18 April 2020 06:42:49 PM

SQUARE_FELIPPA_RULE_TEST
  C++ version
  Test the SQUARE_FELIPPA_RULE library.

SQUARE_MONOMIAL_TEST
  For a square in 2D,
  SQUARE_MONOMIAL returns the exact value of the
  integral of X^ALPHA Y^BETA

  Volume = 4

     ALPHA      BETA      INTEGRAL

         0         0               4
         0         1               0
         0         2         1.33333
         0         3               0
         0         4             0.8
         1         0               0
         1         1               0
         1         2               0
         1         3               0
         2         0         1.33333
         2         1               0
         2         2        0.444444
         3         0               0
         3         1               0
         4         0             0.8

SQUARE_QUAD_TEST
  For a square in 2D,
  we approximate monomial integrals with:
  SQUARE_RULE, which returns M by N point rules..

  Monomial exponents:    0   0

       1       1               4
       2       2               4
       3       3               4
       4       4               4
       5       5               4
       3       5               4

   Exact                       4

  Monomial exponents:    1   0

       1       1               0
       2       2               0
       3       3               0
       4       4    -1.38778e-17
       5       5     3.46945e-17
       3       5               0

   Exact                       0

  Monomial exponents:    0   1

       1       1               0
       2       2               0
       3       3               0
       4       4     1.38778e-17
       5       5     3.46945e-17
       3       5    -1.11022e-16

   Exact                       0

  Monomial exponents:    2   0

       1       1               0
       2       2         1.33333
       3       3         1.33333
       4       4         1.33333
       5       5         1.33333
       3       5         1.33333

   Exact                 1.33333

  Monomial exponents:    1   1

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5    -6.93889e-18
       3       5               0

   Exact                       0

  Monomial exponents:    0   2

       1       1               0
       2       2         1.33333
       3       3         1.33333
       4       4         1.33333
       5       5         1.33333
       3       5         1.33333

   Exact                 1.33333

  Monomial exponents:    3   0

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5     1.38778e-17
       3       5               0

   Exact                       0

  Monomial exponents:    2   1

       1       1               0
       2       2               0
       3       3               0
       4       4    -2.77556e-17
       5       5     8.32667e-17
       3       5               0

   Exact                       0

  Monomial exponents:    1   2

       1       1               0
       2       2               0
       3       3               0
       4       4     1.38778e-17
       5       5               0
       3       5               0

   Exact                       0

  Monomial exponents:    0   3

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5     2.77556e-17
       3       5    -1.38778e-17

   Exact                       0

  Monomial exponents:    4   0

       1       1               0
       2       2        0.444444
       3       3             0.8
       4       4             0.8
       5       5             0.8
       3       5             0.8

   Exact                     0.8

  Monomial exponents:    3   1

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5               0
       3       5               0

   Exact                       0

  Monomial exponents:    2   2

       1       1               0
       2       2        0.444444
       3       3        0.444444
       4       4        0.444444
       5       5        0.444444
       3       5        0.444444

   Exact                0.444444

  Monomial exponents:    1   3

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5               0
       3       5               0

   Exact                       0

  Monomial exponents:    0   4

       1       1               0
       2       2        0.444444
       3       3             0.8
       4       4             0.8
       5       5             0.8
       3       5             0.8

   Exact                     0.8

  Monomial exponents:    5   0

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5     1.38778e-17
       3       5               0

   Exact                       0

  Monomial exponents:    4   1

       1       1               0
       2       2               0
       3       3               0
       4       4     1.38778e-17
       5       5     2.08167e-17
       3       5    -2.77556e-17

   Exact                       0

  Monomial exponents:    3   2

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5               0
       3       5               0

   Exact                       0

  Monomial exponents:    2   3

       1       1               0
       2       2               0
       3       3               0
       4       4    -1.38778e-17
       5       5     6.93889e-18
       3       5    -1.38778e-17

   Exact                       0

  Monomial exponents:    1   4

       1       1               0
       2       2               0
       3       3               0
       4       4               0
       5       5    -6.93889e-18
       3       5               0

   Exact                       0

  Monomial exponents:    0   5

       1       1               0
       2       2               0
       3       3    -1.38778e-17
       4       4     6.93889e-18
       5       5    -6.93889e-18
       3       5     2.77556e-17

   Exact                       0

SQUARE_FELIPPA_RULE_TEST
  Normal end of execution.

18 April 2020 06:42:49 PM