25 December 2011 02:55:14 PM SANDIA_CUBATURE_PRB C++ version Test the SANDIA_CUBATURE library. CN_GEG_TESTS Demonstrate the use of quadrature rules for the region CN_GEG, that is, the hypercube [-1,+1]^N, with the weight W(ALPHA;X) = product ( 1 <= I <= N ) (1-X(I)^2)^ALPHA We use the formulas to integrate various monomials of the form X(1)^E(1) * X(2)^E(2) * ... X(N)^E(N) and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 ALPHA = -0.5 EXPON = 0 Degree = 0 CN_GEG_01_1: 1 3.14159 0 CN_GEG_02_XIU: 2 3.14159 0 GW_02_XIU: 2 3.14159 3.9968e-15 CN_GEG_03_XIU: 2 3.14159 0 EXACT 3.14159 N = 1 ALPHA = 0 EXPON = 0 Degree = 0 CN_GEG_01_1: 1 2 0 CN_GEG_02_XIU: 2 2 0 GW_02_XIU: 2 2 2.22045e-16 CN_GEG_03_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = 0.5 EXPON = 0 Degree = 0 CN_GEG_01_1: 1 1.5708 0 CN_GEG_02_XIU: 2 1.5708 0 GW_02_XIU: 2 1.5708 1.55431e-15 CN_GEG_03_XIU: 2 1.5708 0 EXACT 1.5708 N = 1 ALPHA = 1 EXPON = 0 Degree = 0 CN_GEG_01_1: 1 1.33333 0 CN_GEG_02_XIU: 2 1.33333 0 GW_02_XIU: 2 1.33333 0 CN_GEG_03_XIU: 2 1.33333 0 EXACT 1.33333 N = 1 ALPHA = 1.5 EXPON = 0 Degree = 0 CN_GEG_01_1: 1 1.1781 0 CN_GEG_02_XIU: 2 1.1781 0 GW_02_XIU: 2 1.1781 8.88178e-16 CN_GEG_03_XIU: 2 1.1781 0 EXACT 1.1781 N = 1 ALPHA = -0.5 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_GEG_03_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = 0 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_GEG_03_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = 0.5 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_GEG_03_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = 1 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_GEG_03_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = 1.5 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_GEG_03_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = -0.5 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 1.5708 6.66134e-16 GW_02_XIU: 2 1.5708 1.33227e-15 CN_GEG_03_XIU: 2 1.5708 1.55431e-15 EXACT 1.5708 N = 1 ALPHA = 0 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.666667 0 GW_02_XIU: 2 0.666667 1.11022e-16 CN_GEG_03_XIU: 2 0.666667 2.22045e-16 EXACT 0.666667 N = 1 ALPHA = 0.5 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.392699 2.22045e-16 GW_02_XIU: 2 0.392699 1.66533e-16 CN_GEG_03_XIU: 2 0.392699 2.22045e-16 EXACT 0.392699 N = 1 ALPHA = 1 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.266667 5.55112e-17 GW_02_XIU: 2 0.266667 5.55112e-17 CN_GEG_03_XIU: 2 0.266667 5.55112e-17 EXACT 0.266667 N = 1 ALPHA = 1.5 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.19635 2.77556e-17 GW_02_XIU: 2 0.19635 1.38778e-16 CN_GEG_03_XIU: 2 0.19635 2.77556e-17 EXACT 0.19635 N = 2 ALPHA = -0.5 EXPON = 0 0 Degree = 0 CN_GEG_01_1: 1 9.8696 0 CN_GEG_02_XIU: 3 9.8696 0 GW_02_XIU: 3 9.8696 2.4869e-14 CN_GEG_03_XIU: 4 9.8696 0 EXACT 9.8696 N = 2 ALPHA = 0 EXPON = 0 0 Degree = 0 CN_GEG_01_1: 1 4 0 CN_GEG_02_XIU: 3 4 0 GW_02_XIU: 3 4 8.88178e-16 CN_GEG_03_XIU: 4 4 0 EXACT 4 N = 2 ALPHA = 0.5 EXPON = 0 0 Degree = 0 CN_GEG_01_1: 1 2.4674 0 CN_GEG_02_XIU: 3 2.4674 0 GW_02_XIU: 3 2.4674 4.88498e-15 CN_GEG_03_XIU: 4 2.4674 0 EXACT 2.4674 N = 2 ALPHA = 1 EXPON = 0 0 Degree = 0 CN_GEG_01_1: 1 1.77778 0 CN_GEG_02_XIU: 3 1.77778 0 GW_02_XIU: 3 1.77778 0 CN_GEG_03_XIU: 4 1.77778 0 EXACT 1.77778 N = 2 ALPHA = 1.5 EXPON = 0 0 Degree = 0 CN_GEG_01_1: 1 1.38791 0 CN_GEG_02_XIU: 3 1.38791 0 GW_02_XIU: 3 1.38791 2.22045e-15 CN_GEG_03_XIU: 4 1.38791 0 EXACT 1.38791 N = 2 ALPHA = -0.5 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 3 1.33227e-15 1.33227e-15 GW_02_XIU: 3 1.77636e-15 1.77636e-15 CN_GEG_03_XIU: 4 -1.6025e-16 1.6025e-16 EXACT 0 N = 2 ALPHA = 0 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 3 6.66134e-16 6.66134e-16 GW_02_XIU: 3 5.55112e-16 5.55112e-16 CN_GEG_03_XIU: 4 -8.89617e-17 8.89617e-17 EXACT 0 N = 2 ALPHA = 0.5 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 3 2.22045e-16 2.22045e-16 GW_02_XIU: 3 3.33067e-16 3.33067e-16 CN_GEG_03_XIU: 4 -5.13219e-17 5.13219e-17 EXACT 0 N = 2 ALPHA = 1 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 3 2.22045e-16 2.22045e-16 GW_02_XIU: 3 2.22045e-16 2.22045e-16 CN_GEG_03_XIU: 4 -1.33364e-17 1.33364e-17 EXACT 0 N = 2 ALPHA = 1.5 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 3 1.11022e-16 1.11022e-16 GW_02_XIU: 3 1.11022e-16 1.11022e-16 CN_GEG_03_XIU: 4 -2.13106e-17 2.13106e-17 EXACT 0 N = 2 ALPHA = -0.5 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 1.33227e-15 1.33227e-15 GW_02_XIU: 3 1.55431e-15 1.55431e-15 CN_GEG_03_XIU: 4 -3.02169e-16 3.02169e-16 EXACT 0 N = 2 ALPHA = 0 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 2.77556e-16 2.77556e-16 GW_02_XIU: 3 3.33067e-16 3.33067e-16 CN_GEG_03_XIU: 4 -8.16431e-17 8.16431e-17 EXACT 0 N = 2 ALPHA = 0.5 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 1.38778e-16 1.38778e-16 GW_02_XIU: 3 1.66533e-16 1.66533e-16 CN_GEG_03_XIU: 4 -3.77712e-17 3.77712e-17 EXACT 0 N = 2 ALPHA = 1 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 8.32667e-17 8.32667e-17 GW_02_XIU: 3 8.32667e-17 8.32667e-17 CN_GEG_03_XIU: 4 -2.17715e-17 2.17715e-17 EXACT 0 N = 2 ALPHA = 1.5 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 6.93889e-17 6.93889e-17 GW_02_XIU: 3 8.32667e-17 8.32667e-17 CN_GEG_03_XIU: 4 -1.41642e-17 1.41642e-17 EXACT 0 N = 2 ALPHA = -0.5 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 4.9348 8.88178e-16 GW_02_XIU: 3 4.9348 1.15463e-14 CN_GEG_03_XIU: 4 4.9348 3.55271e-15 EXACT 4.9348 N = 2 ALPHA = 0 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 1.33333 2.22045e-16 GW_02_XIU: 3 1.33333 0 CN_GEG_03_XIU: 4 1.33333 4.44089e-16 EXACT 1.33333 N = 2 ALPHA = 0.5 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.61685 5.55112e-16 GW_02_XIU: 3 0.61685 6.66134e-16 CN_GEG_03_XIU: 4 0.61685 4.44089e-16 EXACT 0.61685 N = 2 ALPHA = 1 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.355556 5.55112e-17 GW_02_XIU: 3 0.355556 5.55112e-17 CN_GEG_03_XIU: 4 0.355556 5.55112e-17 EXACT 0.355556 N = 2 ALPHA = 1.5 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.231319 5.55112e-17 GW_02_XIU: 3 0.231319 4.16334e-16 CN_GEG_03_XIU: 4 0.231319 2.77556e-17 EXACT 0.231319 N = 3 ALPHA = -0.5 EXPON = 0 0 0 Degree = 0 CN_GEG_01_1: 1 31.0063 0 CN_GEG_02_XIU: 4 31.0063 0 GW_02_XIU: 4 31.0063 1.1724e-13 CN_GEG_03_XIU: 6 31.0063 0 EXACT 31.0063 N = 3 ALPHA = 0 EXPON = 0 0 0 Degree = 0 CN_GEG_01_1: 1 8 0 CN_GEG_02_XIU: 4 8 0 GW_02_XIU: 4 8 2.66454e-15 CN_GEG_03_XIU: 6 8 8.88178e-16 EXACT 8 N = 3 ALPHA = 0.5 EXPON = 0 0 0 Degree = 0 CN_GEG_01_1: 1 3.87578 0 CN_GEG_02_XIU: 4 3.87578 0 GW_02_XIU: 4 3.87578 1.15463e-14 CN_GEG_03_XIU: 6 3.87578 0 EXACT 3.87578 N = 3 ALPHA = 1 EXPON = 0 0 0 Degree = 0 CN_GEG_01_1: 1 2.37037 0 CN_GEG_02_XIU: 4 2.37037 0 GW_02_XIU: 4 2.37037 0 CN_GEG_03_XIU: 6 2.37037 0 EXACT 2.37037 N = 3 ALPHA = 1.5 EXPON = 0 0 0 Degree = 0 CN_GEG_01_1: 1 1.6351 0 CN_GEG_02_XIU: 4 1.6351 0 GW_02_XIU: 4 1.6351 3.77476e-15 CN_GEG_03_XIU: 6 1.6351 2.22045e-16 EXACT 1.6351 N = 3 ALPHA = -0.5 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_GEG_03_XIU: 6 0 0 EXACT 0 N = 3 ALPHA = 0 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_GEG_03_XIU: 6 0 0 EXACT 0 N = 3 ALPHA = 0.5 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_GEG_03_XIU: 6 0 0 EXACT 0 N = 3 ALPHA = 1 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_GEG_03_XIU: 6 0 0 EXACT 0 N = 3 ALPHA = 1.5 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_GEG_03_XIU: 6 0 0 EXACT 0 N = 3 ALPHA = -0.5 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 9.49293e-16 9.49293e-16 GW_02_XIU: 4 9.49293e-16 9.49293e-16 CN_GEG_03_XIU: 6 6.6543e-17 6.6543e-17 EXACT 0 N = 3 ALPHA = 0 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 1.63286e-16 1.63286e-16 GW_02_XIU: 4 1.63286e-16 1.63286e-16 CN_GEG_03_XIU: 6 1.15352e-16 1.15352e-16 EXACT 0 N = 3 ALPHA = 0.5 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 5.93308e-17 5.93308e-17 GW_02_XIU: 4 5.93308e-17 5.93308e-17 CN_GEG_03_XIU: 6 5.96701e-17 5.96701e-17 EXACT 0 N = 3 ALPHA = 1 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 2.90287e-17 2.90287e-17 GW_02_XIU: 4 2.90287e-17 2.90287e-17 CN_GEG_03_XIU: 6 1.68063e-17 1.68063e-17 EXACT 0 N = 3 ALPHA = 1.5 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 1.66868e-17 1.66868e-17 GW_02_XIU: 4 1.66868e-17 1.66868e-17 CN_GEG_03_XIU: 6 -1.43238e-18 1.43238e-18 EXACT 0 N = 3 ALPHA = -0.5 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 15.5031 3.55271e-15 GW_02_XIU: 4 15.5031 5.50671e-14 CN_GEG_03_XIU: 6 15.5031 7.10543e-15 EXACT 15.5031 N = 3 ALPHA = 0 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 2.66667 0 GW_02_XIU: 4 2.66667 8.88178e-16 CN_GEG_03_XIU: 6 2.66667 1.33227e-15 EXACT 2.66667 N = 3 ALPHA = 0.5 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.968946 7.77156e-16 GW_02_XIU: 4 0.968946 2.10942e-15 CN_GEG_03_XIU: 6 0.968946 6.66134e-16 EXACT 0.968946 N = 3 ALPHA = 1 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.474074 1.11022e-16 GW_02_XIU: 4 0.474074 1.11022e-16 CN_GEG_03_XIU: 6 0.474074 1.11022e-16 EXACT 0.474074 N = 3 ALPHA = 1.5 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.272516 0 GW_02_XIU: 4 0.272516 6.66134e-16 CN_GEG_03_XIU: 6 0.272516 5.55112e-17 EXACT 0.272516 N = 4 ALPHA = -0.5 EXPON = 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 97.4091 0 CN_GEG_02_XIU: 5 97.4091 0 GW_02_XIU: 5 97.4091 4.9738e-13 CN_GEG_03_XIU: 8 97.4091 1.42109e-14 EXACT 97.4091 N = 4 ALPHA = 0 EXPON = 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 16 0 CN_GEG_02_XIU: 5 16 0 GW_02_XIU: 5 16 7.10543e-15 CN_GEG_03_XIU: 8 16 0 EXACT 16 N = 4 ALPHA = 0.5 EXPON = 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 6.08807 0 CN_GEG_02_XIU: 5 6.08807 0 GW_02_XIU: 5 6.08807 2.39808e-14 CN_GEG_03_XIU: 8 6.08807 0 EXACT 6.08807 N = 4 ALPHA = 1 EXPON = 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 3.16049 0 CN_GEG_02_XIU: 5 3.16049 0 GW_02_XIU: 5 3.16049 0 CN_GEG_03_XIU: 8 3.16049 0 EXACT 3.16049 N = 4 ALPHA = 1.5 EXPON = 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 1.9263 2.22045e-16 CN_GEG_02_XIU: 5 1.9263 2.22045e-16 GW_02_XIU: 5 1.9263 5.77316e-15 CN_GEG_03_XIU: 8 1.9263 4.44089e-16 EXACT 1.9263 N = 4 ALPHA = -0.5 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 5 3.55271e-15 3.55271e-15 GW_02_XIU: 5 3.55271e-15 3.55271e-15 CN_GEG_03_XIU: 8 -1.78287e-14 1.78287e-14 EXACT 0 N = 4 ALPHA = 0 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 5 6.66134e-16 6.66134e-16 GW_02_XIU: 5 6.66134e-16 6.66134e-16 CN_GEG_03_XIU: 8 -2.53217e-15 2.53217e-15 EXACT 0 N = 4 ALPHA = 0.5 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 5 2.22045e-16 2.22045e-16 GW_02_XIU: 5 2.22045e-16 2.22045e-16 CN_GEG_03_XIU: 8 -8.39489e-16 8.39489e-16 EXACT 0 N = 4 ALPHA = 1 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 5 8.32667e-17 8.32667e-17 GW_02_XIU: 5 8.32667e-17 8.32667e-17 CN_GEG_03_XIU: 8 -3.77882e-16 3.77882e-16 EXACT 0 N = 4 ALPHA = 1.5 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 5 2.77556e-17 2.77556e-17 GW_02_XIU: 5 2.77556e-17 2.77556e-17 CN_GEG_03_XIU: 8 -2.13172e-16 2.13172e-16 EXACT 0 N = 4 ALPHA = -0.5 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.66454e-15 2.66454e-15 GW_02_XIU: 5 2.66454e-15 2.66454e-15 CN_GEG_03_XIU: 8 -1.20594e-15 1.20594e-15 EXACT 0 N = 4 ALPHA = 0 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.22045e-16 2.22045e-16 GW_02_XIU: 5 1.11022e-16 1.11022e-16 CN_GEG_03_XIU: 8 -1.04528e-16 1.04528e-16 EXACT 0 N = 4 ALPHA = 0.5 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 8.32667e-17 8.32667e-17 GW_02_XIU: 5 8.32667e-17 8.32667e-17 CN_GEG_03_XIU: 8 -3.76855e-17 3.76855e-17 EXACT 0 N = 4 ALPHA = 1 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.77556e-17 2.77556e-17 GW_02_XIU: 5 2.77556e-17 2.77556e-17 CN_GEG_03_XIU: 8 -1.09493e-17 1.09493e-17 EXACT 0 N = 4 ALPHA = 1.5 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.77556e-17 2.77556e-17 GW_02_XIU: 5 2.77556e-17 2.77556e-17 CN_GEG_03_XIU: 8 -5.78088e-18 5.78088e-18 EXACT 0 N = 4 ALPHA = -0.5 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 48.7045 2.13163e-14 GW_02_XIU: 5 48.7045 2.34479e-13 CN_GEG_03_XIU: 8 48.7045 2.84217e-14 EXACT 48.7045 N = 4 ALPHA = 0 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 5.33333 0 GW_02_XIU: 5 5.33333 3.55271e-15 CN_GEG_03_XIU: 8 5.33333 2.66454e-15 EXACT 5.33333 N = 4 ALPHA = 0.5 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 1.52202 8.88178e-16 GW_02_XIU: 5 1.52202 5.10703e-15 CN_GEG_03_XIU: 8 1.52202 1.33227e-15 EXACT 1.52202 N = 4 ALPHA = 1 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.632099 1.11022e-16 GW_02_XIU: 5 0.632099 1.11022e-16 CN_GEG_03_XIU: 8 0.632099 2.22045e-16 EXACT 0.632099 N = 4 ALPHA = 1.5 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.32105 5.55112e-17 GW_02_XIU: 5 0.32105 9.99201e-16 CN_GEG_03_XIU: 8 0.32105 0 EXACT 0.32105 N = 5 ALPHA = -0.5 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 306.02 0 CN_GEG_02_XIU: 6 306.02 0 GW_02_XIU: 6 306.02 1.93268e-12 CN_GEG_03_XIU: 10 306.02 0 EXACT 306.02 N = 5 ALPHA = 0 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 32 0 CN_GEG_02_XIU: 6 32 3.55271e-15 GW_02_XIU: 6 32 2.13163e-14 CN_GEG_03_XIU: 10 32 3.55271e-15 EXACT 32 N = 5 ALPHA = 0.5 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 9.56312 0 CN_GEG_02_XIU: 6 9.56312 0 GW_02_XIU: 6 9.56312 4.79616e-14 CN_GEG_03_XIU: 10 9.56312 1.77636e-15 EXACT 9.56312 N = 5 ALPHA = 1 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 4.21399 0 CN_GEG_02_XIU: 6 4.21399 0 GW_02_XIU: 6 4.21399 0 CN_GEG_03_XIU: 10 4.21399 8.88178e-16 EXACT 4.21399 N = 5 ALPHA = 1.5 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 2.26937 4.44089e-16 CN_GEG_02_XIU: 6 2.26937 4.44089e-16 GW_02_XIU: 6 2.26937 8.88178e-15 CN_GEG_03_XIU: 10 2.26937 0 EXACT 2.26937 N = 5 ALPHA = -0.5 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_GEG_03_XIU: 10 0 0 EXACT 0 N = 5 ALPHA = 0 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_GEG_03_XIU: 10 0 0 EXACT 0 N = 5 ALPHA = 0.5 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_GEG_03_XIU: 10 0 0 EXACT 0 N = 5 ALPHA = 1 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_GEG_03_XIU: 10 0 0 EXACT 0 N = 5 ALPHA = 1.5 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_GEG_03_XIU: 10 0 0 EXACT 0 N = 5 ALPHA = -0.5 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 1.77636e-14 1.77636e-14 GW_02_XIU: 6 1.77636e-14 1.77636e-14 CN_GEG_03_XIU: 10 -3.89893e-16 3.89893e-16 EXACT 0 N = 5 ALPHA = 0 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 6.66134e-16 6.66134e-16 GW_02_XIU: 6 6.66134e-16 6.66134e-16 CN_GEG_03_XIU: 10 1.43618e-16 1.43618e-16 EXACT 0 N = 5 ALPHA = 0.5 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 2.22045e-16 2.22045e-16 GW_02_XIU: 6 2.22045e-16 2.22045e-16 CN_GEG_03_XIU: 10 -3.38477e-17 3.38477e-17 EXACT 0 N = 5 ALPHA = 1 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 8.32667e-17 8.32667e-17 GW_02_XIU: 6 8.32667e-17 8.32667e-17 CN_GEG_03_XIU: 10 1.42259e-17 1.42259e-17 EXACT 0 N = 5 ALPHA = 1.5 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 4.85723e-17 4.85723e-17 GW_02_XIU: 6 4.85723e-17 4.85723e-17 CN_GEG_03_XIU: 10 9.22771e-18 9.22771e-18 EXACT 0 N = 5 ALPHA = -0.5 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 153.01 0 GW_02_XIU: 6 153.01 9.66338e-13 CN_GEG_03_XIU: 10 153.01 8.52651e-14 EXACT 153.01 N = 5 ALPHA = 0 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 10.6667 3.55271e-15 GW_02_XIU: 6 10.6667 5.32907e-15 CN_GEG_03_XIU: 10 10.6667 5.32907e-15 EXACT 10.6667 N = 5 ALPHA = 0.5 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 2.39078 2.66454e-15 GW_02_XIU: 6 2.39078 9.76996e-15 CN_GEG_03_XIU: 10 2.39078 2.22045e-15 EXACT 2.39078 N = 5 ALPHA = 1 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.842798 2.22045e-16 GW_02_XIU: 6 0.842798 2.22045e-16 CN_GEG_03_XIU: 10 0.842798 0 EXACT 0.842798 N = 5 ALPHA = 1.5 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.378229 0 GW_02_XIU: 6 0.378229 1.66533e-15 CN_GEG_03_XIU: 10 0.378229 0 EXACT 0.378229 N = 6 ALPHA = -0.5 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 961.389 0 CN_GEG_02_XIU: 7 961.389 1.13687e-13 GW_02_XIU: 7 961.389 7.27596e-12 CN_GEG_03_XIU: 12 961.389 1.13687e-13 EXACT 961.389 N = 6 ALPHA = 0 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 64 0 CN_GEG_02_XIU: 7 64 1.42109e-14 GW_02_XIU: 7 64 3.55271e-14 CN_GEG_03_XIU: 12 64 0 EXACT 64 N = 6 ALPHA = 0.5 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 15.0217 1.77636e-15 CN_GEG_02_XIU: 7 15.0217 1.77636e-15 GW_02_XIU: 7 15.0217 9.05942e-14 CN_GEG_03_XIU: 12 15.0217 3.55271e-15 EXACT 15.0217 N = 6 ALPHA = 1 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 5.61866 8.88178e-16 CN_GEG_02_XIU: 7 5.61866 0 GW_02_XIU: 7 5.61866 0 CN_GEG_03_XIU: 12 5.61866 8.88178e-16 EXACT 5.61866 N = 6 ALPHA = 1.5 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_01_1: 1 2.67354 4.44089e-16 CN_GEG_02_XIU: 7 2.67354 0 GW_02_XIU: 7 2.67354 1.28786e-14 CN_GEG_03_XIU: 12 2.67354 0 EXACT 2.67354 N = 6 ALPHA = -0.5 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 7 -3.55271e-14 3.55271e-14 GW_02_XIU: 7 -6.39488e-14 6.39488e-14 CN_GEG_03_XIU: 12 -2.47739e-13 2.47739e-13 EXACT 0 N = 6 ALPHA = 0 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 7 -3.55271e-15 3.55271e-15 GW_02_XIU: 7 -4.44089e-15 4.44089e-15 CN_GEG_03_XIU: 12 -1.41424e-14 1.41424e-14 EXACT 0 N = 6 ALPHA = 0.5 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 7 -7.77156e-16 7.77156e-16 GW_02_XIU: 7 -6.66134e-16 6.66134e-16 CN_GEG_03_XIU: 12 -2.61892e-15 2.61892e-15 EXACT 0 N = 6 ALPHA = 1 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 7 -2.498e-16 2.498e-16 GW_02_XIU: 7 -2.498e-16 2.498e-16 CN_GEG_03_XIU: 12 -9.42871e-16 9.42871e-16 EXACT 0 N = 6 ALPHA = 1.5 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0 CN_GEG_02_XIU: 7 -1.249e-16 1.249e-16 GW_02_XIU: 7 -1.11022e-16 1.11022e-16 CN_GEG_03_XIU: 12 -4.06349e-16 4.06349e-16 EXACT 0 N = 6 ALPHA = -0.5 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 2.84217e-14 2.84217e-14 GW_02_XIU: 7 1.42109e-14 1.42109e-14 CN_GEG_03_XIU: 12 -1.25173e-14 1.25173e-14 EXACT 0 N = 6 ALPHA = 0 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 1.33227e-15 1.33227e-15 GW_02_XIU: 7 1.33227e-15 1.33227e-15 CN_GEG_03_XIU: 12 -4.26771e-16 4.26771e-16 EXACT 0 N = 6 ALPHA = 0.5 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 1.11022e-16 1.11022e-16 GW_02_XIU: 7 2.22045e-16 2.22045e-16 CN_GEG_03_XIU: 12 -9.77912e-17 9.77912e-17 EXACT 0 N = 6 ALPHA = 1 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 2.77556e-17 2.77556e-17 GW_02_XIU: 7 2.77556e-17 2.77556e-17 CN_GEG_03_XIU: 12 -3.19947e-17 3.19947e-17 EXACT 0 N = 6 ALPHA = 1.5 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0 0 GW_02_XIU: 7 6.93889e-18 6.93889e-18 CN_GEG_03_XIU: 12 -4.3119e-18 4.3119e-18 EXACT 0 N = 6 ALPHA = -0.5 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 480.695 1.7053e-13 GW_02_XIU: 7 480.695 3.46745e-12 CN_GEG_03_XIU: 12 480.695 2.27374e-13 EXACT 480.695 N = 6 ALPHA = 0 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 21.3333 0 GW_02_XIU: 7 21.3333 1.06581e-14 CN_GEG_03_XIU: 12 21.3333 7.10543e-15 EXACT 21.3333 N = 6 ALPHA = 0.5 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 3.75543 2.22045e-15 GW_02_XIU: 7 3.75543 1.9984e-14 CN_GEG_03_XIU: 12 3.75543 3.10862e-15 EXACT 3.75543 N = 6 ALPHA = 1 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 1.12373 2.22045e-16 GW_02_XIU: 7 1.12373 2.22045e-16 CN_GEG_03_XIU: 12 1.12373 4.44089e-16 EXACT 1.12373 N = 6 ALPHA = 1.5 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.44559 0 GW_02_XIU: 7 0.44559 2.22045e-15 CN_GEG_03_XIU: 12 0.44559 1.11022e-16 EXACT 0.44559 CN_JAC_TESTS Demonstrate the use of quadrature rules for the region CN_JAC, that is, the hypercube [-1,+1]^N, with the weight W(ALPHA,BETA;X) = product ( 1 <= I <= N ) (1-X(I))^ALPHA (1+X(I))^BETA We use the formulas to integrate various monomials of the form X(1)^E(1) * X(2)^E(2) * ... X(N)^E(N) and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 ALPHA = 0 BETA = 0 EXPON = 0 Degree = 0 CN_JAC_01_1: 1 2 0 CN_JAC_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = 1 BETA = 0 EXPON = 0 Degree = 0 CN_JAC_01_1: 1 2 0 CN_JAC_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = 0 BETA = 2 EXPON = 0 Degree = 0 CN_JAC_01_1: 1 2.66667 0 CN_JAC_02_XIU: 2 2.66667 0 GW_02_XIU: 2 2.66667 4.44089e-16 EXACT 2.66667 N = 1 ALPHA = 0.5 BETA = 1.5 EXPON = 0 Degree = 0 CN_JAC_01_1: 1 1.5708 0 CN_JAC_02_XIU: 2 1.5708 0 GW_02_XIU: 2 1.5708 4.44089e-16 EXACT 1.5708 N = 1 ALPHA = 0 BETA = 0 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 EXACT 0 N = 1 ALPHA = 1 BETA = 0 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 -0.666667 0 CN_JAC_02_XIU: 2 -0.666667 1.11022e-16 GW_02_XIU: 2 -0.666667 1.11022e-16 EXACT -0.666667 N = 1 ALPHA = 0 BETA = 2 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 1.33333 0 CN_JAC_02_XIU: 2 1.33333 2.22045e-16 GW_02_XIU: 2 1.33333 0 EXACT 1.33333 N = 1 ALPHA = 0.5 BETA = 1.5 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0.392699 5.55112e-17 CN_JAC_02_XIU: 2 0.392699 5.55112e-17 GW_02_XIU: 2 0.392699 0 EXACT 0.392699 N = 1 ALPHA = 0 BETA = 0 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 0 GW_02_XIU: 2 0.666667 0 EXACT 0.666667 N = 1 ALPHA = 1 BETA = 0 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 2.22045e-16 GW_02_XIU: 2 0.666667 2.22045e-16 EXACT 0.666667 N = 1 ALPHA = 0 BETA = 2 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 1.06667 0 GW_02_XIU: 2 1.06667 2.22045e-16 EXACT 1.06667 N = 1 ALPHA = 0.5 BETA = 1.5 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.392699 0 GW_02_XIU: 2 0.392699 5.55112e-17 EXACT 0.392699 N = 2 ALPHA = 0 BETA = 0 EXPON = 0 0 Degree = 0 CN_JAC_01_1: 1 4 0 CN_JAC_02_XIU: 3 4 0 GW_02_XIU: 3 4 0 EXACT 4 N = 2 ALPHA = 1 BETA = 0 EXPON = 0 0 Degree = 0 CN_JAC_01_1: 1 4 0 CN_JAC_02_XIU: 3 4 0 GW_02_XIU: 3 4 0 EXACT 4 N = 2 ALPHA = 0 BETA = 2 EXPON = 0 0 Degree = 0 CN_JAC_01_1: 1 7.11111 0 CN_JAC_02_XIU: 3 7.11111 0 GW_02_XIU: 3 7.11111 1.77636e-15 EXACT 7.11111 N = 2 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 Degree = 0 CN_JAC_01_1: 1 2.4674 0 CN_JAC_02_XIU: 3 2.4674 0 GW_02_XIU: 3 2.4674 1.33227e-15 EXACT 2.4674 N = 2 ALPHA = 0 BETA = 0 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 3 6.66134e-16 6.66134e-16 GW_02_XIU: 3 6.66134e-16 6.66134e-16 EXACT 0 N = 2 ALPHA = 1 BETA = 0 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 -1.33333 0 CN_JAC_02_XIU: 3 -1.33333 6.66134e-16 GW_02_XIU: 3 -1.33333 6.66134e-16 EXACT -1.33333 N = 2 ALPHA = 0 BETA = 2 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 3.55556 0 CN_JAC_02_XIU: 3 3.55556 4.44089e-16 GW_02_XIU: 3 3.55556 0 EXACT 3.55556 N = 2 ALPHA = 0.5 BETA = 1.5 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0.61685 0 CN_JAC_02_XIU: 3 0.61685 1.11022e-16 GW_02_XIU: 3 0.61685 4.44089e-16 EXACT 0.61685 N = 2 ALPHA = 0 BETA = 0 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 2.77556e-16 2.77556e-16 GW_02_XIU: 3 2.77556e-16 2.77556e-16 EXACT 0 N = 2 ALPHA = 1 BETA = 0 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.444444 0 GW_02_XIU: 3 0.444444 0 EXACT 0.444444 N = 2 ALPHA = 0 BETA = 2 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 1.77778 8.88178e-16 GW_02_XIU: 3 1.77778 2.22045e-16 EXACT 1.77778 N = 2 ALPHA = 0.5 BETA = 1.5 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.154213 1.38778e-16 GW_02_XIU: 3 0.154213 2.22045e-16 EXACT 0.154213 N = 2 ALPHA = 0 BETA = 0 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 2.22045e-16 GW_02_XIU: 3 1.33333 2.22045e-16 EXACT 1.33333 N = 2 ALPHA = 1 BETA = 0 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 2.22045e-16 GW_02_XIU: 3 1.33333 2.22045e-16 EXACT 1.33333 N = 2 ALPHA = 0 BETA = 2 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 2.84444 0 GW_02_XIU: 3 2.84444 8.88178e-16 EXACT 2.84444 N = 2 ALPHA = 0.5 BETA = 1.5 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 0.61685 1.11022e-16 GW_02_XIU: 3 0.61685 4.44089e-16 EXACT 0.61685 N = 3 ALPHA = 0 BETA = 0 EXPON = 0 0 0 Degree = 0 CN_JAC_01_1: 1 8 0 CN_JAC_02_XIU: 4 8 0 GW_02_XIU: 4 8 0 EXACT 8 N = 3 ALPHA = 1 BETA = 0 EXPON = 0 0 0 Degree = 0 CN_JAC_01_1: 1 8 0 CN_JAC_02_XIU: 4 8 0 GW_02_XIU: 4 8 0 EXACT 8 N = 3 ALPHA = 0 BETA = 2 EXPON = 0 0 0 Degree = 0 CN_JAC_01_1: 1 18.963 0 CN_JAC_02_XIU: 4 18.963 0 GW_02_XIU: 4 18.963 7.10543e-15 EXACT 18.963 N = 3 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 Degree = 0 CN_JAC_01_1: 1 3.87578 0 CN_JAC_02_XIU: 4 3.87578 0 GW_02_XIU: 4 3.87578 3.10862e-15 EXACT 3.87578 N = 3 ALPHA = 0 BETA = 0 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 EXACT 0 N = 3 ALPHA = 1 BETA = 0 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 -2.66667 0 CN_JAC_02_XIU: 4 -2.66667 4.44089e-16 GW_02_XIU: 4 -2.66667 4.44089e-16 EXACT -2.66667 N = 3 ALPHA = 0 BETA = 2 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 9.48148 0 CN_JAC_02_XIU: 4 9.48148 1.77636e-15 GW_02_XIU: 4 9.48148 1.77636e-15 EXACT 9.48148 N = 3 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.968946 1.11022e-16 CN_JAC_02_XIU: 4 0.968946 2.22045e-16 GW_02_XIU: 4 0.968946 7.77156e-16 EXACT 0.968946 N = 3 ALPHA = 0 BETA = 0 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 1.63286e-16 1.63286e-16 GW_02_XIU: 4 1.63286e-16 1.63286e-16 EXACT 0 N = 3 ALPHA = 1 BETA = 0 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.888889 2.22045e-16 GW_02_XIU: 4 0.888889 2.22045e-16 EXACT 0.888889 N = 3 ALPHA = 0 BETA = 2 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 4.74074 1.77636e-15 GW_02_XIU: 4 4.74074 0 EXACT 4.74074 N = 3 ALPHA = 0.5 BETA = 1.5 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.242237 5.55112e-17 GW_02_XIU: 4 0.242237 2.77556e-16 EXACT 0.242237 N = 3 ALPHA = 0 BETA = 0 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 0 GW_02_XIU: 4 2.66667 0 EXACT 2.66667 N = 3 ALPHA = 1 BETA = 0 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 8.88178e-16 GW_02_XIU: 4 2.66667 8.88178e-16 EXACT 2.66667 N = 3 ALPHA = 0 BETA = 2 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 7.58519 8.88178e-16 GW_02_XIU: 4 7.58519 3.55271e-15 EXACT 7.58519 N = 3 ALPHA = 0.5 BETA = 1.5 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 0.968946 1.11022e-16 GW_02_XIU: 4 0.968946 8.88178e-16 EXACT 0.968946 N = 4 ALPHA = 0 BETA = 0 EXPON = 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 16 0 CN_JAC_02_XIU: 5 16 0 GW_02_XIU: 5 16 0 EXACT 16 N = 4 ALPHA = 1 BETA = 0 EXPON = 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 16 0 CN_JAC_02_XIU: 5 16 0 GW_02_XIU: 5 16 0 EXACT 16 N = 4 ALPHA = 0 BETA = 2 EXPON = 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 50.5679 0 CN_JAC_02_XIU: 5 50.5679 0 GW_02_XIU: 5 50.5679 2.13163e-14 EXACT 50.5679 N = 4 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 6.08807 0 CN_JAC_02_XIU: 5 6.08807 8.88178e-16 GW_02_XIU: 5 6.08807 7.10543e-15 EXACT 6.08807 N = 4 ALPHA = 0 BETA = 0 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 5 6.66134e-16 6.66134e-16 GW_02_XIU: 5 6.66134e-16 6.66134e-16 EXACT 0 N = 4 ALPHA = 1 BETA = 0 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -5.33333 0 CN_JAC_02_XIU: 5 -5.33333 8.88178e-16 GW_02_XIU: 5 -5.33333 8.88178e-16 EXACT -5.33333 N = 4 ALPHA = 0 BETA = 2 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 25.284 0 CN_JAC_02_XIU: 5 25.284 7.10543e-15 GW_02_XIU: 5 25.284 7.10543e-15 EXACT 25.284 N = 4 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 1.52202 2.22045e-16 CN_JAC_02_XIU: 5 1.52202 0 GW_02_XIU: 5 1.52202 1.77636e-15 EXACT 1.52202 N = 4 ALPHA = 0 BETA = 0 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 2.22045e-16 2.22045e-16 GW_02_XIU: 5 2.22045e-16 2.22045e-16 EXACT 0 N = 4 ALPHA = 1 BETA = 0 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.77778 0 GW_02_XIU: 5 1.77778 0 EXACT 1.77778 N = 4 ALPHA = 0 BETA = 2 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 12.642 3.55271e-15 GW_02_XIU: 5 12.642 0 EXACT 12.642 N = 4 ALPHA = 0.5 BETA = 1.5 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 0.380504 1.66533e-16 GW_02_XIU: 5 0.380504 6.10623e-16 EXACT 0.380504 N = 4 ALPHA = 0 BETA = 0 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 0 GW_02_XIU: 5 5.33333 0 EXACT 5.33333 N = 4 ALPHA = 1 BETA = 0 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 8.88178e-16 GW_02_XIU: 5 5.33333 8.88178e-16 EXACT 5.33333 N = 4 ALPHA = 0 BETA = 2 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 20.2272 3.55271e-15 GW_02_XIU: 5 20.2272 1.06581e-14 EXACT 20.2272 N = 4 ALPHA = 0.5 BETA = 1.5 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.52202 0 GW_02_XIU: 5 1.52202 1.77636e-15 EXACT 1.52202 N = 5 ALPHA = 0 BETA = 0 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 32 0 CN_JAC_02_XIU: 6 32 3.55271e-15 GW_02_XIU: 6 32 3.55271e-15 EXACT 32 N = 5 ALPHA = 1 BETA = 0 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 32 0 CN_JAC_02_XIU: 6 32 3.55271e-15 GW_02_XIU: 6 32 3.55271e-15 EXACT 32 N = 5 ALPHA = 0 BETA = 2 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 134.848 0 CN_JAC_02_XIU: 6 134.848 0 GW_02_XIU: 6 134.848 8.52651e-14 EXACT 134.848 N = 5 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 9.56312 0 CN_JAC_02_XIU: 6 9.56312 0 GW_02_XIU: 6 9.56312 1.42109e-14 EXACT 9.56312 N = 5 ALPHA = 0 BETA = 0 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 EXACT 0 N = 5 ALPHA = 1 BETA = 0 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -10.6667 0 CN_JAC_02_XIU: 6 -10.6667 1.77636e-15 GW_02_XIU: 6 -10.6667 1.77636e-15 EXACT -10.6667 N = 5 ALPHA = 0 BETA = 2 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 67.4239 0 CN_JAC_02_XIU: 6 67.4239 1.42109e-14 GW_02_XIU: 6 67.4239 2.84217e-14 EXACT 67.4239 N = 5 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 2.39078 0 CN_JAC_02_XIU: 6 2.39078 0 GW_02_XIU: 6 2.39078 2.66454e-15 EXACT 2.39078 N = 5 ALPHA = 0 BETA = 0 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 6.66134e-16 6.66134e-16 GW_02_XIU: 6 6.66134e-16 6.66134e-16 EXACT 0 N = 5 ALPHA = 1 BETA = 0 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 3.55556 4.44089e-16 GW_02_XIU: 6 3.55556 4.44089e-16 EXACT 3.55556 N = 5 ALPHA = 0 BETA = 2 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 33.7119 2.13163e-14 GW_02_XIU: 6 33.7119 0 EXACT 33.7119 N = 5 ALPHA = 0.5 BETA = 1.5 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 0.597695 1.11022e-16 GW_02_XIU: 6 0.597695 9.99201e-16 EXACT 0.597695 N = 5 ALPHA = 0 BETA = 0 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 3.55271e-15 GW_02_XIU: 6 10.6667 3.55271e-15 EXACT 10.6667 N = 5 ALPHA = 1 BETA = 0 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 1.77636e-15 GW_02_XIU: 6 10.6667 1.77636e-15 EXACT 10.6667 N = 5 ALPHA = 0 BETA = 2 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 53.9391 0 GW_02_XIU: 6 53.9391 3.55271e-14 EXACT 53.9391 N = 5 ALPHA = 0.5 BETA = 1.5 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 2.39078 4.44089e-16 GW_02_XIU: 6 2.39078 3.9968e-15 EXACT 2.39078 N = 6 ALPHA = 0 BETA = 0 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 64 0 CN_JAC_02_XIU: 7 64 1.42109e-14 GW_02_XIU: 7 64 1.42109e-14 EXACT 64 N = 6 ALPHA = 1 BETA = 0 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 64 0 CN_JAC_02_XIU: 7 64 1.42109e-14 GW_02_XIU: 7 64 1.42109e-14 EXACT 64 N = 6 ALPHA = 0 BETA = 2 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 359.594 0 CN_JAC_02_XIU: 7 359.594 0 GW_02_XIU: 7 359.594 2.84217e-13 EXACT 359.594 N = 6 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_01_1: 1 15.0217 1.77636e-15 CN_JAC_02_XIU: 7 15.0217 1.77636e-15 GW_02_XIU: 7 15.0217 2.66454e-14 EXACT 15.0217 N = 6 ALPHA = 0 BETA = 0 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0 CN_JAC_02_XIU: 7 -3.55271e-15 3.55271e-15 GW_02_XIU: 7 -3.55271e-15 3.55271e-15 EXACT 0 N = 6 ALPHA = 1 BETA = 0 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -21.3333 0 CN_JAC_02_XIU: 7 -21.3333 3.55271e-15 GW_02_XIU: 7 -21.3333 3.55271e-15 EXACT -21.3333 N = 6 ALPHA = 0 BETA = 2 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 179.797 0 CN_JAC_02_XIU: 7 179.797 2.84217e-14 GW_02_XIU: 7 179.797 1.13687e-13 EXACT 179.797 N = 6 ALPHA = 0.5 BETA = 1.5 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 3.75543 8.88178e-16 CN_JAC_02_XIU: 7 3.75543 8.88178e-16 GW_02_XIU: 7 3.75543 4.88498e-15 EXACT 3.75543 N = 6 ALPHA = 0 BETA = 0 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 1.33227e-15 1.33227e-15 GW_02_XIU: 7 1.33227e-15 1.33227e-15 EXACT 0 N = 6 ALPHA = 1 BETA = 0 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 7.11111 1.77636e-15 GW_02_XIU: 7 7.11111 1.77636e-15 EXACT 7.11111 N = 6 ALPHA = 0 BETA = 2 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 89.8985 1.42109e-14 GW_02_XIU: 7 89.8985 5.68434e-14 EXACT 89.8985 N = 6 ALPHA = 0.5 BETA = 1.5 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 0.938857 2.22045e-16 GW_02_XIU: 7 0.938857 1.55431e-15 EXACT 0.938857 N = 6 ALPHA = 0 BETA = 0 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 0 GW_02_XIU: 7 21.3333 0 EXACT 21.3333 N = 6 ALPHA = 1 BETA = 0 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 3.55271e-15 GW_02_XIU: 7 21.3333 3.55271e-15 EXACT 21.3333 N = 6 ALPHA = 0 BETA = 2 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 143.838 2.84217e-14 GW_02_XIU: 7 143.838 1.42109e-13 EXACT 143.838 N = 6 ALPHA = 0.5 BETA = 1.5 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 3.75543 4.44089e-16 GW_02_XIU: 7 3.75543 5.77316e-15 EXACT 3.75543 CN_LEG_TESTS Demonstrate the use of quadrature rules for the region CN_LEG, that is, the hypercube [-1,+1]^N, with the Legendre weight W(X) = 1. We use the formulas to integrate various monomials of the form X(1)^E(1) * X(2)^E(2) * ... X(N)^E(N) and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 EXPON = 0 Degree = 0 CN_LEG_01_1: 1 2 0 CN_LEG_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 CN_LEG_03_1: 2 2 0 CN_LEG_03_XIU: 2 2 0 EXACT 2 N = 1 EXPON = 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 CN_LEG_03_1: 2 0 0 CN_LEG_03_XIU: 2 0 0 EXACT 0 N = 1 EXPON = 2 Degree = 2 CN_LEG_02_XIU: 2 0.666667 0 GW_02_XIU: 2 0.666667 0 CN_LEG_03_1: 2 0.666667 2.22045e-16 CN_LEG_03_XIU: 2 0.666667 2.22045e-16 EXACT 0.666667 N = 1 EXPON = 3 Degree = 3 CN_LEG_03_1: 2 0 0 CN_LEG_03_XIU: 2 0 0 EXACT 0 N = 1 EXPON = 4 Degree = 4 EXACT 0.4 N = 2 EXPON = 0 0 Degree = 0 CN_LEG_01_1: 1 4 0 CN_LEG_02_XIU: 3 4 0 GW_02_XIU: 3 4 0 CN_LEG_03_1: 4 4 0 CN_LEG_03_XIU: 4 4 0 CN_LEG_05_2: 9 4 0 EXACT 4 N = 2 EXPON = 0 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 3 6.66134e-16 6.66134e-16 GW_02_XIU: 3 6.66134e-16 6.66134e-16 CN_LEG_03_1: 4 -8.89617e-17 8.89617e-17 CN_LEG_03_XIU: 4 -8.89617e-17 8.89617e-17 CN_LEG_05_2: 9 0 0 EXACT 0 N = 2 EXPON = 1 1 Degree = 2 CN_LEG_02_XIU: 3 2.77556e-16 2.77556e-16 GW_02_XIU: 3 2.77556e-16 2.77556e-16 CN_LEG_03_1: 4 -8.16431e-17 8.16431e-17 CN_LEG_03_XIU: 4 -8.16431e-17 8.16431e-17 CN_LEG_05_2: 9 0 0 EXACT 0 N = 2 EXPON = 2 0 Degree = 2 CN_LEG_02_XIU: 3 1.33333 2.22045e-16 GW_02_XIU: 3 1.33333 2.22045e-16 CN_LEG_03_1: 4 1.33333 4.44089e-16 CN_LEG_03_XIU: 4 1.33333 4.44089e-16 CN_LEG_05_2: 9 1.33333 2.22045e-16 EXACT 1.33333 N = 2 EXPON = 3 0 Degree = 3 CN_LEG_03_1: 4 0 0 CN_LEG_03_XIU: 4 0 0 CN_LEG_05_2: 9 0 0 EXACT 0 N = 2 EXPON = 0 4 Degree = 4 CN_LEG_05_2: 9 0.8 2.22045e-16 EXACT 0.8 N = 2 EXPON = 3 2 Degree = 5 CN_LEG_05_2: 9 0 0 EXACT 0 N = 3 EXPON = 0 0 0 Degree = 0 CN_LEG_01_1: 1 8 0 CN_LEG_02_XIU: 4 8 0 GW_02_XIU: 4 8 0 CN_LEG_03_1: 6 8 8.88178e-16 CN_LEG_03_XIU: 6 8 8.88178e-16 CN_LEG_05_2: 19 8 0 EXACT 8 N = 3 EXPON = 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 4 0 0 GW_02_XIU: 4 0 0 CN_LEG_03_1: 6 0 0 CN_LEG_03_XIU: 6 0 0 CN_LEG_05_2: 19 0 0 EXACT 0 N = 3 EXPON = 1 1 0 Degree = 2 CN_LEG_02_XIU: 4 1.63286e-16 1.63286e-16 GW_02_XIU: 4 1.63286e-16 1.63286e-16 CN_LEG_03_1: 6 1.15352e-16 1.15352e-16 CN_LEG_03_XIU: 6 1.15352e-16 1.15352e-16 CN_LEG_05_2: 19 0 0 EXACT 0 N = 3 EXPON = 2 0 0 Degree = 2 CN_LEG_02_XIU: 4 2.66667 0 GW_02_XIU: 4 2.66667 0 CN_LEG_03_1: 6 2.66667 1.33227e-15 CN_LEG_03_XIU: 6 2.66667 1.33227e-15 CN_LEG_05_2: 19 2.66667 4.44089e-16 EXACT 2.66667 N = 3 EXPON = 3 0 0 Degree = 3 CN_LEG_03_1: 6 -1.11022e-16 1.11022e-16 CN_LEG_03_XIU: 6 -1.11022e-16 1.11022e-16 CN_LEG_05_2: 19 0 0 EXACT 0 N = 3 EXPON = 0 0 4 Degree = 4 CN_LEG_05_2: 19 1.6 4.44089e-16 EXACT 1.6 N = 3 EXPON = 3 2 0 Degree = 5 CN_LEG_05_2: 19 0 0 EXACT 0 N = 4 EXPON = 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 16 0 CN_LEG_02_XIU: 5 16 0 GW_02_XIU: 5 16 0 CN_LEG_03_1: 8 16 0 CN_LEG_03_XIU: 8 16 0 CN_LEG_05_1(1): 22 16 1.06581e-14 CN_LEG_05_1(2): 22 16 1.77636e-14 CN_LEG_05_2: 33 16 3.55271e-15 EXACT 16 N = 4 EXPON = 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 5 6.66134e-16 6.66134e-16 GW_02_XIU: 5 6.66134e-16 6.66134e-16 CN_LEG_03_1: 8 -2.53217e-15 2.53217e-15 CN_LEG_03_XIU: 8 -2.53217e-15 2.53217e-15 CN_LEG_05_1(1): 22 0 0 CN_LEG_05_1(2): 22 8.32667e-17 8.32667e-17 CN_LEG_05_2: 33 0 0 EXACT 0 N = 4 EXPON = 1 1 0 0 Degree = 2 CN_LEG_02_XIU: 5 2.22045e-16 2.22045e-16 GW_02_XIU: 5 2.22045e-16 2.22045e-16 CN_LEG_03_1: 8 -1.04528e-16 1.04528e-16 CN_LEG_03_XIU: 8 -1.04528e-16 1.04528e-16 CN_LEG_05_1(1): 22 -1.15186e-15 1.15186e-15 CN_LEG_05_1(2): 22 -1.94289e-16 1.94289e-16 CN_LEG_05_2: 33 0 0 EXACT 0 N = 4 EXPON = 2 0 0 0 Degree = 2 CN_LEG_02_XIU: 5 5.33333 0 GW_02_XIU: 5 5.33333 0 CN_LEG_03_1: 8 5.33333 2.66454e-15 CN_LEG_03_XIU: 8 5.33333 2.66454e-15 CN_LEG_05_1(1): 22 5.33333 4.44089e-15 CN_LEG_05_1(2): 22 5.33333 4.44089e-15 CN_LEG_05_2: 33 5.33333 8.88178e-16 EXACT 5.33333 N = 4 EXPON = 3 0 0 0 Degree = 3 CN_LEG_03_1: 8 0 0 CN_LEG_03_XIU: 8 0 0 CN_LEG_05_1(1): 22 1.07553e-16 1.07553e-16 CN_LEG_05_1(2): 22 1.11022e-16 1.11022e-16 CN_LEG_05_2: 33 0 0 EXACT 0 N = 4 EXPON = 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 22 3.2 3.10862e-15 CN_LEG_05_1(2): 22 3.2 6.21725e-15 CN_LEG_05_2: 33 3.2 8.88178e-16 EXACT 3.2 N = 4 EXPON = 3 2 0 0 Degree = 5 CN_LEG_05_1(1): 22 8.45678e-18 8.45678e-18 CN_LEG_05_1(2): 22 0 0 CN_LEG_05_2: 33 0 0 EXACT 0 N = 5 EXPON = 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 32 0 CN_LEG_02_XIU: 6 32 3.55271e-15 GW_02_XIU: 6 32 3.55271e-15 CN_LEG_03_1: 10 32 3.55271e-15 CN_LEG_03_XIU: 10 32 3.55271e-15 CN_LEG_05_1(1): 32 32 4.26326e-14 CN_LEG_05_1(2): 32 32 5.68434e-14 CN_LEG_05_2: 51 32 3.19744e-14 EXACT 32 N = 5 EXPON = 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 6 0 0 GW_02_XIU: 6 0 0 CN_LEG_03_1: 10 0 0 CN_LEG_03_XIU: 10 0 0 CN_LEG_05_1(1): 32 -1.11022e-16 1.11022e-16 CN_LEG_05_1(2): 32 3.33067e-16 3.33067e-16 CN_LEG_05_2: 51 0 0 EXACT 0 N = 5 EXPON = 1 1 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 6.66134e-16 6.66134e-16 GW_02_XIU: 6 6.66134e-16 6.66134e-16 CN_LEG_03_1: 10 1.43618e-16 1.43618e-16 CN_LEG_03_XIU: 10 1.43618e-16 1.43618e-16 CN_LEG_05_1(1): 32 9.99201e-16 9.99201e-16 CN_LEG_05_1(2): 32 -6.93889e-17 6.93889e-17 CN_LEG_05_2: 51 0 0 EXACT 0 N = 5 EXPON = 2 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 10.6667 3.55271e-15 GW_02_XIU: 6 10.6667 3.55271e-15 CN_LEG_03_1: 10 10.6667 5.32907e-15 CN_LEG_03_XIU: 10 10.6667 5.32907e-15 CN_LEG_05_1(1): 32 10.6667 1.06581e-14 CN_LEG_05_1(2): 32 10.6667 0 CN_LEG_05_2: 51 10.6667 1.77636e-15 EXACT 10.6667 N = 5 EXPON = 3 0 0 0 0 Degree = 3 CN_LEG_03_1: 10 2.22045e-16 2.22045e-16 CN_LEG_03_XIU: 10 2.22045e-16 2.22045e-16 CN_LEG_05_1(1): 32 -4.44089e-16 4.44089e-16 CN_LEG_05_1(2): 32 1.66533e-16 1.66533e-16 CN_LEG_05_2: 51 0 0 EXACT 0 N = 5 EXPON = 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 32 6.4 7.99361e-15 CN_LEG_05_1(2): 32 6.4 1.33227e-14 CN_LEG_05_2: 51 6.4 1.77636e-15 EXACT 6.4 N = 5 EXPON = 3 2 0 0 0 Degree = 5 CN_LEG_05_1(1): 32 1.66533e-16 1.66533e-16 CN_LEG_05_1(2): 32 -1.09288e-16 1.09288e-16 CN_LEG_05_2: 51 0 0 EXACT 0 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 64 0 CN_LEG_02_XIU: 7 64 1.42109e-14 GW_02_XIU: 7 64 1.42109e-14 CN_LEG_03_1: 12 64 0 CN_LEG_03_XIU: 12 64 0 CN_LEG_05_1(1): 44 64 2.84217e-14 CN_LEG_05_2: 73 64 9.9476e-14 EXACT 64 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0 CN_LEG_02_XIU: 7 -3.55271e-15 3.55271e-15 GW_02_XIU: 7 -3.55271e-15 3.55271e-15 CN_LEG_03_1: 12 -1.41424e-14 1.41424e-14 CN_LEG_03_XIU: 12 -1.41424e-14 1.41424e-14 CN_LEG_05_1(1): 44 6.66134e-16 6.66134e-16 CN_LEG_05_2: 73 0 0 EXACT 0 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 1.33227e-15 1.33227e-15 GW_02_XIU: 7 1.33227e-15 1.33227e-15 CN_LEG_03_1: 12 -4.26771e-16 4.26771e-16 CN_LEG_03_XIU: 12 -4.26771e-16 4.26771e-16 CN_LEG_05_1(1): 44 0 0 CN_LEG_05_2: 73 0 0 EXACT 0 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 21.3333 0 GW_02_XIU: 7 21.3333 0 CN_LEG_03_1: 12 21.3333 7.10543e-15 CN_LEG_03_XIU: 12 21.3333 7.10543e-15 CN_LEG_05_1(1): 44 21.3333 2.13163e-14 CN_LEG_05_2: 73 21.3333 7.10543e-15 EXACT 21.3333 N = 6 EXPON = 3 0 0 0 0 0 Degree = 3 CN_LEG_03_1: 12 -3.55271e-15 3.55271e-15 CN_LEG_03_XIU: 12 -3.55271e-15 3.55271e-15 CN_LEG_05_1(1): 44 1.11022e-16 1.11022e-16 CN_LEG_05_2: 73 0 0 EXACT 0 N = 6 EXPON = 0 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 44 12.8 2.13163e-14 CN_LEG_05_2: 73 12.8 7.10543e-15 EXACT 12.8 N = 6 EXPON = 3 2 0 0 0 0 Degree = 5 CN_LEG_05_1(1): 44 0 0 CN_LEG_05_2: 73 0 0 EXACT 0 EN_HER_TESTS Demonstrate the use of Stroud rules for the region EN_HER, that is, all of N-dimensional space, with the weight function W(X) = exp ( - X1^2 - X2^2 ... -XN^2 ) We use the formulas to integrate various monomials of the form X1^ALPHA1 * X2^ALPHA2 * ... XN^ALPHAN and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 EXPON = 0 Degree = 0 EN_HER_01_1: 1 1.77245 2.22045e-16 EN_HER_02_XIU: 2 1.77245 2.22045e-16 GW_02_XIU: 2 1.77245 2.22045e-16 EN_HER_03_1: 2 1.77245 2.22045e-16 EN_HER_03_XIU: 2 1.77245 2.22045e-16 EN_HER_05_2: 3 1.77245 2.22045e-16 EXACT 1.77245 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 1.11022e-16 GW_02_XIU: 2 0.886227 1.11022e-16 EN_HER_03_1: 2 0.886227 1.11022e-16 EN_HER_03_XIU: 2 0.886227 3.33067e-16 EN_HER_05_2: 3 0.886227 1.11022e-16 EXACT 0.886227 N = 1 EXPON = 0 Degree = 0 EN_HER_01_1: 1 1.77245 2.22045e-16 EN_HER_02_XIU: 2 1.77245 2.22045e-16 GW_02_XIU: 2 1.77245 2.22045e-16 EN_HER_03_1: 2 1.77245 2.22045e-16 EN_HER_03_XIU: 2 1.77245 2.22045e-16 EN_HER_05_2: 3 1.77245 2.22045e-16 EXACT 1.77245 N = 1 EXPON = 1 Degree = 1 EN_HER_01_1: 1 0 0 EN_HER_02_XIU: 2 0 0 GW_02_XIU: 2 0 0 EN_HER_03_1: 2 0 0 EN_HER_03_XIU: 2 0 0 EN_HER_05_2: 3 0 0 EXACT 0 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 1.11022e-16 GW_02_XIU: 2 0.886227 1.11022e-16 EN_HER_03_1: 2 0.886227 1.11022e-16 EN_HER_03_XIU: 2 0.886227 3.33067e-16 EN_HER_05_2: 3 0.886227 1.11022e-16 EXACT 0.886227 N = 2 EXPON = 0 0 Degree = 0 EN_HER_01_1: 1 3.14159 8.88178e-16 EN_HER_02_XIU: 3 3.14159 4.44089e-16 GW_02_XIU: 3 3.14159 4.44089e-16 EN_HER_03_1: 4 3.14159 8.88178e-16 EN_HER_03_XIU: 4 3.14159 8.88178e-16 EN_HER_05_1(1): 8 3.14159 1.77636e-15 EN_HER_05_2: 9 3.14159 1.77636e-15 EXACT 3.14159 N = 2 EXPON = 2 0 Degree = 2 EN_HER_02_XIU: 3 1.5708 6.66134e-16 GW_02_XIU: 3 1.5708 6.66134e-16 EN_HER_03_1: 4 1.5708 4.44089e-16 EN_HER_03_XIU: 4 1.5708 4.44089e-16 EN_HER_05_1(1): 8 1.5708 1.77636e-15 EN_HER_05_2: 9 1.5708 2.22045e-16 EXACT 1.5708 N = 2 EXPON = 0 4 Degree = 4 EN_HER_05_1(1): 8 2.35619 6.66134e-15 EN_HER_05_2: 9 2.35619 0 EXACT 2.35619 N = 2 EXPON = 1 2 Degree = 3 EN_HER_03_1: 4 0 0 EN_HER_03_XIU: 4 -9.61835e-17 9.61835e-17 EN_HER_05_1(1): 8 0 0 EN_HER_05_2: 9 0 0 EXACT 0 N = 2 EXPON = 2 2 Degree = 4 EN_HER_05_1(1): 8 0.785398 1.22125e-15 EN_HER_05_2: 9 0.785398 2.22045e-16 EXACT 0.785398 N = 3 EXPON = 0 0 0 Degree = 0 EN_HER_01_1: 1 5.56833 2.66454e-15 EN_HER_02_XIU: 4 5.56833 2.66454e-15 GW_02_XIU: 4 5.56833 2.66454e-15 EN_HER_03_1: 6 5.56833 2.66454e-15 EN_HER_03_XIU: 6 5.56833 2.66454e-15 EN_HER_05_1(1): 14 5.56833 3.55271e-15 EN_HER_05_1(2): 14 5.56833 3.55271e-15 EN_HER_05_2: 19 5.56833 8.88178e-16 EXACT 5.56833 N = 3 EXPON = 2 0 0 Degree = 2 EN_HER_02_XIU: 4 2.78416 0 GW_02_XIU: 4 2.78416 0 EN_HER_03_1: 6 2.78416 1.77636e-15 EN_HER_03_XIU: 6 2.78416 1.33227e-15 EN_HER_05_1(1): 14 2.78416 2.66454e-15 EN_HER_05_1(2): 14 2.78416 4.44089e-15 EN_HER_05_2: 19 2.78416 1.33227e-15 EXACT 2.78416 N = 3 EXPON = 0 4 0 Degree = 4 EN_HER_05_1(1): 14 4.17625 8.88178e-16 EN_HER_05_1(2): 14 4.17625 1.86517e-14 EN_HER_05_2: 19 4.17625 1.77636e-15 EXACT 4.17625 N = 4 EXPON = 0 0 0 0 Degree = 0 EN_HER_01_1: 1 9.8696 7.10543e-15 EN_HER_02_XIU: 5 9.8696 5.32907e-15 GW_02_XIU: 5 9.8696 7.10543e-15 EN_HER_03_1: 8 9.8696 7.10543e-15 EN_HER_03_XIU: 8 9.8696 7.10543e-15 EN_HER_05_1(1): 22 9.8696 1.77636e-15 EN_HER_05_2: 33 9.8696 7.10543e-15 EXACT 9.8696 N = 4 EXPON = 2 0 0 0 Degree = 2 EN_HER_02_XIU: 5 4.9348 8.88178e-16 GW_02_XIU: 5 4.9348 1.77636e-15 EN_HER_03_1: 8 4.9348 2.66454e-15 EN_HER_03_XIU: 8 4.9348 3.55271e-15 EN_HER_05_1(1): 22 4.9348 1.77636e-15 EN_HER_05_2: 33 4.9348 4.44089e-15 EXACT 4.9348 N = 4 EXPON = 0 4 0 0 Degree = 4 EN_HER_05_1(1): 22 7.4022 1.42109e-14 EN_HER_05_2: 33 7.4022 5.32907e-15 EXACT 7.4022 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 17.4934 1.42109e-14 EN_HER_02_XIU: 6 17.4934 1.42109e-14 GW_02_XIU: 6 17.4934 1.42109e-14 EN_HER_03_1: 10 17.4934 1.42109e-14 EN_HER_03_XIU: 10 17.4934 1.42109e-14 EN_HER_05_1(1): 32 17.4934 7.10543e-15 EN_HER_05_1(2): 32 17.4934 7.10543e-15 EN_HER_05_2: 51 17.4934 2.84217e-14 EXACT 17.4934 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EN_HER_02_XIU: 6 8.74671 1.77636e-15 GW_02_XIU: 6 8.74671 1.77636e-15 EN_HER_03_1: 10 8.74671 5.32907e-15 EN_HER_03_XIU: 10 8.74671 7.10543e-15 EN_HER_05_1(1): 32 8.74671 3.41061e-13 EN_HER_05_1(2): 32 8.74671 3.55271e-14 EN_HER_05_2: 51 8.74671 8.88178e-15 EXACT 8.74671 N = 5 EXPON = 0 4 0 0 0 Degree = 4 EN_HER_05_1(1): 32 13.1201 4.56524e-13 EN_HER_05_1(2): 32 13.1201 8.17124e-14 EN_HER_05_2: 51 13.1201 5.32907e-15 EXACT 13.1201 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 31.0063 3.19744e-14 EN_HER_02_XIU: 7 31.0063 2.84217e-14 GW_02_XIU: 7 31.0063 2.84217e-14 EN_HER_03_1: 12 31.0063 3.19744e-14 EN_HER_03_XIU: 12 31.0063 3.19744e-14 EN_HER_05_1(1): 44 31.0063 2.84217e-14 EN_HER_05_1(2): 44 31.0063 2.84217e-14 EN_HER_05_2: 73 31.0063 1.06581e-14 EXACT 31.0063 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 7 15.5031 1.06581e-14 GW_02_XIU: 7 15.5031 1.06581e-14 EN_HER_03_1: 12 15.5031 1.95399e-14 EN_HER_03_XIU: 12 15.5031 1.59872e-14 EN_HER_05_1(1): 44 15.5031 6.39488e-14 EN_HER_05_1(2): 44 15.5031 3.19744e-14 EN_HER_05_2: 73 15.5031 7.10543e-15 EXACT 15.5031 N = 6 EXPON = 0 4 0 0 0 0 Degree = 4 EN_HER_05_1(1): 44 23.2547 2.30926e-13 EN_HER_05_1(2): 44 23.2547 1.3145e-13 EN_HER_05_2: 73 23.2547 0 EXACT 23.2547 N = 7 EXPON = 0 0 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 54.9572 6.39488e-14 EN_HER_02_XIU: 8 54.9572 5.68434e-14 GW_02_XIU: 8 54.9572 6.39488e-14 EN_HER_03_1: 14 54.9572 8.52651e-14 EN_HER_03_XIU: 14 54.9572 8.52651e-14 EN_HER_05_1(1): 58 54.9572 2.13163e-14 EN_HER_05_2: 99 54.9572 1.7053e-13 EXACT 54.9572 N = 7 EXPON = 2 0 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 8 27.4786 2.13163e-14 GW_02_XIU: 8 27.4786 2.13163e-14 EN_HER_03_1: 14 27.4786 3.19744e-14 EN_HER_03_XIU: 14 27.4786 3.19744e-14 EN_HER_05_1(1): 58 27.4786 1.49214e-13 EN_HER_05_2: 99 27.4786 2.13163e-14 EXACT 27.4786 N = 7 EXPON = 0 4 0 0 0 0 0 Degree = 4 EN_HER_05_1(1): 58 41.2179 4.90274e-13 EN_HER_05_2: 99 41.2179 2.13163e-14 EXACT 41.2179 EPN_GLG_TESTS Demonstrate the use of quadrature rules for the region EPN_GLG, that is, the positive half space [0,+oo)^N, with the weight W(ALPHA;X) = product ( 1 <= I <= N ) X(I)^ALPHA exp ( -X(I) ) We use the formulas to integrate various monomials of the form X(1)^E(1) * X(2)^E(2) * ... X(N)^E(N) and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 ALPHA = -0.5 EXPON = 0 Degree = 0 EPN_GLG_01_1: 1 1.77245 0 EPN_GLG_02_XIU: 2 1.77245 0 GW_02_XIU: 2 1.77245 0 EXACT 1.77245 N = 1 ALPHA = 0 EXPON = 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 2 1 0 GW_02_XIU: 2 1 0 EXACT 1 N = 1 ALPHA = 0.5 EXPON = 0 Degree = 0 EPN_GLG_01_1: 1 0.886227 0 EPN_GLG_02_XIU: 2 0.886227 0 GW_02_XIU: 2 0.886227 0 EXACT 0.886227 N = 1 ALPHA = 1 EXPON = 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 2 1 0 GW_02_XIU: 2 1 0 EXACT 1 N = 1 ALPHA = 2 EXPON = 0 Degree = 0 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = -0.5 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 0.886227 0 EPN_GLG_02_XIU: 2 0.886227 2.22045e-16 GW_02_XIU: 2 0.886227 2.22045e-16 EXACT 0.886227 N = 1 ALPHA = 0 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 2 1 0 GW_02_XIU: 2 1 0 EXACT 1 N = 1 ALPHA = 0.5 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1.32934 0 EPN_GLG_02_XIU: 2 1.32934 0 GW_02_XIU: 2 1.32934 0 EXACT 1.32934 N = 1 ALPHA = 1 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = 2 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 6 0 EPN_GLG_02_XIU: 2 6 0 GW_02_XIU: 2 6 0 EXACT 6 N = 1 ALPHA = -0.5 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 1.32934 0 GW_02_XIU: 2 1.32934 0 EXACT 1.32934 N = 1 ALPHA = 0 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 1 ALPHA = 0.5 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 3.32335 0 GW_02_XIU: 2 3.32335 0 EXACT 3.32335 N = 1 ALPHA = 1 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 6 0 GW_02_XIU: 2 6 0 EXACT 6 N = 1 ALPHA = 2 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 24 7.10543e-15 GW_02_XIU: 2 24 7.10543e-15 EXACT 24 N = 2 ALPHA = -0.5 EXPON = 0 0 Degree = 0 EPN_GLG_01_1: 1 3.14159 0 EPN_GLG_02_XIU: 3 3.14159 0 GW_02_XIU: 3 3.14159 0 EXACT 3.14159 N = 2 ALPHA = 0 EXPON = 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 3 1 0 GW_02_XIU: 3 1 0 EXACT 1 N = 2 ALPHA = 0.5 EXPON = 0 0 Degree = 0 EPN_GLG_01_1: 1 0.785398 0 EPN_GLG_02_XIU: 3 0.785398 0 GW_02_XIU: 3 0.785398 0 EXACT 0.785398 N = 2 ALPHA = 1 EXPON = 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 3 1 0 GW_02_XIU: 3 1 0 EXACT 1 N = 2 ALPHA = 2 EXPON = 0 0 Degree = 0 EPN_GLG_01_1: 1 4 0 EPN_GLG_02_XIU: 3 4 0 GW_02_XIU: 3 4 0 EXACT 4 N = 2 ALPHA = -0.5 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.5708 0 EPN_GLG_02_XIU: 3 1.5708 6.66134e-16 GW_02_XIU: 3 1.5708 6.66134e-16 EXACT 1.5708 N = 2 ALPHA = 0 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 3 1 3.33067e-16 GW_02_XIU: 3 1 3.33067e-16 EXACT 1 N = 2 ALPHA = 0.5 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.1781 2.22045e-16 EPN_GLG_02_XIU: 3 1.1781 0 GW_02_XIU: 3 1.1781 0 EXACT 1.1781 N = 2 ALPHA = 1 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 3 2 4.44089e-16 GW_02_XIU: 3 2 4.44089e-16 EXACT 2 N = 2 ALPHA = 2 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 12 0 EPN_GLG_02_XIU: 3 12 1.77636e-15 GW_02_XIU: 3 12 1.77636e-15 EXACT 12 N = 2 ALPHA = -0.5 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 0.785398 0 GW_02_XIU: 3 0.785398 0 EXACT 0.785398 N = 2 ALPHA = 0 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1 0 GW_02_XIU: 3 1 0 EXACT 1 N = 2 ALPHA = 0.5 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1.76715 4.44089e-16 GW_02_XIU: 3 1.76715 4.44089e-16 EXACT 1.76715 N = 2 ALPHA = 1 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 4 4.44089e-16 GW_02_XIU: 3 4 4.44089e-16 EXACT 4 N = 2 ALPHA = 2 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 36 0 GW_02_XIU: 3 36 0 EXACT 36 N = 2 ALPHA = -0.5 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.35619 8.88178e-16 GW_02_XIU: 3 2.35619 8.88178e-16 EXACT 2.35619 N = 2 ALPHA = 0 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2 8.88178e-16 GW_02_XIU: 3 2 8.88178e-16 EXACT 2 N = 2 ALPHA = 0.5 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.94524 4.44089e-16 GW_02_XIU: 3 2.94524 4.44089e-16 EXACT 2.94524 N = 2 ALPHA = 1 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 6 8.88178e-16 GW_02_XIU: 3 6 8.88178e-16 EXACT 6 N = 2 ALPHA = 2 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 48 0 GW_02_XIU: 3 48 0 EXACT 48 N = 3 ALPHA = -0.5 EXPON = 0 0 0 Degree = 0 EPN_GLG_01_1: 1 5.56833 0 EPN_GLG_02_XIU: 4 5.56833 0 GW_02_XIU: 4 5.56833 0 EXACT 5.56833 N = 3 ALPHA = 0 EXPON = 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 4 1 0 GW_02_XIU: 4 1 0 EXACT 1 N = 3 ALPHA = 0.5 EXPON = 0 0 0 Degree = 0 EPN_GLG_01_1: 1 0.696041 0 EPN_GLG_02_XIU: 4 0.696041 0 GW_02_XIU: 4 0.696041 0 EXACT 0.696041 N = 3 ALPHA = 1 EXPON = 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 4 1 0 GW_02_XIU: 4 1 0 EXACT 1 N = 3 ALPHA = 2 EXPON = 0 0 0 Degree = 0 EPN_GLG_01_1: 1 8 0 EPN_GLG_02_XIU: 4 8 0 GW_02_XIU: 4 8 0 EXACT 8 N = 3 ALPHA = -0.5 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.78416 0 EPN_GLG_02_XIU: 4 2.78416 0 GW_02_XIU: 4 2.78416 0 EXACT 2.78416 N = 3 ALPHA = 0 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 4 1 0 GW_02_XIU: 4 1 0 EXACT 1 N = 3 ALPHA = 0.5 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.04406 0 EPN_GLG_02_XIU: 4 1.04406 0 GW_02_XIU: 4 1.04406 0 EXACT 1.04406 N = 3 ALPHA = 1 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 4 2 0 GW_02_XIU: 4 2 0 EXACT 2 N = 3 ALPHA = 2 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 24 0 EPN_GLG_02_XIU: 4 24 0 GW_02_XIU: 4 24 0 EXACT 24 N = 3 ALPHA = -0.5 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.39208 2.22045e-16 GW_02_XIU: 4 1.39208 2.22045e-16 EXACT 1.39208 N = 3 ALPHA = 0 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1 1.11022e-16 GW_02_XIU: 4 1 1.11022e-16 EXACT 1 N = 3 ALPHA = 0.5 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.56609 4.44089e-16 GW_02_XIU: 4 1.56609 4.44089e-16 EXACT 1.56609 N = 3 ALPHA = 1 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 4 0 GW_02_XIU: 4 4 0 EXACT 4 N = 3 ALPHA = 2 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 72 0 GW_02_XIU: 4 72 0 EXACT 72 N = 3 ALPHA = -0.5 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 4.17625 2.66454e-15 GW_02_XIU: 4 4.17625 2.66454e-15 EXACT 4.17625 N = 3 ALPHA = 0 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2 0 GW_02_XIU: 4 2 0 EXACT 2 N = 3 ALPHA = 0.5 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2.61015 4.44089e-16 GW_02_XIU: 4 2.61015 4.44089e-16 EXACT 2.61015 N = 3 ALPHA = 1 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 6 0 GW_02_XIU: 4 6 0 EXACT 6 N = 3 ALPHA = 2 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 96 2.84217e-14 GW_02_XIU: 4 96 2.84217e-14 EXACT 96 N = 4 ALPHA = -0.5 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 9.8696 1.77636e-15 EPN_GLG_02_XIU: 5 9.8696 1.77636e-15 GW_02_XIU: 5 9.8696 1.77636e-15 EXACT 9.8696 N = 4 ALPHA = 0 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 ALPHA = 0.5 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 0.61685 1.11022e-16 EPN_GLG_02_XIU: 5 0.61685 1.11022e-16 GW_02_XIU: 5 0.61685 1.11022e-16 EXACT 0.61685 N = 4 ALPHA = 1 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 ALPHA = 2 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 16 0 EPN_GLG_02_XIU: 5 16 0 GW_02_XIU: 5 16 0 EXACT 16 N = 4 ALPHA = -0.5 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 4.9348 8.88178e-16 EPN_GLG_02_XIU: 5 4.9348 1.77636e-15 GW_02_XIU: 5 4.9348 1.77636e-15 EXACT 4.9348 N = 4 ALPHA = 0 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 ALPHA = 0.5 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.925275 1.11022e-16 EPN_GLG_02_XIU: 5 0.925275 1.11022e-16 GW_02_XIU: 5 0.925275 1.11022e-16 EXACT 0.925275 N = 4 ALPHA = 1 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 5 2 0 GW_02_XIU: 5 2 0 EXACT 2 N = 4 ALPHA = 2 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 48 0 EPN_GLG_02_XIU: 5 48 0 GW_02_XIU: 5 48 0 EXACT 48 N = 4 ALPHA = -0.5 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.4674 4.44089e-16 GW_02_XIU: 5 2.4674 4.44089e-16 EXACT 2.4674 N = 4 ALPHA = 0 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 ALPHA = 0.5 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1.38791 4.44089e-16 GW_02_XIU: 5 1.38791 4.44089e-16 EXACT 1.38791 N = 4 ALPHA = 1 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 4 0 GW_02_XIU: 5 4 0 EXACT 4 N = 4 ALPHA = 2 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 144 0 GW_02_XIU: 5 144 0 EXACT 144 N = 4 ALPHA = -0.5 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 7.4022 1.77636e-15 GW_02_XIU: 5 7.4022 1.77636e-15 EXACT 7.4022 N = 4 ALPHA = 0 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2 0 GW_02_XIU: 5 2 0 EXACT 2 N = 4 ALPHA = 0.5 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.31319 4.44089e-16 GW_02_XIU: 5 2.31319 4.44089e-16 EXACT 2.31319 N = 4 ALPHA = 1 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 6 0 GW_02_XIU: 5 6 0 EXACT 6 N = 4 ALPHA = 2 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 192 2.84217e-14 GW_02_XIU: 5 192 2.84217e-14 EXACT 192 N = 5 ALPHA = -0.5 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 17.4934 3.55271e-15 EPN_GLG_02_XIU: 6 17.4934 3.55271e-15 GW_02_XIU: 6 17.4934 3.55271e-15 EXACT 17.4934 N = 5 ALPHA = 0 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 6 1 1.11022e-16 GW_02_XIU: 6 1 1.11022e-16 EXACT 1 N = 5 ALPHA = 0.5 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 0.546669 1.11022e-16 EPN_GLG_02_XIU: 6 0.546669 1.11022e-16 GW_02_XIU: 6 0.546669 1.11022e-16 EXACT 0.546669 N = 5 ALPHA = 1 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 6 1 1.11022e-16 GW_02_XIU: 6 1 1.11022e-16 EXACT 1 N = 5 ALPHA = 2 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 32 0 EPN_GLG_02_XIU: 6 32 3.55271e-15 GW_02_XIU: 6 32 3.55271e-15 EXACT 32 N = 5 ALPHA = -0.5 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 8.74671 1.77636e-15 EPN_GLG_02_XIU: 6 8.74671 3.55271e-15 GW_02_XIU: 6 8.74671 3.55271e-15 EXACT 8.74671 N = 5 ALPHA = 0 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 6 1 0 GW_02_XIU: 6 1 0 EXACT 1 N = 5 ALPHA = 0.5 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.820004 1.11022e-16 EPN_GLG_02_XIU: 6 0.820004 1.11022e-16 GW_02_XIU: 6 0.820004 1.11022e-16 EXACT 0.820004 N = 5 ALPHA = 1 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 6 2 0 GW_02_XIU: 6 2 0 EXACT 2 N = 5 ALPHA = 2 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 96 0 EPN_GLG_02_XIU: 6 96 1.42109e-14 GW_02_XIU: 6 96 1.42109e-14 EXACT 96 N = 5 ALPHA = -0.5 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4.37335 8.88178e-16 GW_02_XIU: 6 4.37335 8.88178e-16 EXACT 4.37335 N = 5 ALPHA = 0 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1 1.11022e-16 GW_02_XIU: 6 1 1.11022e-16 EXACT 1 N = 5 ALPHA = 0.5 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1.23001 0 GW_02_XIU: 6 1.23001 0 EXACT 1.23001 N = 5 ALPHA = 1 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4 8.88178e-16 GW_02_XIU: 6 4 8.88178e-16 EXACT 4 N = 5 ALPHA = 2 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 288 0 GW_02_XIU: 6 288 0 EXACT 288 N = 5 ALPHA = -0.5 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 13.1201 5.32907e-15 GW_02_XIU: 6 13.1201 5.32907e-15 EXACT 13.1201 N = 5 ALPHA = 0 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2 0 GW_02_XIU: 6 2 0 EXACT 2 N = 5 ALPHA = 0.5 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2.05001 0 GW_02_XIU: 6 2.05001 0 EXACT 2.05001 N = 5 ALPHA = 1 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 6 0 GW_02_XIU: 6 6 0 EXACT 6 N = 5 ALPHA = 2 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 384 0 GW_02_XIU: 6 384 0 EXACT 384 N = 6 ALPHA = -0.5 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 31.0063 7.10543e-15 EPN_GLG_02_XIU: 7 31.0063 3.55271e-15 GW_02_XIU: 7 31.0063 3.55271e-15 EXACT 31.0063 N = 6 ALPHA = 0 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 7 1 2.22045e-16 GW_02_XIU: 7 1 2.22045e-16 EXACT 1 N = 6 ALPHA = 0.5 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 0.484473 1.11022e-16 EPN_GLG_02_XIU: 7 0.484473 5.55112e-17 GW_02_XIU: 7 0.484473 5.55112e-17 EXACT 0.484473 N = 6 ALPHA = 1 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 7 1 2.22045e-16 GW_02_XIU: 7 1 2.22045e-16 EXACT 1 N = 6 ALPHA = 2 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_01_1: 1 64 0 EPN_GLG_02_XIU: 7 64 1.42109e-14 GW_02_XIU: 7 64 1.42109e-14 EXACT 64 N = 6 ALPHA = -0.5 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 15.5031 3.55271e-15 EPN_GLG_02_XIU: 7 15.5031 3.55271e-15 GW_02_XIU: 7 15.5031 3.55271e-15 EXACT 15.5031 N = 6 ALPHA = 0 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0 EPN_GLG_02_XIU: 7 1 0 GW_02_XIU: 7 1 0 EXACT 1 N = 6 ALPHA = 0.5 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.72671 2.22045e-16 EPN_GLG_02_XIU: 7 0.72671 2.22045e-16 GW_02_XIU: 7 0.72671 2.22045e-16 EXACT 0.72671 N = 6 ALPHA = 1 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0 EPN_GLG_02_XIU: 7 2 0 GW_02_XIU: 7 2 0 EXACT 2 N = 6 ALPHA = 2 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 192 0 EPN_GLG_02_XIU: 7 192 0 GW_02_XIU: 7 192 0 EXACT 192 N = 6 ALPHA = -0.5 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 7.75157 2.66454e-15 GW_02_XIU: 7 7.75157 2.66454e-15 EXACT 7.75157 N = 6 ALPHA = 0 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1 0 GW_02_XIU: 7 1 0 EXACT 1 N = 6 ALPHA = 0.5 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.09006 2.22045e-16 GW_02_XIU: 7 1.09006 2.22045e-16 EXACT 1.09006 N = 6 ALPHA = 1 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 4 4.44089e-16 GW_02_XIU: 7 4 4.44089e-16 EXACT 4 N = 6 ALPHA = 2 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 576 0 GW_02_XIU: 7 576 0 EXACT 576 N = 6 ALPHA = -0.5 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 23.2547 7.10543e-15 GW_02_XIU: 7 23.2547 7.10543e-15 EXACT 23.2547 N = 6 ALPHA = 0 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 2 0 GW_02_XIU: 7 2 0 EXACT 2 N = 6 ALPHA = 0.5 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.81677 2.22045e-16 GW_02_XIU: 7 1.81677 2.22045e-16 EXACT 1.81677 N = 6 ALPHA = 1 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 6 8.88178e-16 GW_02_XIU: 7 6 8.88178e-16 EXACT 6 N = 6 ALPHA = 2 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 768 0 GW_02_XIU: 7 768 0 EXACT 768 EPN_LAG_TESTS Demonstrate the use of quadrature rules for the region EPN_LAG, that is, the positive half space [0,+oo)^N, with the weight W(X) = product ( 1 <= I <= N ) exp ( -X(I) ) We use the formulas to integrate various monomials of the form X(1)^E(1) * X(2)^E(2) * ... X(N)^E(N) and compare to the exact integral. The precision of each formula is known, and we only use a formula if its precision indicates it should be able to produce an exact result. N = 1 EXPON = 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 2 1 0 GW_02_XIU: 2 1 0 EXACT 1 N = 1 EXPON = 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 2 1 0 GW_02_XIU: 2 1 0 EXACT 1 N = 1 EXPON = 2 Degree = 2 EPN_LAG_02_XIU: 2 2 0 GW_02_XIU: 2 2 0 EXACT 2 N = 2 EXPON = 0 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 3 1 0 GW_02_XIU: 3 1 0 EXACT 1 N = 2 EXPON = 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 3 1 3.33067e-16 GW_02_XIU: 3 1 3.33067e-16 EXACT 1 N = 2 EXPON = 1 1 Degree = 2 EPN_LAG_02_XIU: 3 1 0 GW_02_XIU: 3 1 0 EXACT 1 N = 2 EXPON = 2 0 Degree = 2 EPN_LAG_02_XIU: 3 2 8.88178e-16 GW_02_XIU: 3 2 8.88178e-16 EXACT 2 N = 3 EXPON = 0 0 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 4 1 0 GW_02_XIU: 4 1 0 EXACT 1 N = 3 EXPON = 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 4 1 0 GW_02_XIU: 4 1 0 EXACT 1 N = 3 EXPON = 1 1 0 Degree = 2 EPN_LAG_02_XIU: 4 1 1.11022e-16 GW_02_XIU: 4 1 1.11022e-16 EXACT 1 N = 3 EXPON = 2 0 0 Degree = 2 EPN_LAG_02_XIU: 4 2 0 GW_02_XIU: 4 2 0 EXACT 2 N = 4 EXPON = 0 0 0 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 EXPON = 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 EXPON = 1 1 0 0 Degree = 2 EPN_LAG_02_XIU: 5 1 0 GW_02_XIU: 5 1 0 EXACT 1 N = 4 EXPON = 2 0 0 0 Degree = 2 EPN_LAG_02_XIU: 5 2 0 GW_02_XIU: 5 2 0 EXACT 2 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 6 1 1.11022e-16 GW_02_XIU: 6 1 1.11022e-16 EXACT 1 N = 5 EXPON = 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 6 1 0 GW_02_XIU: 6 1 0 EXACT 1 N = 5 EXPON = 1 1 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 1 1.11022e-16 GW_02_XIU: 6 1 1.11022e-16 EXACT 1 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 2 0 GW_02_XIU: 6 2 0 EXACT 2 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 7 1 2.22045e-16 GW_02_XIU: 7 1 2.22045e-16 EXACT 1 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0 EPN_LAG_02_XIU: 7 1 0 GW_02_XIU: 7 1 0 EXACT 1 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 1 0 GW_02_XIU: 7 1 0 EXACT 1 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 2 0 GW_02_XIU: 7 2 0 EXACT 2 GW_TESTS Demonstrate the use of quadrature rules for a Golub Welsch rule defined over some interval and some weight function for which the three term recursion of the orthogonal polynomials is known. Chebyshev1: 3.28987 1 0 3.28987 -0.5 0.866025 3.28987 -0.5 -0.866025 Chebyshev2: 0.822467 0.707107 0 0.822467 -0.353553 0.612372 0.822467 -0.353553 -0.612372 Gegenbauer: ALPHA = 1 0.592593 0.632456 0 0.592593 -0.316228 0.547723 0.592593 -0.316228 -0.547723 Generalized Hermite: ALPHA = 1 0.333333 2 0 0.333333 -1 1.73205 0.333333 -1 -1.73205 Generalized Laguerre: ALPHA = 1 0.333333 -4.44089e-16 2 0.333333 3 0.267949 0.333333 3 3.73205 Hermite (physicist): 1.0472 1 0 1.0472 -0.5 0.866025 1.0472 -0.5 -0.866025 Hermite ( probabilist): 2.0944 1.41421 0 2.0944 -0.707107 1.22474 2.0944 -0.707107 -1.22474 Jacobi: ALPHA = 0.5 BETA = 1.5 0.822467 0.862372 0.25 0.822467 -0.0561862 0.78033 0.822467 -0.0561862 -0.28033 Laguerre: 0.333333 -0.414214 1 0.333333 1.70711 -0.224745 0.333333 1.70711 2.22474 Legendre: 1.33333 0.816497 0 1.33333 -0.408248 0.707107 1.33333 -0.408248 -0.707107 SANDIA_CUBATURE_PRB Normal end of execution. 25 December 2011 02:55:14 PM