8 September 2021 9:10:54.754 AM CUBE_FELIPPA_RULE_TEST FORTRAN90 version Test CUBE_FELIPPA_RULE(). CUBE_MONOMIAL_TEST For the cube_, CUBE_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Z^GAMMA over the cube [A1,B1]x[A2,B2]x[A3,B3] Volume = 8.00000 ALPHA BETA GAMMA INTEGRAL 0 0 0 8.00000 0 0 1 0.00000 0 0 2 2.66667 0 0 3 0.00000 0 0 4 1.60000 0 1 0 0.00000 0 1 1 0.00000 0 1 2 0.00000 0 1 3 0.00000 0 2 0 2.66667 0 2 1 0.00000 0 2 2 0.888889 0 3 0 0.00000 0 3 1 0.00000 0 4 0 1.60000 1 0 0 0.00000 1 0 1 0.00000 1 0 2 0.00000 1 0 3 0.00000 1 1 0 0.00000 1 1 1 0.00000 1 1 2 0.00000 1 2 0 0.00000 1 2 1 0.00000 1 3 0 0.00000 2 0 0 2.66667 2 0 1 0.00000 2 0 2 0.888889 2 1 0 0.00000 2 1 1 0.00000 2 2 0 0.888889 3 0 0 0.00000 3 0 1 0.00000 3 1 0 0.00000 4 0 0 1.60000 CUBE_QUAD_TEST For the cube, we approximate monomial integrals with CUBE_RULE, which returns N1 by N2 by N3 point rules. Monomial exponents: 0 0 0 1 1 1 8.00000 2 2 2 8.00000 3 3 3 8.00000 4 4 4 8.00000 5 5 5 8.00000 3 5 2 8.00000 Exact 8.00000 Monomial exponents: 1 0 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.381639E-16 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.277556E-16 4 4 4 0.277556E-16 5 5 5 -0.867362E-16 3 5 2 -0.333067E-15 Exact 0.00000 Monomial exponents: 0 0 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.277556E-16 4 4 4 0.555112E-16 5 5 5 -0.346945E-17 3 5 2 -0.111022E-15 Exact 0.00000 Monomial exponents: 2 0 0 1 1 1 0.00000 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 1 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 2 0 1 1 1 0.00000 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 1 0 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.208167E-16 5 5 5 0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.416334E-16 5 5 5 -0.173472E-17 3 5 2 -0.416334E-16 Exact 0.00000 Monomial exponents: 0 0 2 1 1 1 0.00000 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 3 0 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.451028E-16 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.312250E-16 5 5 5 -0.867362E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 1 2 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.346945E-17 5 5 5 0.520417E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 3 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.693889E-16 4 4 4 0.00000 5 5 5 -0.156125E-16 3 5 2 -0.138778E-16 Exact 0.00000 Monomial exponents: 2 0 1 1 1 1 0.00000 2 2 2 -0.555112E-16 3 3 3 0.00000 4 4 4 -0.242861E-16 5 5 5 -0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 1 1 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.346945E-17 5 5 5 -0.867362E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 2 1 1 1 1 0.00000 2 2 2 -0.555112E-16 3 3 3 -0.138778E-16 4 4 4 0.00000 5 5 5 0.954098E-16 3 5 2 -0.485723E-16 Exact 0.00000 Monomial exponents: 1 0 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.346945E-17 5 5 5 -0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.138778E-16 4 4 4 -0.555112E-16 5 5 5 0.537764E-16 3 5 2 -0.277556E-16 Exact 0.00000 Monomial exponents: 0 0 3 1 1 1 0.00000 2 2 2 -0.555112E-16 3 3 3 -0.138778E-16 4 4 4 -0.277556E-16 5 5 5 0.178677E-15 3 5 2 0.312250E-16 Exact 0.00000 Monomial exponents: 4 0 0 1 1 1 0.00000 2 2 2 0.888889 3 3 3 1.60000 4 4 4 1.60000 5 5 5 1.60000 3 5 2 1.60000 Exact 1.60000 Monomial exponents: 3 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 2 0 1 1 1 0.00000 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 3 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.693889E-17 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 4 0 1 1 1 0.00000 2 2 2 0.888889 3 3 3 1.60000 4 4 4 1.60000 5 5 5 1.60000 3 5 2 1.60000 Exact 1.60000 Monomial exponents: 3 0 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 -0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 1 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.104083E-16 5 5 5 0.693889E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 1 2 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.346945E-17 5 5 5 -0.520417E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 3 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.208167E-16 4 4 4 0.346945E-17 5 5 5 0.173472E-16 3 5 2 -0.346945E-16 Exact 0.00000 Monomial exponents: 2 0 2 1 1 1 0.00000 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 1 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.346945E-17 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 2 2 1 1 1 0.00000 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 0 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.693889E-17 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.208167E-16 4 4 4 -0.242861E-16 5 5 5 0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 0 4 1 1 1 0.00000 2 2 2 0.888889 3 3 3 1.60000 4 4 4 1.60000 5 5 5 1.60000 3 5 2 0.888889 Exact 1.60000 Monomial exponents: 5 0 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 4 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.138778E-16 5 5 5 0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 3 2 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 -0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 3 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.156125E-16 3 5 2 -0.138778E-16 Exact 0.00000 Monomial exponents: 1 4 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.693889E-17 5 5 5 -0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 5 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.138778E-16 4 4 4 -0.173472E-16 5 5 5 0.745931E-16 3 5 2 0.277556E-16 Exact 0.00000 Monomial exponents: 4 0 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.693889E-16 4 4 4 0.693889E-17 5 5 5 -0.433681E-16 3 5 2 -0.138778E-16 Exact 0.00000 Monomial exponents: 3 1 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.173472E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 2 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.451028E-16 5 5 5 -0.520417E-17 3 5 2 -0.277556E-16 Exact 0.00000 Monomial exponents: 1 3 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.346945E-17 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 4 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.416334E-16 4 4 4 -0.173472E-16 5 5 5 -0.867362E-17 3 5 2 -0.693889E-17 Exact 0.00000 Monomial exponents: 3 0 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 1 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 0.867362E-17 3 5 2 -0.693889E-17 Exact 0.00000 Monomial exponents: 1 2 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.346945E-17 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 3 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.138778E-16 4 4 4 0.138778E-16 5 5 5 0.520417E-17 3 5 2 0.693889E-17 Exact 0.00000 Monomial exponents: 2 0 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.693889E-16 4 4 4 0.00000 5 5 5 0.867362E-17 3 5 2 0.693889E-17 Exact 0.00000 Monomial exponents: 1 1 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.00000 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 2 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.416334E-16 4 4 4 0.416334E-16 5 5 5 -0.225514E-16 3 5 2 -0.346945E-17 Exact 0.00000 Monomial exponents: 1 0 4 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.693889E-17 5 5 5 -0.346945E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 4 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.138778E-16 4 4 4 0.242861E-16 5 5 5 0.190820E-16 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 0 5 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.416334E-16 4 4 4 0.104083E-16 5 5 5 -0.225514E-16 3 5 2 -0.121431E-16 Exact 0.00000 Monomial exponents: 6 0 0 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.14286 5 5 5 1.14286 3 5 2 0.960000 Exact 1.14286 Monomial exponents: 5 1 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 4 2 0 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 3 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 -0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 4 0 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 1 5 0 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 -0.954098E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 6 0 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.14286 5 5 5 1.14286 3 5 2 1.14286 Exact 1.14286 Monomial exponents: 5 0 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 4 1 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 -0.607153E-17 3 5 2 -0.693889E-17 Exact 0.00000 Monomial exponents: 3 2 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 -0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 3 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 -0.173472E-17 3 5 2 -0.138778E-16 Exact 0.00000 Monomial exponents: 1 4 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 5 1 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.138778E-16 4 4 4 0.00000 5 5 5 -0.607153E-17 3 5 2 0.208167E-16 Exact 0.00000 Monomial exponents: 4 0 2 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 1 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.346945E-17 5 5 5 0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 2 2 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.296296 4 4 4 0.296296 5 5 5 0.296296 3 5 2 0.296296 Exact 0.296296 Monomial exponents: 1 3 2 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 -0.346945E-17 5 5 5 -0.260209E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 4 2 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 0 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 0.867362E-18 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 2 1 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 0.867362E-17 3 5 2 -0.346945E-17 Exact 0.00000 Monomial exponents: 1 2 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.00000 5 5 5 -0.260209E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 3 3 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.138778E-16 4 4 4 0.00000 5 5 5 -0.607153E-17 3 5 2 0.346945E-17 Exact 0.00000 Monomial exponents: 2 0 4 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.296296 Exact 0.533333 Monomial exponents: 1 1 4 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.346945E-17 5 5 5 0.260209E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 2 4 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.296296 Exact 0.533333 Monomial exponents: 1 0 5 1 1 1 0.00000 2 2 2 0.00000 3 3 3 0.00000 4 4 4 0.693889E-17 5 5 5 0.780626E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 1 5 1 1 1 0.00000 2 2 2 0.00000 3 3 3 -0.138778E-16 4 4 4 0.138778E-16 5 5 5 -0.607153E-17 3 5 2 0.00000 Exact 0.00000 Monomial exponents: 0 0 6 1 1 1 0.00000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.14286 5 5 5 1.14286 3 5 2 0.296296 Exact 1.14286 CUBE_FELIPPA_RULE_TEST Normal end of execution. 8 September 2021 9:10:54.755 AM