONOMIAL_INTEGRAL returns the exact integral
  of a monomial over the interior of the 
  symmetric unit square in 2D.

  Number of sample points used is   4192

  Ex  Ey     MC-Estimate           Exact      Error

   7   5    0.115352E-02     0.00000        0.12E-02
   4   3   -0.931352E-02     0.00000        0.93E-02
   3   7    0.518733E-02     0.00000        0.52E-02
   4   1   -0.132359E-01     0.00000        0.13E-01
   2   4    0.261714        0.266667        0.50E-02
   4   7   -0.491355E-02     0.00000        0.49E-02
   4   0    0.770498        0.800000        0.30E-01
   7   2    0.660554E-02     0.00000        0.66E-02
   0   6    0.547282        0.571429        0.24E-01
   7   6    0.277357E-02     0.00000        0.28E-02
   3   2    0.110746E-01     0.00000        0.11E-01
   1   6    0.484819E-02     0.00000        0.48E-02
   2   3   -0.102337E-01     0.00000        0.10E-01
   5   6    0.382763E-02     0.00000        0.38E-02
   1   0    0.629790E-01     0.00000        0.63E-01
   6   4    0.111213        0.114286        0.31E-02
   5   7    0.301148E-02     0.00000        0.30E-02
   6   3   -0.849472E-02     0.00000        0.85E-02
   3   7    0.518733E-02     0.00000        0.52E-02
   6   2    0.183929        0.190476        0.65E-02
 
SQUARE_INTEGRALS_TEST
  Normal end of execution.
 
09 May 2025   9:45:48.662 PM