16-Jan-2023 06:12:46 sandia_cubature_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sandia_cubature(). 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 = -0.500000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 3.14159 0.000000e+00 CN_GEG_01_1: 1 3.14159 0.000000e+00 CN_GEG_02_XIU: 2 3.14159 0.000000e+00 GW_02_XIU: 2 3.14159 3.996803e-15 CN_GEG_03_XIU: 2 3.14159 0.000000e+00 EXACT: 3.14159 N = 1 ALPHA = 0.000000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 2 0.000000e+00 CN_GEG_01_1: 1 2 0.000000e+00 CN_GEG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 2.220446e-16 CN_GEG_03_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = 0.500000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.5708 0.000000e+00 CN_GEG_01_1: 1 1.5708 0.000000e+00 CN_GEG_02_XIU: 2 1.5708 0.000000e+00 GW_02_XIU: 2 1.5708 1.554312e-15 CN_GEG_03_XIU: 2 1.5708 0.000000e+00 EXACT: 1.5708 N = 1 ALPHA = 1.000000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.33333 0.000000e+00 CN_GEG_01_1: 1 1.33333 0.000000e+00 CN_GEG_02_XIU: 2 1.33333 0.000000e+00 GW_02_XIU: 2 1.33333 0.000000e+00 CN_GEG_03_XIU: 2 1.33333 0.000000e+00 EXACT: 1.33333 N = 1 ALPHA = 1.500000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.1781 0.000000e+00 CN_GEG_01_1: 1 1.1781 0.000000e+00 CN_GEG_02_XIU: 2 1.1781 0.000000e+00 GW_02_XIU: 2 1.1781 6.661338e-16 CN_GEG_03_XIU: 2 1.1781 0.000000e+00 EXACT: 1.1781 N = 1 ALPHA = -0.500000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_GEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = 0.000000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_GEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = 0.500000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_GEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = 1.000000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_GEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = 1.500000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_GEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = -0.500000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 1.5708 6.661338e-16 GW_02_XIU: 2 1.5708 1.332268e-15 CN_GEG_03_XIU: 2 1.5708 1.554312e-15 EXACT: 1.5708 N = 1 ALPHA = 0.000000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.666667 0.000000e+00 GW_02_XIU: 2 0.666667 1.110223e-16 CN_GEG_03_XIU: 2 0.666667 2.220446e-16 EXACT: 0.666667 N = 1 ALPHA = 0.500000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.392699 2.220446e-16 GW_02_XIU: 2 0.392699 1.665335e-16 CN_GEG_03_XIU: 2 0.392699 2.220446e-16 EXACT: 0.392699 N = 1 ALPHA = 1.000000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.266667 5.551115e-17 GW_02_XIU: 2 0.266667 5.551115e-17 CN_GEG_03_XIU: 2 0.266667 5.551115e-17 EXACT: 0.266667 N = 1 ALPHA = 1.500000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.19635 2.775558e-17 GW_02_XIU: 2 0.19635 1.387779e-16 CN_GEG_03_XIU: 2 0.19635 2.775558e-17 EXACT: 0.19635 N = 2 ALPHA = -0.500000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 9.8696 0.000000e+00 CN_GEG_01_1: 1 9.8696 0.000000e+00 CN_GEG_02_XIU: 3 9.8696 0.000000e+00 GW_02_XIU: 3 9.8696 2.486900e-14 CN_GEG_03_XIU: 4 9.8696 0.000000e+00 EXACT: 9.8696 N = 2 ALPHA = 0.000000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 4 0.000000e+00 CN_GEG_01_1: 1 4 0.000000e+00 CN_GEG_02_XIU: 3 4 0.000000e+00 GW_02_XIU: 3 4 8.881784e-16 CN_GEG_03_XIU: 4 4 0.000000e+00 EXACT: 4 N = 2 ALPHA = 0.500000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 2.4674 0.000000e+00 CN_GEG_01_1: 1 2.4674 0.000000e+00 CN_GEG_02_XIU: 3 2.4674 0.000000e+00 GW_02_XIU: 3 2.4674 4.884981e-15 CN_GEG_03_XIU: 4 2.4674 0.000000e+00 EXACT: 2.4674 N = 2 ALPHA = 1.000000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 1.77778 0.000000e+00 CN_GEG_01_1: 1 1.77778 0.000000e+00 CN_GEG_02_XIU: 3 1.77778 0.000000e+00 GW_02_XIU: 3 1.77778 0.000000e+00 CN_GEG_03_XIU: 4 1.77778 0.000000e+00 EXACT: 1.77778 N = 2 ALPHA = 1.500000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 1.38791 0.000000e+00 CN_GEG_01_1: 1 1.38791 0.000000e+00 CN_GEG_02_XIU: 3 1.38791 0.000000e+00 GW_02_XIU: 3 1.38791 1.554312e-15 CN_GEG_03_XIU: 4 1.38791 0.000000e+00 EXACT: 1.38791 N = 2 ALPHA = -0.500000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 3 4.44089e-16 4.440892e-16 GW_02_XIU: 3 8.88178e-16 8.881784e-16 CN_GEG_03_XIU: 4 0 0.000000e+00 EXACT: 0 N = 2 ALPHA = 0.000000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 3 1.11022e-16 1.110223e-16 GW_02_XIU: 3 2.22045e-16 2.220446e-16 CN_GEG_03_XIU: 4 -1.11022e-16 1.110223e-16 EXACT: 0 N = 2 ALPHA = 0.500000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 3 1.11022e-16 1.110223e-16 GW_02_XIU: 3 1.11022e-16 1.110223e-16 CN_GEG_03_XIU: 4 -5.55112e-17 5.551115e-17 EXACT: 0 N = 2 ALPHA = 1.000000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 3 5.55112e-17 5.551115e-17 GW_02_XIU: 3 5.55112e-17 5.551115e-17 CN_GEG_03_XIU: 4 0 0.000000e+00 EXACT: 0 N = 2 ALPHA = 1.500000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 3 2.77556e-17 2.775558e-17 GW_02_XIU: 3 2.77556e-17 2.775558e-17 CN_GEG_03_XIU: 4 -2.77556e-17 2.775558e-17 EXACT: 0 N = 2 ALPHA = -0.500000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 1.77636e-15 1.776357e-15 GW_02_XIU: 3 1.9984e-15 1.998401e-15 CN_GEG_03_XIU: 4 -3.02169e-16 3.021695e-16 EXACT: 0 N = 2 ALPHA = 0.000000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 4.44089e-16 4.440892e-16 GW_02_XIU: 3 4.44089e-16 4.440892e-16 CN_GEG_03_XIU: 4 -8.16431e-17 8.164312e-17 EXACT: 0 N = 2 ALPHA = 0.500000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 2.22045e-16 2.220446e-16 GW_02_XIU: 3 2.22045e-16 2.220446e-16 CN_GEG_03_XIU: 4 -3.77712e-17 3.777119e-17 EXACT: 0 N = 2 ALPHA = 1.000000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 1.11022e-16 1.110223e-16 GW_02_XIU: 3 1.11022e-16 1.110223e-16 CN_GEG_03_XIU: 4 -2.17715e-17 2.177150e-17 EXACT: 0 N = 2 ALPHA = 1.500000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 9.71445e-17 9.714451e-17 GW_02_XIU: 3 9.71445e-17 9.714451e-17 CN_GEG_03_XIU: 4 -1.41642e-17 1.416419e-17 EXACT: 0 N = 2 ALPHA = -0.500000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 4.9348 8.881784e-16 GW_02_XIU: 3 4.9348 1.154632e-14 CN_GEG_03_XIU: 4 4.9348 3.552714e-15 EXACT: 4.9348 N = 2 ALPHA = 0.000000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 1.33333 2.220446e-16 GW_02_XIU: 3 1.33333 0.000000e+00 CN_GEG_03_XIU: 4 1.33333 4.440892e-16 EXACT: 1.33333 N = 2 ALPHA = 0.500000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.61685 5.551115e-16 GW_02_XIU: 3 0.61685 6.661338e-16 CN_GEG_03_XIU: 4 0.61685 4.440892e-16 EXACT: 0.61685 N = 2 ALPHA = 1.000000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.355556 1.110223e-16 GW_02_XIU: 3 0.355556 1.110223e-16 CN_GEG_03_XIU: 4 0.355556 5.551115e-17 EXACT: 0.355556 N = 2 ALPHA = 1.500000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.231319 1.665335e-16 GW_02_XIU: 3 0.231319 4.163336e-16 CN_GEG_03_XIU: 4 0.231319 1.110223e-16 EXACT: 0.231319 N = 3 ALPHA = -0.500000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 31.0063 0.000000e+00 CN_GEG_01_1: 1 31.0063 0.000000e+00 CN_GEG_02_XIU: 4 31.0063 0.000000e+00 GW_02_XIU: 4 31.0063 1.172396e-13 CN_GEG_03_XIU: 6 31.0063 0.000000e+00 EXACT: 31.0063 N = 3 ALPHA = 0.000000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 8 0.000000e+00 CN_GEG_01_1: 1 8 0.000000e+00 CN_GEG_02_XIU: 4 8 0.000000e+00 GW_02_XIU: 4 8 2.664535e-15 CN_GEG_03_XIU: 6 8 0.000000e+00 EXACT: 8 N = 3 ALPHA = 0.500000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 3.87578 0.000000e+00 CN_GEG_01_1: 1 3.87578 0.000000e+00 CN_GEG_02_XIU: 4 3.87578 0.000000e+00 GW_02_XIU: 4 3.87578 1.154632e-14 CN_GEG_03_XIU: 6 3.87578 4.440892e-16 EXACT: 3.87578 N = 3 ALPHA = 1.000000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.37037 4.440892e-16 CN_GEG_01_1: 1 2.37037 4.440892e-16 CN_GEG_02_XIU: 4 2.37037 4.440892e-16 GW_02_XIU: 4 2.37037 4.440892e-16 CN_GEG_03_XIU: 6 2.37037 4.440892e-16 EXACT: 2.37037 N = 3 ALPHA = 1.500000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 1.6351 0.000000e+00 CN_GEG_01_1: 1 1.6351 0.000000e+00 CN_GEG_02_XIU: 4 1.6351 0.000000e+00 GW_02_XIU: 4 1.6351 2.664535e-15 CN_GEG_03_XIU: 6 1.6351 0.000000e+00 EXACT: 1.6351 N = 3 ALPHA = -0.500000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_GEG_03_XIU: 6 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = 0.000000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_GEG_03_XIU: 6 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = 0.500000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_GEG_03_XIU: 6 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = 1.000000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_GEG_03_XIU: 6 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = 1.500000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_GEG_03_XIU: 6 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = -0.500000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 9.49293e-16 9.492934e-16 GW_02_XIU: 4 9.49293e-16 9.492934e-16 CN_GEG_03_XIU: 6 4.44089e-16 4.440892e-16 EXACT: 0 N = 3 ALPHA = 0.000000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 1.63286e-16 1.632862e-16 GW_02_XIU: 4 1.63286e-16 1.632862e-16 CN_GEG_03_XIU: 6 1.66533e-16 1.665335e-16 EXACT: 0 N = 3 ALPHA = 0.500000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 5.93308e-17 5.933084e-17 GW_02_XIU: 4 5.93308e-17 5.933084e-17 CN_GEG_03_XIU: 6 5.55112e-17 5.551115e-17 EXACT: 0 N = 3 ALPHA = 1.000000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 2.90287e-17 2.902866e-17 GW_02_XIU: 4 2.90287e-17 2.902866e-17 CN_GEG_03_XIU: 6 1.38778e-17 1.387779e-17 EXACT: 0 N = 3 ALPHA = 1.500000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 1.66868e-17 1.668680e-17 GW_02_XIU: 4 1.66868e-17 1.668680e-17 CN_GEG_03_XIU: 6 1.38778e-17 1.387779e-17 EXACT: 0 N = 3 ALPHA = -0.500000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 15.5031 3.552714e-15 GW_02_XIU: 4 15.5031 5.506706e-14 CN_GEG_03_XIU: 6 15.5031 7.105427e-15 EXACT: 15.5031 N = 3 ALPHA = 0.000000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 2.66667 0.000000e+00 GW_02_XIU: 4 2.66667 8.881784e-16 CN_GEG_03_XIU: 6 2.66667 1.332268e-15 EXACT: 2.66667 N = 3 ALPHA = 0.500000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.968946 7.771561e-16 GW_02_XIU: 4 0.968946 2.109424e-15 CN_GEG_03_XIU: 6 0.968946 7.771561e-16 EXACT: 0.968946 N = 3 ALPHA = 1.000000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.474074 0.000000e+00 GW_02_XIU: 4 0.474074 0.000000e+00 CN_GEG_03_XIU: 6 0.474074 1.110223e-16 EXACT: 0.474074 N = 3 ALPHA = 1.500000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.272516 1.665335e-16 GW_02_XIU: 4 0.272516 6.106227e-16 CN_GEG_03_XIU: 6 0.272516 1.665335e-16 EXACT: 0.272516 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 97.4091 0.000000e+00 CN_GEG_01_1: 1 97.4091 0.000000e+00 CN_GEG_02_XIU: 5 97.4091 0.000000e+00 GW_02_XIU: 5 97.4091 4.831691e-13 CN_GEG_03_XIU: 8 97.4091 0.000000e+00 EXACT: 97.4091 N = 4 ALPHA = 0.000000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 16 0.000000e+00 CN_GEG_01_1: 1 16 0.000000e+00 CN_GEG_02_XIU: 5 16 0.000000e+00 GW_02_XIU: 5 16 8.881784e-15 CN_GEG_03_XIU: 8 16 0.000000e+00 EXACT: 16 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 6.08807 0.000000e+00 CN_GEG_01_1: 1 6.08807 0.000000e+00 CN_GEG_02_XIU: 5 6.08807 0.000000e+00 GW_02_XIU: 5 6.08807 2.486900e-14 CN_GEG_03_XIU: 8 6.08807 0.000000e+00 EXACT: 6.08807 N = 4 ALPHA = 1.000000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 3.16049 4.440892e-16 CN_GEG_01_1: 1 3.16049 4.440892e-16 CN_GEG_02_XIU: 5 3.16049 4.440892e-16 GW_02_XIU: 5 3.16049 4.440892e-16 CN_GEG_03_XIU: 8 3.16049 4.440892e-16 EXACT: 3.16049 N = 4 ALPHA = 1.500000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 1.9263 0.000000e+00 CN_GEG_01_1: 1 1.9263 0.000000e+00 CN_GEG_02_XIU: 5 1.9263 0.000000e+00 GW_02_XIU: 5 1.9263 4.440892e-15 CN_GEG_03_XIU: 8 1.9263 0.000000e+00 EXACT: 1.9263 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 5 7.10543e-15 7.105427e-15 GW_02_XIU: 5 7.10543e-15 7.105427e-15 CN_GEG_03_XIU: 8 -1.77636e-14 1.776357e-14 EXACT: 0 N = 4 ALPHA = 0.000000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 5 1.11022e-15 1.110223e-15 GW_02_XIU: 5 1.11022e-15 1.110223e-15 CN_GEG_03_XIU: 8 -2.44249e-15 2.442491e-15 EXACT: 0 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 5 3.33067e-16 3.330669e-16 GW_02_XIU: 5 3.33067e-16 3.330669e-16 CN_GEG_03_XIU: 8 -7.77156e-16 7.771561e-16 EXACT: 0 N = 4 ALPHA = 1.000000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 5 1.38778e-16 1.387779e-16 GW_02_XIU: 5 1.38778e-16 1.387779e-16 CN_GEG_03_XIU: 8 -3.88578e-16 3.885781e-16 EXACT: 0 N = 4 ALPHA = 1.500000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 5 8.32667e-17 8.326673e-17 GW_02_XIU: 5 8.32667e-17 8.326673e-17 CN_GEG_03_XIU: 8 -1.94289e-16 1.942890e-16 EXACT: 0 N = 4 ALPHA = -0.500000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.66454e-15 2.664535e-15 GW_02_XIU: 5 3.55271e-15 3.552714e-15 CN_GEG_03_XIU: 8 8.88178e-16 8.881784e-16 EXACT: 0 N = 4 ALPHA = 0.000000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.22045e-16 2.220446e-16 GW_02_XIU: 5 1.11022e-16 1.110223e-16 CN_GEG_03_XIU: 8 1.11022e-16 1.110223e-16 EXACT: 0 N = 4 ALPHA = 0.500000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 8.32667e-17 8.326673e-17 GW_02_XIU: 5 8.32667e-17 8.326673e-17 CN_GEG_03_XIU: 8 2.77556e-17 2.775558e-17 EXACT: 0 N = 4 ALPHA = 1.000000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 4.16334e-17 4.163336e-17 GW_02_XIU: 5 4.16334e-17 4.163336e-17 CN_GEG_03_XIU: 8 0 0.000000e+00 EXACT: 0 N = 4 ALPHA = 1.500000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 2.77556e-17 2.775558e-17 GW_02_XIU: 5 2.77556e-17 2.775558e-17 CN_GEG_03_XIU: 8 6.93889e-18 6.938894e-18 EXACT: 0 N = 4 ALPHA = -0.500000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 48.7045 1.421085e-14 GW_02_XIU: 5 48.7045 2.273737e-13 CN_GEG_03_XIU: 8 48.7045 2.842171e-14 EXACT: 48.7045 N = 4 ALPHA = 0.000000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 5.33333 8.881784e-16 GW_02_XIU: 5 5.33333 3.552714e-15 CN_GEG_03_XIU: 8 5.33333 8.881784e-16 EXACT: 5.33333 N = 4 ALPHA = 0.500000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 1.52202 8.881784e-16 GW_02_XIU: 5 1.52202 5.329071e-15 CN_GEG_03_XIU: 8 1.52202 1.332268e-15 EXACT: 1.52202 N = 4 ALPHA = 1.000000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.632099 0.000000e+00 GW_02_XIU: 5 0.632099 0.000000e+00 CN_GEG_03_XIU: 8 0.632099 0.000000e+00 EXACT: 0.632099 N = 4 ALPHA = 1.500000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.32105 5.551115e-17 GW_02_XIU: 5 0.32105 8.326673e-16 CN_GEG_03_XIU: 8 0.32105 1.665335e-16 EXACT: 0.32105 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 306.02 5.684342e-14 CN_GEG_01_1: 1 306.02 5.684342e-14 CN_GEG_02_XIU: 6 306.02 5.684342e-14 GW_02_XIU: 6 306.02 1.932676e-12 CN_GEG_03_XIU: 10 306.02 5.684342e-14 EXACT: 306.02 N = 5 ALPHA = 0.000000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 32 0.000000e+00 CN_GEG_01_1: 1 32 0.000000e+00 CN_GEG_02_XIU: 6 32 0.000000e+00 GW_02_XIU: 6 32 1.776357e-14 CN_GEG_03_XIU: 10 32 0.000000e+00 EXACT: 32 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 9.56312 1.776357e-15 CN_GEG_01_1: 1 9.56312 1.776357e-15 CN_GEG_02_XIU: 6 9.56312 1.776357e-15 GW_02_XIU: 6 9.56312 4.796163e-14 CN_GEG_03_XIU: 10 9.56312 1.776357e-15 EXACT: 9.56312 N = 5 ALPHA = 1.000000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 4.21399 8.881784e-16 CN_GEG_01_1: 1 4.21399 8.881784e-16 CN_GEG_02_XIU: 6 4.21399 8.881784e-16 GW_02_XIU: 6 4.21399 8.881784e-16 CN_GEG_03_XIU: 10 4.21399 8.881784e-16 EXACT: 4.21399 N = 5 ALPHA = 1.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.26937 0.000000e+00 CN_GEG_01_1: 1 2.26937 0.000000e+00 CN_GEG_02_XIU: 6 2.26937 0.000000e+00 GW_02_XIU: 6 2.26937 6.217249e-15 CN_GEG_03_XIU: 10 2.26937 0.000000e+00 EXACT: 2.26937 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 0.000000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 1.000000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 1.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = -0.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 2.13163e-14 2.131628e-14 GW_02_XIU: 6 2.13163e-14 2.131628e-14 CN_GEG_03_XIU: 10 -3.55271e-15 3.552714e-15 EXACT: 0 N = 5 ALPHA = 0.000000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 1.33227e-15 1.332268e-15 GW_02_XIU: 6 1.33227e-15 1.332268e-15 CN_GEG_03_XIU: 10 2.22045e-16 2.220446e-16 EXACT: 0 N = 5 ALPHA = 0.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 3.33067e-16 3.330669e-16 GW_02_XIU: 6 3.33067e-16 3.330669e-16 CN_GEG_03_XIU: 10 2.77556e-17 2.775558e-17 EXACT: 0 N = 5 ALPHA = 1.000000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 1.11022e-16 1.110223e-16 GW_02_XIU: 6 1.11022e-16 1.110223e-16 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 1.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 5.55112e-17 5.551115e-17 GW_02_XIU: 6 5.55112e-17 5.551115e-17 CN_GEG_03_XIU: 10 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = -0.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 153.01 2.842171e-14 GW_02_XIU: 6 153.01 9.379164e-13 CN_GEG_03_XIU: 10 153.01 1.136868e-13 EXACT: 153.01 N = 5 ALPHA = 0.000000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 10.6667 3.552714e-15 GW_02_XIU: 6 10.6667 5.329071e-15 CN_GEG_03_XIU: 10 10.6667 5.329071e-15 EXACT: 10.6667 N = 5 ALPHA = 0.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 2.39078 2.220446e-15 GW_02_XIU: 6 2.39078 9.325873e-15 CN_GEG_03_XIU: 10 2.39078 1.776357e-15 EXACT: 2.39078 N = 5 ALPHA = 1.000000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.842798 0.000000e+00 GW_02_XIU: 6 0.842798 0.000000e+00 CN_GEG_03_XIU: 10 0.842798 0.000000e+00 EXACT: 0.842798 N = 5 ALPHA = 1.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.378229 1.665335e-16 GW_02_XIU: 6 0.378229 1.221245e-15 CN_GEG_03_XIU: 10 0.378229 1.110223e-16 EXACT: 0.378229 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 961.389 1.136868e-13 CN_GEG_01_1: 1 961.389 1.136868e-13 CN_GEG_02_XIU: 7 961.389 1.136868e-13 GW_02_XIU: 7 961.389 7.275958e-12 CN_GEG_03_XIU: 12 961.389 0.000000e+00 EXACT: 961.389 N = 6 ALPHA = 0.000000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 64 0.000000e+00 CN_GEG_01_1: 1 64 0.000000e+00 CN_GEG_02_XIU: 7 64 7.105427e-15 GW_02_XIU: 7 64 4.263256e-14 CN_GEG_03_XIU: 12 64 7.105427e-15 EXACT: 64 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 15.0217 1.776357e-15 CN_GEG_01_1: 1 15.0217 1.776357e-15 CN_GEG_02_XIU: 7 15.0217 1.776357e-15 GW_02_XIU: 7 15.0217 9.059420e-14 CN_GEG_03_XIU: 12 15.0217 0.000000e+00 EXACT: 15.0217 N = 6 ALPHA = 1.000000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 5.61866 0.000000e+00 CN_GEG_01_1: 1 5.61866 0.000000e+00 CN_GEG_02_XIU: 7 5.61866 0.000000e+00 GW_02_XIU: 7 5.61866 0.000000e+00 CN_GEG_03_XIU: 12 5.61866 0.000000e+00 EXACT: 5.61866 N = 6 ALPHA = 1.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.67354 0.000000e+00 CN_GEG_01_1: 1 2.67354 0.000000e+00 CN_GEG_02_XIU: 7 2.67354 0.000000e+00 GW_02_XIU: 7 2.67354 8.881784e-15 CN_GEG_03_XIU: 12 2.67354 0.000000e+00 EXACT: 2.67354 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 7 -6.39488e-14 6.394885e-14 GW_02_XIU: 7 -6.39488e-14 6.394885e-14 CN_GEG_03_XIU: 12 -2.62901e-13 2.629008e-13 EXACT: 0 N = 6 ALPHA = 0.000000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 7 -3.10862e-15 3.108624e-15 GW_02_XIU: 7 -3.9968e-15 3.996803e-15 CN_GEG_03_XIU: 12 -1.46549e-14 1.465494e-14 EXACT: 0 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 7 -7.77156e-16 7.771561e-16 GW_02_XIU: 7 -6.66134e-16 6.661338e-16 CN_GEG_03_XIU: 12 -2.60902e-15 2.609024e-15 EXACT: 0 N = 6 ALPHA = 1.000000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 7 -2.498e-16 2.498002e-16 GW_02_XIU: 7 -2.498e-16 2.498002e-16 CN_GEG_03_XIU: 12 -9.71445e-16 9.714451e-16 EXACT: 0 N = 6 ALPHA = 1.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0 0.000000e+00 CN_GEG_02_XIU: 7 -1.249e-16 1.249001e-16 GW_02_XIU: 7 -1.249e-16 1.249001e-16 CN_GEG_03_XIU: 12 -4.16334e-16 4.163336e-16 EXACT: 0 N = 6 ALPHA = -0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 3.55271e-14 3.552714e-14 GW_02_XIU: 7 4.26326e-14 4.263256e-14 CN_GEG_03_XIU: 12 -2.13163e-14 2.131628e-14 EXACT: 0 N = 6 ALPHA = 0.000000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 2.44249e-15 2.442491e-15 GW_02_XIU: 7 2.44249e-15 2.442491e-15 CN_GEG_03_XIU: 12 -4.44089e-16 4.440892e-16 EXACT: 0 N = 6 ALPHA = 0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 2.22045e-16 2.220446e-16 GW_02_XIU: 7 3.33067e-16 3.330669e-16 CN_GEG_03_XIU: 12 5.55112e-17 5.551115e-17 EXACT: 0 N = 6 ALPHA = 1.000000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 9.71445e-17 9.714451e-17 GW_02_XIU: 7 9.71445e-17 9.714451e-17 CN_GEG_03_XIU: 12 -4.16334e-17 4.163336e-17 EXACT: 0 N = 6 ALPHA = 1.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 2.08167e-17 2.081668e-17 GW_02_XIU: 7 2.77556e-17 2.775558e-17 CN_GEG_03_XIU: 12 -6.93889e-18 6.938894e-18 EXACT: 0 N = 6 ALPHA = -0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 480.695 2.842171e-13 GW_02_XIU: 7 480.695 3.467449e-12 CN_GEG_03_XIU: 12 480.695 3.979039e-13 EXACT: 480.695 N = 6 ALPHA = 0.000000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 21.3333 0.000000e+00 GW_02_XIU: 7 21.3333 1.421085e-14 CN_GEG_03_XIU: 12 21.3333 7.105427e-15 EXACT: 21.3333 N = 6 ALPHA = 0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 3.75543 2.220446e-15 GW_02_XIU: 7 3.75543 1.998401e-14 CN_GEG_03_XIU: 12 3.75543 3.108624e-15 EXACT: 3.75543 N = 6 ALPHA = 1.000000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 1.12373 0.000000e+00 GW_02_XIU: 7 1.12373 0.000000e+00 CN_GEG_03_XIU: 12 1.12373 2.220446e-16 EXACT: 1.12373 N = 6 ALPHA = 1.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.44559 1.665335e-16 GW_02_XIU: 7 0.44559 1.609823e-15 CN_GEG_03_XIU: 12 0.44559 2.220446e-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 = 0.000000 BETA = 0.000000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2 0.000000e+00 CN_JAC_01_1: 1 2 0.000000e+00 CN_JAC_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2 0.000000e+00 CN_JAC_01_1: 1 2 0.000000e+00 CN_JAC_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2.66667 0.000000e+00 CN_JAC_01_1: 1 2.66667 0.000000e+00 CN_JAC_02_XIU: 2 2.66667 0.000000e+00 GW_02_XIU: 2 2.66667 4.440892e-16 EXACT: 2.66667 N = 1 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 1.5708 0.000000e+00 CN_JAC_01_1: 1 1.5708 0.000000e+00 CN_JAC_02_XIU: 2 1.5708 0.000000e+00 GW_02_XIU: 2 1.5708 2.220446e-16 EXACT: 1.5708 N = 1 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 -0.666667 0.000000e+00 CN_JAC_02_XIU: 2 -0.666667 1.110223e-16 GW_02_XIU: 2 -0.666667 1.110223e-16 EXACT: -0.666667 N = 1 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 1.33333 0.000000e+00 CN_JAC_02_XIU: 2 1.33333 2.220446e-16 GW_02_XIU: 2 1.33333 0.000000e+00 EXACT: 1.33333 N = 1 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0.392699 0.000000e+00 CN_JAC_02_XIU: 2 0.392699 5.551115e-17 GW_02_XIU: 2 0.392699 0.000000e+00 EXACT: 0.392699 N = 1 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 0.000000e+00 GW_02_XIU: 2 0.666667 0.000000e+00 EXACT: 0.666667 N = 1 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 2.220446e-16 GW_02_XIU: 2 0.666667 2.220446e-16 EXACT: 0.666667 N = 1 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 1.06667 0.000000e+00 GW_02_XIU: 2 1.06667 2.220446e-16 EXACT: 1.06667 N = 1 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.392699 5.551115e-17 GW_02_XIU: 2 0.392699 5.551115e-17 EXACT: 0.392699 N = 2 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 4 0.000000e+00 CN_JAC_01_1: 1 4 0.000000e+00 CN_JAC_02_XIU: 3 4 0.000000e+00 GW_02_XIU: 3 4 0.000000e+00 EXACT: 4 N = 2 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 4 0.000000e+00 CN_JAC_01_1: 1 4 0.000000e+00 CN_JAC_02_XIU: 3 4 0.000000e+00 GW_02_XIU: 3 4 0.000000e+00 EXACT: 4 N = 2 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 7.11111 0.000000e+00 CN_JAC_01_1: 1 7.11111 0.000000e+00 CN_JAC_02_XIU: 3 7.11111 0.000000e+00 GW_02_XIU: 3 7.11111 1.776357e-15 EXACT: 7.11111 N = 2 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 2.4674 0.000000e+00 CN_JAC_01_1: 1 2.4674 0.000000e+00 CN_JAC_02_XIU: 3 2.4674 0.000000e+00 GW_02_XIU: 3 2.4674 8.881784e-16 EXACT: 2.4674 N = 2 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 3 1.11022e-16 1.110223e-16 GW_02_XIU: 3 1.11022e-16 1.110223e-16 EXACT: 0 N = 2 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 -1.33333 0.000000e+00 CN_JAC_02_XIU: 3 -1.33333 2.220446e-16 GW_02_XIU: 3 -1.33333 2.220446e-16 EXACT: -1.33333 N = 2 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 3.55556 0.000000e+00 CN_JAC_02_XIU: 3 3.55556 4.440892e-16 GW_02_XIU: 3 3.55556 0.000000e+00 EXACT: 3.55556 N = 2 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0.61685 0.000000e+00 CN_JAC_02_XIU: 3 0.61685 1.110223e-16 GW_02_XIU: 3 0.61685 3.330669e-16 EXACT: 0.61685 N = 2 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 4.44089e-16 4.440892e-16 GW_02_XIU: 3 4.44089e-16 4.440892e-16 EXACT: 0 N = 2 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.444444 1.665335e-16 GW_02_XIU: 3 0.444444 1.665335e-16 EXACT: 0.444444 N = 2 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 1.77778 8.881784e-16 GW_02_XIU: 3 1.77778 4.440892e-16 EXACT: 1.77778 N = 2 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.154213 1.665335e-16 GW_02_XIU: 3 0.154213 2.220446e-16 EXACT: 0.154213 N = 2 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 2.220446e-16 GW_02_XIU: 3 1.33333 2.220446e-16 EXACT: 1.33333 N = 2 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 4.440892e-16 GW_02_XIU: 3 1.33333 4.440892e-16 EXACT: 1.33333 N = 2 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 2.84444 4.440892e-16 GW_02_XIU: 3 2.84444 4.440892e-16 EXACT: 2.84444 N = 2 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 0.61685 0.000000e+00 GW_02_XIU: 3 0.61685 3.330669e-16 EXACT: 0.61685 N = 3 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 8 0.000000e+00 CN_JAC_01_1: 1 8 0.000000e+00 CN_JAC_02_XIU: 4 8 0.000000e+00 GW_02_XIU: 4 8 0.000000e+00 EXACT: 8 N = 3 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 8 0.000000e+00 CN_JAC_01_1: 1 8 0.000000e+00 CN_JAC_02_XIU: 4 8 0.000000e+00 GW_02_XIU: 4 8 0.000000e+00 EXACT: 8 N = 3 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 18.963 0.000000e+00 CN_JAC_01_1: 1 18.963 0.000000e+00 CN_JAC_02_XIU: 4 18.963 0.000000e+00 GW_02_XIU: 4 18.963 1.065814e-14 EXACT: 18.963 N = 3 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 3.87578 0.000000e+00 CN_JAC_01_1: 1 3.87578 0.000000e+00 CN_JAC_02_XIU: 4 3.87578 0.000000e+00 GW_02_XIU: 4 3.87578 1.776357e-15 EXACT: 3.87578 N = 3 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 EXACT: 0 N = 3 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 -2.66667 0.000000e+00 CN_JAC_02_XIU: 4 -2.66667 4.440892e-16 GW_02_XIU: 4 -2.66667 4.440892e-16 EXACT: -2.66667 N = 3 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 9.48148 0.000000e+00 CN_JAC_02_XIU: 4 9.48148 1.776357e-15 GW_02_XIU: 4 9.48148 3.552714e-15 EXACT: 9.48148 N = 3 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.968946 0.000000e+00 CN_JAC_02_XIU: 4 0.968946 0.000000e+00 GW_02_XIU: 4 0.968946 5.551115e-16 EXACT: 0.968946 N = 3 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 1.63286e-16 1.632862e-16 GW_02_XIU: 4 1.63286e-16 1.632862e-16 EXACT: 0 N = 3 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.888889 2.220446e-16 GW_02_XIU: 4 0.888889 2.220446e-16 EXACT: 0.888889 N = 3 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 4.74074 1.776357e-15 GW_02_XIU: 4 4.74074 1.776357e-15 EXACT: 4.74074 N = 3 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.242237 8.326673e-17 GW_02_XIU: 4 0.242237 2.220446e-16 EXACT: 0.242237 N = 3 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 0.000000e+00 GW_02_XIU: 4 2.66667 0.000000e+00 EXACT: 2.66667 N = 3 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 8.881784e-16 GW_02_XIU: 4 2.66667 8.881784e-16 EXACT: 2.66667 N = 3 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 7.58519 8.881784e-16 GW_02_XIU: 4 7.58519 3.552714e-15 EXACT: 7.58519 N = 3 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 0.968946 1.110223e-16 GW_02_XIU: 4 0.968946 5.551115e-16 EXACT: 0.968946 N = 4 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 16 0.000000e+00 CN_JAC_01_1: 1 16 0.000000e+00 CN_JAC_02_XIU: 5 16 0.000000e+00 GW_02_XIU: 5 16 0.000000e+00 EXACT: 16 N = 4 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 16 0.000000e+00 CN_JAC_01_1: 1 16 0.000000e+00 CN_JAC_02_XIU: 5 16 0.000000e+00 GW_02_XIU: 5 16 0.000000e+00 EXACT: 16 N = 4 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 50.5679 7.105427e-15 CN_JAC_01_1: 1 50.5679 7.105427e-15 CN_JAC_02_XIU: 5 50.5679 7.105427e-15 GW_02_XIU: 5 50.5679 2.842171e-14 EXACT: 50.5679 N = 4 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 6.08807 0.000000e+00 CN_JAC_01_1: 1 6.08807 0.000000e+00 CN_JAC_02_XIU: 5 6.08807 0.000000e+00 GW_02_XIU: 5 6.08807 3.552714e-15 EXACT: 6.08807 N = 4 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 5 1.11022e-15 1.110223e-15 GW_02_XIU: 5 1.11022e-15 1.110223e-15 EXACT: 0 N = 4 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -5.33333 0.000000e+00 CN_JAC_02_XIU: 5 -5.33333 0.000000e+00 GW_02_XIU: 5 -5.33333 0.000000e+00 EXACT: -5.33333 N = 4 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 25.284 3.552714e-15 CN_JAC_02_XIU: 5 25.284 1.065814e-14 GW_02_XIU: 5 25.284 7.105427e-15 EXACT: 25.284 N = 4 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 1.52202 0.000000e+00 CN_JAC_02_XIU: 5 1.52202 4.440892e-16 GW_02_XIU: 5 1.52202 1.332268e-15 EXACT: 1.52202 N = 4 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 2.22045e-16 2.220446e-16 GW_02_XIU: 5 2.22045e-16 2.220446e-16 EXACT: 0 N = 4 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.77778 0.000000e+00 GW_02_XIU: 5 1.77778 0.000000e+00 EXACT: 1.77778 N = 4 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 12.642 5.329071e-15 GW_02_XIU: 5 12.642 3.552714e-15 EXACT: 12.642 N = 4 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 0.380504 1.665335e-16 GW_02_XIU: 5 0.380504 4.440892e-16 EXACT: 0.380504 N = 4 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 8.881784e-16 GW_02_XIU: 5 5.33333 8.881784e-16 EXACT: 5.33333 N = 4 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 1.776357e-15 GW_02_XIU: 5 5.33333 1.776357e-15 EXACT: 5.33333 N = 4 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 20.2272 0.000000e+00 GW_02_XIU: 5 20.2272 1.421085e-14 EXACT: 20.2272 N = 4 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.52202 0.000000e+00 GW_02_XIU: 5 1.52202 8.881784e-16 EXACT: 1.52202 N = 5 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 32 0.000000e+00 CN_JAC_01_1: 1 32 0.000000e+00 CN_JAC_02_XIU: 6 32 0.000000e+00 GW_02_XIU: 6 32 0.000000e+00 EXACT: 32 N = 5 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 32 0.000000e+00 CN_JAC_01_1: 1 32 0.000000e+00 CN_JAC_02_XIU: 6 32 0.000000e+00 GW_02_XIU: 6 32 0.000000e+00 EXACT: 32 N = 5 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 134.848 0.000000e+00 CN_JAC_01_1: 1 134.848 0.000000e+00 CN_JAC_02_XIU: 6 134.848 0.000000e+00 GW_02_XIU: 6 134.848 1.136868e-13 EXACT: 134.848 N = 5 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 9.56312 1.776357e-15 CN_JAC_01_1: 1 9.56312 1.776357e-15 CN_JAC_02_XIU: 6 9.56312 1.776357e-15 GW_02_XIU: 6 9.56312 8.881784e-15 EXACT: 9.56312 N = 5 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 EXACT: 0 N = 5 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -10.6667 0.000000e+00 CN_JAC_02_XIU: 6 -10.6667 1.776357e-15 GW_02_XIU: 6 -10.6667 1.776357e-15 EXACT: -10.6667 N = 5 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 67.4239 0.000000e+00 CN_JAC_02_XIU: 6 67.4239 1.421085e-14 GW_02_XIU: 6 67.4239 4.263256e-14 EXACT: 67.4239 N = 5 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 2.39078 4.440892e-16 CN_JAC_02_XIU: 6 2.39078 4.440892e-16 GW_02_XIU: 6 2.39078 1.776357e-15 EXACT: 2.39078 N = 5 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 1.33227e-15 1.332268e-15 GW_02_XIU: 6 1.33227e-15 1.332268e-15 EXACT: 0 N = 5 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 3.55556 4.440892e-16 GW_02_XIU: 6 3.55556 4.440892e-16 EXACT: 3.55556 N = 5 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 33.7119 2.131628e-14 GW_02_XIU: 6 33.7119 2.131628e-14 EXACT: 33.7119 N = 5 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 0.597695 4.440892e-16 GW_02_XIU: 6 0.597695 8.881784e-16 EXACT: 0.597695 N = 5 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 3.552714e-15 GW_02_XIU: 6 10.6667 3.552714e-15 EXACT: 10.6667 N = 5 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 1.776357e-15 GW_02_XIU: 6 10.6667 1.776357e-15 EXACT: 10.6667 N = 5 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 53.9391 0.000000e+00 GW_02_XIU: 6 53.9391 4.263256e-14 EXACT: 53.9391 N = 5 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 2.39078 1.332268e-15 GW_02_XIU: 6 2.39078 2.664535e-15 EXACT: 2.39078 N = 6 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 64 0.000000e+00 CN_JAC_01_1: 1 64 0.000000e+00 CN_JAC_02_XIU: 7 64 7.105427e-15 GW_02_XIU: 7 64 7.105427e-15 EXACT: 64 N = 6 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 64 0.000000e+00 CN_JAC_01_1: 1 64 0.000000e+00 CN_JAC_02_XIU: 7 64 7.105427e-15 GW_02_XIU: 7 64 7.105427e-15 EXACT: 64 N = 6 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 359.594 5.684342e-14 CN_JAC_01_1: 1 359.594 5.684342e-14 CN_JAC_02_XIU: 7 359.594 5.684342e-14 GW_02_XIU: 7 359.594 2.842171e-13 EXACT: 359.594 N = 6 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 15.0217 1.776357e-15 CN_JAC_01_1: 1 15.0217 1.776357e-15 CN_JAC_02_XIU: 7 15.0217 1.776357e-15 GW_02_XIU: 7 15.0217 1.598721e-14 EXACT: 15.0217 N = 6 ALPHA = 0.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0 0.000000e+00 CN_JAC_02_XIU: 7 -3.10862e-15 3.108624e-15 GW_02_XIU: 7 -3.10862e-15 3.108624e-15 EXACT: 0 N = 6 ALPHA = 1.000000 BETA = 0.000000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -21.3333 0.000000e+00 CN_JAC_02_XIU: 7 -21.3333 3.552714e-15 GW_02_XIU: 7 -21.3333 3.552714e-15 EXACT: -21.3333 N = 6 ALPHA = 0.000000 BETA = 2.000000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 179.797 2.842171e-14 CN_JAC_02_XIU: 7 179.797 5.684342e-14 GW_02_XIU: 7 179.797 1.421085e-13 EXACT: 179.797 N = 6 ALPHA = 0.500000 BETA = 1.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 3.75543 4.440892e-16 CN_JAC_02_XIU: 7 3.75543 4.440892e-16 GW_02_XIU: 7 3.75543 2.664535e-15 EXACT: 3.75543 N = 6 ALPHA = 0.000000 BETA = 0.000000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 2.44249e-15 2.442491e-15 GW_02_XIU: 7 2.44249e-15 2.442491e-15 EXACT: 0 N = 6 ALPHA = 1.000000 BETA = 0.000000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 7.11111 0.000000e+00 GW_02_XIU: 7 7.11111 0.000000e+00 EXACT: 7.11111 N = 6 ALPHA = 0.000000 BETA = 2.000000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 89.8985 2.842171e-14 GW_02_XIU: 7 89.8985 5.684342e-14 EXACT: 89.8985 N = 6 ALPHA = 0.500000 BETA = 1.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 0.938857 3.330669e-16 GW_02_XIU: 7 0.938857 1.110223e-15 EXACT: 0.938857 N = 6 ALPHA = 0.000000 BETA = 0.000000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 0.000000e+00 GW_02_XIU: 7 21.3333 0.000000e+00 EXACT: 21.3333 N = 6 ALPHA = 1.000000 BETA = 0.000000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 3.552714e-15 GW_02_XIU: 7 21.3333 3.552714e-15 EXACT: 21.3333 N = 6 ALPHA = 0.000000 BETA = 2.000000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 143.838 0.000000e+00 GW_02_XIU: 7 143.838 1.421085e-13 EXACT: 143.838 N = 6 ALPHA = 0.500000 BETA = 1.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 3.75543 4.440892e-16 GW_02_XIU: 7 3.75543 3.552714e-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 0.000000e+00 CN_LEG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 CN_LEG_03_1: 2 2 0.000000e+00 CN_LEG_03_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 EXPON = 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 CN_LEG_03_1: 2 0 0.000000e+00 CN_LEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 EXPON = 2 Degree = 2 CN_LEG_02_XIU: 2 0.666667 0.000000e+00 GW_02_XIU: 2 0.666667 0.000000e+00 CN_LEG_03_1: 2 0.666667 2.220446e-16 CN_LEG_03_XIU: 2 0.666667 2.220446e-16 EXACT: 0.666667 N = 1 EXPON = 3 Degree = 3 CN_LEG_03_1: 2 0 0.000000e+00 CN_LEG_03_XIU: 2 0 0.000000e+00 EXACT: 0 N = 1 EXPON = 4 Degree = 4 EXACT: 0.4 N = 2 EXPON = 0 0 Degree = 0 CN_LEG_01_1: 1 4 0.000000e+00 CN_LEG_02_XIU: 3 4 0.000000e+00 GW_02_XIU: 3 4 0.000000e+00 CN_LEG_03_1: 4 4 0.000000e+00 CN_LEG_03_XIU: 4 4 0.000000e+00 CN_LEG_05_2: 9 4 0.000000e+00 EXACT: 4 N = 2 EXPON = 0 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 3 1.11022e-16 1.110223e-16 GW_02_XIU: 3 1.11022e-16 1.110223e-16 CN_LEG_03_1: 4 -1.11022e-16 1.110223e-16 CN_LEG_03_XIU: 4 -1.11022e-16 1.110223e-16 CN_LEG_05_2: 9 0 0.000000e+00 EXACT: 0 N = 2 EXPON = 1 1 Degree = 2 CN_LEG_02_XIU: 3 4.44089e-16 4.440892e-16 GW_02_XIU: 3 4.44089e-16 4.440892e-16 CN_LEG_03_1: 4 -8.16431e-17 8.164312e-17 CN_LEG_03_XIU: 4 -8.16431e-17 8.164312e-17 CN_LEG_05_2: 9 0 0.000000e+00 EXACT: 0 N = 2 EXPON = 2 0 Degree = 2 CN_LEG_02_XIU: 3 1.33333 2.220446e-16 GW_02_XIU: 3 1.33333 2.220446e-16 CN_LEG_03_1: 4 1.33333 4.440892e-16 CN_LEG_03_XIU: 4 1.33333 4.440892e-16 CN_LEG_05_2: 9 1.33333 2.220446e-16 EXACT: 1.33333 N = 2 EXPON = 0 3 Degree = 3 CN_LEG_03_1: 4 0 0.000000e+00 CN_LEG_03_XIU: 4 0 0.000000e+00 CN_LEG_05_2: 9 0 0.000000e+00 EXACT: 0 N = 2 EXPON = 0 4 Degree = 4 CN_LEG_05_2: 9 0.8 0.000000e+00 EXACT: 0.8 N = 2 EXPON = 2 3 Degree = 5 CN_LEG_05_2: 9 0 0.000000e+00 EXACT: 0 N = 3 EXPON = 0 0 0 Degree = 0 CN_LEG_01_1: 1 8 0.000000e+00 CN_LEG_02_XIU: 4 8 0.000000e+00 GW_02_XIU: 4 8 0.000000e+00 CN_LEG_03_1: 6 8 0.000000e+00 CN_LEG_03_XIU: 6 8 0.000000e+00 CN_LEG_05_2: 19 8 0.000000e+00 EXACT: 8 N = 3 EXPON = 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 4 0 0.000000e+00 GW_02_XIU: 4 0 0.000000e+00 CN_LEG_03_1: 6 0 0.000000e+00 CN_LEG_03_XIU: 6 0 0.000000e+00 CN_LEG_05_2: 19 0 0.000000e+00 EXACT: 0 N = 3 EXPON = 1 1 0 Degree = 2 CN_LEG_02_XIU: 4 1.63286e-16 1.632862e-16 GW_02_XIU: 4 1.63286e-16 1.632862e-16 CN_LEG_03_1: 6 1.66533e-16 1.665335e-16 CN_LEG_03_XIU: 6 1.66533e-16 1.665335e-16 CN_LEG_05_2: 19 0 0.000000e+00 EXACT: 0 N = 3 EXPON = 2 0 0 Degree = 2 CN_LEG_02_XIU: 4 2.66667 0.000000e+00 GW_02_XIU: 4 2.66667 0.000000e+00 CN_LEG_03_1: 6 2.66667 1.332268e-15 CN_LEG_03_XIU: 6 2.66667 1.332268e-15 CN_LEG_05_2: 19 2.66667 4.440892e-16 EXACT: 2.66667 N = 3 EXPON = 0 0 3 Degree = 3 CN_LEG_03_1: 6 0 0.000000e+00 CN_LEG_03_XIU: 6 0 0.000000e+00 CN_LEG_05_2: 19 0 0.000000e+00 EXACT: 0 N = 3 EXPON = 0 0 4 Degree = 4 CN_LEG_05_2: 19 1.6 0.000000e+00 EXACT: 1.6 N = 3 EXPON = 2 0 3 Degree = 5 CN_LEG_05_2: 19 0 0.000000e+00 EXACT: 0 N = 4 EXPON = 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 16 0.000000e+00 CN_LEG_02_XIU: 5 16 0.000000e+00 GW_02_XIU: 5 16 0.000000e+00 CN_LEG_03_1: 8 16 0.000000e+00 CN_LEG_03_XIU: 8 16 0.000000e+00 CN_LEG_05_1(1): 22 16 7.105427e-15 CN_LEG_05_1(2): 22 16 3.552714e-15 CN_LEG_05_2: 33 16 3.552714e-15 EXACT: 16 N = 4 EXPON = 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 5 1.11022e-15 1.110223e-15 GW_02_XIU: 5 1.11022e-15 1.110223e-15 CN_LEG_03_1: 8 -2.44249e-15 2.442491e-15 CN_LEG_03_XIU: 8 -2.44249e-15 2.442491e-15 CN_LEG_05_1(1): 22 0 0.000000e+00 CN_LEG_05_1(2): 22 8.32667e-17 8.326673e-17 CN_LEG_05_2: 33 0 0.000000e+00 EXACT: 0 N = 4 EXPON = 1 1 0 0 Degree = 2 CN_LEG_02_XIU: 5 2.22045e-16 2.220446e-16 GW_02_XIU: 5 2.22045e-16 2.220446e-16 CN_LEG_03_1: 8 1.11022e-16 1.110223e-16 CN_LEG_03_XIU: 8 1.11022e-16 1.110223e-16 CN_LEG_05_1(1): 22 -1.22125e-15 1.221245e-15 CN_LEG_05_1(2): 22 -2.22045e-16 2.220446e-16 CN_LEG_05_2: 33 0 0.000000e+00 EXACT: 0 N = 4 EXPON = 2 0 0 0 Degree = 2 CN_LEG_02_XIU: 5 5.33333 8.881784e-16 GW_02_XIU: 5 5.33333 8.881784e-16 CN_LEG_03_1: 8 5.33333 8.881784e-16 CN_LEG_03_XIU: 8 5.33333 8.881784e-16 CN_LEG_05_1(1): 22 5.33333 4.440892e-15 CN_LEG_05_1(2): 22 5.33333 7.993606e-15 CN_LEG_05_2: 33 5.33333 8.881784e-16 EXACT: 5.33333 N = 4 EXPON = 0 0 0 3 Degree = 3 CN_LEG_03_1: 8 -1.9984e-15 1.998401e-15 CN_LEG_03_XIU: 8 -1.9984e-15 1.998401e-15 CN_LEG_05_1(1): 22 0 0.000000e+00 CN_LEG_05_1(2): 22 -6.93889e-18 6.938894e-18 CN_LEG_05_2: 33 0 0.000000e+00 EXACT: 0 N = 4 EXPON = 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 22 3.2 3.552714e-15 CN_LEG_05_1(2): 22 3.2 5.773160e-15 CN_LEG_05_2: 33 3.2 0.000000e+00 EXACT: 3.2 N = 4 EXPON = 2 0 0 3 Degree = 5 CN_LEG_05_1(1): 22 -2.77556e-17 2.775558e-17 CN_LEG_05_1(2): 22 -2.77556e-17 2.775558e-17 CN_LEG_05_2: 33 0 0.000000e+00 EXACT: 0 N = 5 EXPON = 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 32 0.000000e+00 CN_LEG_02_XIU: 6 32 0.000000e+00 GW_02_XIU: 6 32 0.000000e+00 CN_LEG_03_1: 10 32 0.000000e+00 CN_LEG_03_XIU: 10 32 0.000000e+00 CN_LEG_05_1(1): 32 32 1.421085e-14 CN_LEG_05_1(2): 32 32 2.842171e-14 CN_LEG_05_2: 51 32 7.105427e-15 EXACT: 32 N = 5 EXPON = 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 6 0 0.000000e+00 GW_02_XIU: 6 0 0.000000e+00 CN_LEG_03_1: 10 0 0.000000e+00 CN_LEG_03_XIU: 10 0 0.000000e+00 CN_LEG_05_1(1): 32 1.11022e-16 1.110223e-16 CN_LEG_05_1(2): 32 2.22045e-16 2.220446e-16 CN_LEG_05_2: 51 0 0.000000e+00 EXACT: 0 N = 5 EXPON = 1 1 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 1.33227e-15 1.332268e-15 GW_02_XIU: 6 1.33227e-15 1.332268e-15 CN_LEG_03_1: 10 2.22045e-16 2.220446e-16 CN_LEG_03_XIU: 10 2.22045e-16 2.220446e-16 CN_LEG_05_1(1): 32 9.99201e-16 9.992007e-16 CN_LEG_05_1(2): 32 4.16334e-17 4.163336e-17 CN_LEG_05_2: 51 0 0.000000e+00 EXACT: 0 N = 5 EXPON = 2 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 10.6667 3.552714e-15 GW_02_XIU: 6 10.6667 3.552714e-15 CN_LEG_03_1: 10 10.6667 5.329071e-15 CN_LEG_03_XIU: 10 10.6667 5.329071e-15 CN_LEG_05_1(1): 32 10.6667 1.598721e-14 CN_LEG_05_1(2): 32 10.6667 8.881784e-15 CN_LEG_05_2: 51 10.6667 1.776357e-15 EXACT: 10.6667 N = 5 EXPON = 0 0 0 0 3 Degree = 3 CN_LEG_03_1: 10 0 0.000000e+00 CN_LEG_03_XIU: 10 0 0.000000e+00 CN_LEG_05_1(1): 32 1.94289e-16 1.942890e-16 CN_LEG_05_1(2): 32 0 0.000000e+00 CN_LEG_05_2: 51 0 0.000000e+00 EXACT: 0 N = 5 EXPON = 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 32 6.4 1.243450e-14 CN_LEG_05_1(2): 32 6.4 1.332268e-14 CN_LEG_05_2: 51 6.4 1.776357e-15 EXACT: 6.4 N = 5 EXPON = 2 0 0 0 3 Degree = 5 CN_LEG_05_1(1): 32 -4.16334e-17 4.163336e-17 CN_LEG_05_1(2): 32 5.55112e-17 5.551115e-17 CN_LEG_05_2: 51 0 0.000000e+00 EXACT: 0 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 64 0.000000e+00 CN_LEG_02_XIU: 7 64 7.105427e-15 GW_02_XIU: 7 64 7.105427e-15 CN_LEG_03_1: 12 64 7.105427e-15 CN_LEG_03_XIU: 12 64 7.105427e-15 CN_LEG_05_1(1): 44 64 5.684342e-14 CN_LEG_05_2: 73 64 5.684342e-14 EXACT: 64 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0 0.000000e+00 CN_LEG_02_XIU: 7 -3.10862e-15 3.108624e-15 GW_02_XIU: 7 -3.10862e-15 3.108624e-15 CN_LEG_03_1: 12 -1.46549e-14 1.465494e-14 CN_LEG_03_XIU: 12 -1.46549e-14 1.465494e-14 CN_LEG_05_1(1): 44 4.44089e-16 4.440892e-16 CN_LEG_05_2: 73 0 0.000000e+00 EXACT: 0 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 2.44249e-15 2.442491e-15 GW_02_XIU: 7 2.44249e-15 2.442491e-15 CN_LEG_03_1: 12 -4.44089e-16 4.440892e-16 CN_LEG_03_XIU: 12 -4.44089e-16 4.440892e-16 CN_LEG_05_1(1): 44 0 0.000000e+00 CN_LEG_05_2: 73 0 0.000000e+00 EXACT: 0 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 21.3333 0.000000e+00 GW_02_XIU: 7 21.3333 0.000000e+00 CN_LEG_03_1: 12 21.3333 7.105427e-15 CN_LEG_03_XIU: 12 21.3333 7.105427e-15 CN_LEG_05_1(1): 44 21.3333 3.552714e-15 CN_LEG_05_2: 73 21.3333 7.105427e-15 EXACT: 21.3333 N = 6 EXPON = 0 0 0 0 0 3 Degree = 3 CN_LEG_03_1: 12 -6.66134e-16 6.661338e-16 CN_LEG_03_XIU: 12 -6.66134e-16 6.661338e-16 CN_LEG_05_1(1): 44 2.22045e-16 2.220446e-16 CN_LEG_05_2: 73 0 0.000000e+00 EXACT: 0 N = 6 EXPON = 0 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 44 12.8 3.552714e-15 CN_LEG_05_2: 73 12.8 0.000000e+00 EXACT: 12.8 N = 6 EXPON = 2 0 0 0 0 3 Degree = 5 CN_LEG_05_1(1): 44 0 0.000000e+00 CN_LEG_05_2: 73 0 0.000000e+00 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 2.220446e-16 EN_HER_02_XIU: 2 1.77245 2.220446e-16 GW_02_XIU: 2 1.77245 2.220446e-16 EN_HER_03_1: 2 1.77245 2.220446e-16 EN_HER_03_2: 2 1.77245 2.220446e-16 EN_HER_03_XIU: 2 1.77245 2.220446e-16 EN_HER_05_2: 3 1.77245 2.220446e-16 EN_HER_05_4: 3 1.77245 4.440892e-16 EN_HER_05_5: 3 1.77245 2.220446e-16 EXACT: 1.77245 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 1.110223e-16 GW_02_XIU: 2 0.886227 1.110223e-16 EN_HER_03_1: 2 0.886227 1.110223e-16 EN_HER_03_2: 2 0.886227 1.110223e-16 EN_HER_03_XIU: 2 0.886227 3.330669e-16 EN_HER_05_2: 3 0.886227 1.110223e-16 EN_HER_05_4: 3 0.886227 3.330669e-16 EN_HER_05_5: 3 0.886227 3.330669e-16 EXACT: 0.886227 N = 1 EXPON = 0 Degree = 4 EN_HER_05_2: 3 1.77245 2.220446e-16 EN_HER_05_4: 3 1.77245 4.440892e-16 EN_HER_05_5: 3 1.77245 2.220446e-16 EXACT: 1.77245 N = 1 EXPON = 6 Degree = 6 EXACT: 3.32335 N = 1 EXPON = 2 Degree = 6 EXACT: 0.886227 N = 1 EXPON = 8 Degree = 8 EXACT: 11.6317 N = 1 EXPON = 10 Degree = 10 EXACT: 52.3428 N = 1 EXPON = 1 Degree = 1 EN_HER_01_1: 1 0 0.000000e+00 EN_HER_02_XIU: 2 0 0.000000e+00 GW_02_XIU: 2 0 0.000000e+00 EN_HER_03_1: 2 0 0.000000e+00 EN_HER_03_2: 2 0 0.000000e+00 EN_HER_03_XIU: 2 0 0.000000e+00 EN_HER_05_2: 3 0 0.000000e+00 EN_HER_05_4: 3 0 0.000000e+00 EN_HER_05_5: 3 0 0.000000e+00 EXACT: 0 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 1.110223e-16 GW_02_XIU: 2 0.886227 1.110223e-16 EN_HER_03_1: 2 0.886227 1.110223e-16 EN_HER_03_2: 2 0.886227 1.110223e-16 EN_HER_03_XIU: 2 0.886227 3.330669e-16 EN_HER_05_2: 3 0.886227 1.110223e-16 EN_HER_05_4: 3 0.886227 3.330669e-16 EN_HER_05_5: 3 0.886227 3.330669e-16 EXACT: 0.886227 N = 2 EXPON = 0 0 Degree = 0 EN_HER_01_1: 1 3.14159 4.440892e-16 EN_HER_02_XIU: 3 3.14159 4.440892e-16 GW_02_XIU: 3 3.14159 4.440892e-16 EN_HER_03_1: 4 3.14159 4.440892e-16 EN_HER_03_2: 4 3.14159 4.440892e-16 EN_HER_03_XIU: 4 3.14159 4.440892e-16 EN_HER_05_1(1): 8 3.14159 4.440892e-16 EN_HER_05_2: 9 3.14159 4.440892e-16 EN_HER_05_4: 7 3.14159 4.440892e-16 EN_HER_05_5: 9 3.14159 4.440892e-16 EXACT: 3.14159 N = 2 EXPON = 2 0 Degree = 2 EN_HER_02_XIU: 3 1.5708 4.440892e-16 GW_02_XIU: 3 1.5708 4.440892e-16 EN_HER_03_1: 4 1.5708 2.220446e-16 EN_HER_03_2: 4 1.5708 2.220446e-16 EN_HER_03_XIU: 4 1.5708 2.220446e-16 EN_HER_05_1(1): 8 1.5708 2.220446e-15 EN_HER_05_2: 9 1.5708 0.000000e+00 EN_HER_05_4: 7 1.5708 6.661338e-16 EN_HER_05_5: 9 1.5708 0.000000e+00 EXACT: 1.5708 N = 2 EXPON = 0 4 Degree = 4 EN_HER_05_1(1): 8 2.35619 7.105427e-15 EN_HER_05_2: 9 2.35619 4.440892e-16 EN_HER_05_4: 7 2.35619 0.000000e+00 EN_HER_05_5: 9 2.35619 4.440892e-16 EXACT: 2.35619 N = 2 EXPON = 6 0 Degree = 6 EXACT: 5.89049 N = 2 EXPON = 2 4 Degree = 6 EXACT: 1.1781 N = 2 EXPON = 0 8 Degree = 8 EXACT: 20.6167 N = 2 EXPON = 10 0 Degree = 10 EXACT: 92.7752 N = 2 EXPON = 1 2 Degree = 3 EN_HER_03_1: 4 0 0.000000e+00 EN_HER_03_2: 4 0 0.000000e+00 EN_HER_03_XIU: 4 -9.61835e-17 9.618353e-17 EN_HER_05_1(1): 8 0 0.000000e+00 EN_HER_05_2: 9 0 0.000000e+00 EN_HER_05_4: 7 0 0.000000e+00 EN_HER_05_5: 9 0 0.000000e+00 EXACT: 0 N = 2 EXPON = 2 2 Degree = 4 EN_HER_05_1(1): 8 0.785398 1.443290e-15 EN_HER_05_2: 9 0.785398 1.110223e-16 EN_HER_05_4: 7 0.785398 1.110223e-16 EN_HER_05_5: 9 0.785398 3.330669e-16 EXACT: 0.785398 N = 3 EXPON = 0 0 0 Degree = 0 EN_HER_01_1: 1 5.56833 8.881784e-16 EN_HER_02_XIU: 4 5.56833 1.776357e-15 GW_02_XIU: 4 5.56833 1.776357e-15 EN_HER_03_1: 6 5.56833 8.881784e-16 EN_HER_03_2: 8 5.56833 8.881784e-16 EN_HER_03_XIU: 6 5.56833 8.881784e-16 EN_HER_05_1(1): 14 5.56833 8.881784e-16 EN_HER_05_1(2): 14 5.56833 8.881784e-16 EN_HER_05_2: 19 5.56833 8.881784e-16 EN_HER_05_3: 14 5.56833 0.000000e+00 EN_HER_05_4: 15 5.56833 8.881784e-16 EN_HER_05_5: 25 5.56833 1.776357e-15 EN_HER_07_1(1): 27 5.56833 8.881784e-16 EN_HER_07_1(2): 27 5.56833 1.776357e-15 EN_HER_07_2: 52 5.56833 0.000000e+00 EN_HER_07_3(1): 45 5.56833 1.740830e-13 EN_HER_07_3(2): 45 5.56833 8.881784e-15 EN_HER_09_1(1): 77 5.56833 0.000000e+00 EN_HER_09_1(2): 77 5.56833 0.000000e+00 EN_HER_11_1(1): 151 5.56833 7.815970e-14 EN_HER_11_1(2): 151 5.56833 8.881784e-15 EXACT: 5.56833 N = 3 EXPON = 2 0 0 Degree = 2 EN_HER_02_XIU: 4 2.78416 4.440892e-16 GW_02_XIU: 4 2.78416 4.440892e-16 EN_HER_03_1: 6 2.78416 8.881784e-16 EN_HER_03_2: 8 2.78416 0.000000e+00 EN_HER_03_XIU: 6 2.78416 0.000000e+00 EN_HER_05_1(1): 14 2.78416 2.220446e-15 EN_HER_05_1(2): 14 2.78416 4.884981e-15 EN_HER_05_2: 19 2.78416 0.000000e+00 EN_HER_05_3: 14 2.78416 4.440892e-16 EN_HER_05_4: 15 2.78416 8.881784e-16 EN_HER_05_5: 25 2.78416 4.440892e-16 EN_HER_07_1(1): 27 2.78416 4.440892e-16 EN_HER_07_1(2): 27 2.78416 0.000000e+00 EN_HER_07_2: 52 2.78416 8.881784e-16 EN_HER_07_3(1): 45 2.78416 1.065814e-14 EN_HER_07_3(2): 45 2.78416 1.598721e-14 EN_HER_09_1(1): 77 2.78416 2.220446e-15 EN_HER_09_1(2): 77 2.78416 2.220446e-15 EN_HER_11_1(1): 151 2.78416 2.664535e-15 EN_HER_11_1(2): 151 2.78416 7.993606e-15 EXACT: 2.78416 N = 3 EXPON = 0 4 0 Degree = 4 EN_HER_05_1(1): 14 4.17625 3.552714e-15 EN_HER_05_1(2): 14 4.17625 2.131628e-14 EN_HER_05_2: 19 4.17625 1.776357e-15 EN_HER_05_3: 14 4.17625 1.776357e-15 EN_HER_05_4: 15 4.17625 8.881784e-16 EN_HER_05_5: 25 4.17625 2.664535e-15 EN_HER_07_1(1): 27 4.17625 8.881784e-16 EN_HER_07_1(2): 27 4.17625 1.776357e-15 EN_HER_07_2: 52 4.17625 0.000000e+00 EN_HER_07_3(1): 45 4.17625 4.618528e-14 EN_HER_07_3(2): 45 4.17625 4.263256e-14 EN_HER_09_1(1): 77 4.17625 2.131628e-14 EN_HER_09_1(2): 77 4.17625 2.131628e-14 EN_HER_11_1(1): 151 4.17625 2.664535e-14 EN_HER_11_1(2): 151 4.17625 3.552714e-14 EXACT: 4.17625 N = 3 EXPON = 0 0 6 Degree = 6 EN_HER_07_1(1): 27 10.4406 0.000000e+00 EN_HER_07_1(2): 27 10.4406 0.000000e+00 EN_HER_07_2: 52 10.4406 1.776357e-15 EN_HER_07_3(1): 45 10.4406 2.007283e-13 EN_HER_07_3(2): 45 10.4406 1.652012e-13 EN_HER_09_1(1): 77 10.4406 1.190159e-13 EN_HER_09_1(2): 77 10.4406 1.190159e-13 EN_HER_11_1(1): 151 10.4406 4.973799e-14 EN_HER_11_1(2): 151 10.4406 1.012523e-13 EXACT: 10.4406 N = 3 EXPON = 2 4 0 Degree = 6 EN_HER_07_1(1): 27 2.08812 0.000000e+00 EN_HER_07_1(2): 27 2.08812 0.000000e+00 EN_HER_07_2: 52 2.08812 8.881784e-16 EN_HER_07_3(1): 45 2.08812 3.774758e-14 EN_HER_07_3(2): 45 2.08812 3.241851e-14 EN_HER_09_1(1): 77 2.08812 1.332268e-14 EN_HER_09_1(2): 77 2.08812 1.332268e-14 EN_HER_11_1(1): 151 2.08812 2.131628e-14 EN_HER_11_1(2): 151 2.08812 2.220446e-14 EXACT: 2.08812 N = 3 EXPON = 8 0 0 Degree = 8 EN_HER_09_1(1): 77 36.5422 6.181722e-13 EN_HER_09_1(2): 77 36.5422 6.181722e-13 EN_HER_11_1(1): 151 36.5422 4.263256e-14 EN_HER_11_1(2): 151 36.5422 2.771117e-13 EXACT: 36.5422 N = 3 EXPON = 0 10 0 Degree = 10 EN_HER_11_1(1): 151 164.44 8.242296e-13 EN_HER_11_1(2): 151 164.44 8.810730e-13 EXACT: 164.44 N = 3 EXPON = 1 2 3 Degree = 6 EN_HER_07_1(1): 27 0 0.000000e+00 EN_HER_07_1(2): 27 0 0.000000e+00 EN_HER_07_2: 52 0 0.000000e+00 EN_HER_07_3(1): 45 0 0.000000e+00 EN_HER_07_3(2): 45 0 0.000000e+00 EN_HER_09_1(1): 77 3.46945e-18 3.469447e-18 EN_HER_09_1(2): 77 3.46945e-18 3.469447e-18 EN_HER_11_1(1): 151 0 0.000000e+00 EN_HER_11_1(2): 151 0 0.000000e+00 EXACT: 0 N = 3 EXPON = 2 2 2 Degree = 6 EN_HER_07_1(1): 27 0.696041 2.220446e-16 EN_HER_07_1(2): 27 0.696041 3.330669e-16 EN_HER_07_2: 52 0.696041 8.881784e-16 EN_HER_07_3(1): 45 0.696041 5.551115e-16 EN_HER_07_3(2): 45 0.696041 1.165734e-14 EN_HER_09_1(1): 77 0.696041 1.554312e-15 EN_HER_09_1(2): 77 0.696041 1.554312e-15 EN_HER_11_1(1): 151 0.696041 6.106227e-15 EN_HER_11_1(2): 151 0.696041 6.772360e-15 EXACT: 0.696041 N = 4 EXPON = 0 0 0 0 Degree = 0 EN_HER_01_1: 1 9.8696 3.552714e-15 EN_HER_02_XIU: 5 9.8696 7.105427e-15 GW_02_XIU: 5 9.8696 7.105427e-15 EN_HER_03_1: 8 9.8696 3.552714e-15 EN_HER_03_2: 16 9.8696 1.776357e-15 EN_HER_03_XIU: 8 9.8696 3.552714e-15 EN_HER_05_1(1): 22 9.8696 7.105427e-15 EN_HER_05_2: 33 9.8696 5.329071e-15 EN_HER_05_3: 24 9.8696 3.552714e-15 EN_HER_05_4: 31 9.8696 3.552714e-15 EN_HER_05_5: 65 9.8696 3.552714e-15 EN_HER_07_1(1): 49 9.8696 3.552714e-15 EN_HER_07_1(2): 49 9.8696 3.552714e-15 EN_HER_07_2: 96 9.8696 3.552714e-15 EN_HER_07_3(1): 97 9.8696 1.136868e-12 EN_HER_07_3(2): 97 9.8696 3.552714e-14 EN_HER_09_1(1): 193 9.8696 3.552714e-14 EN_HER_09_1(2): 193 9.8696 3.552714e-15 EN_HER_11_1(1): 417 9.8696 1.676881e-12 EN_HER_11_1(2): 417 9.8696 4.973799e-13 EXACT: 9.8696 N = 4 EXPON = 2 0 0 0 Degree = 2 EN_HER_02_XIU: 5 4.9348 1.776357e-15 GW_02_XIU: 5 4.9348 1.776357e-15 EN_HER_03_1: 8 4.9348 8.881784e-16 EN_HER_03_2: 16 4.9348 8.881784e-16 EN_HER_03_XIU: 8 4.9348 1.776357e-15 EN_HER_05_1(1): 22 4.9348 3.552714e-15 EN_HER_05_2: 33 4.9348 2.664535e-15 EN_HER_05_3: 24 4.9348 8.881784e-16 EN_HER_05_4: 31 4.9348 2.664535e-15 EN_HER_05_5: 65 4.9348 1.776357e-15 EN_HER_07_1(1): 49 4.9348 3.552714e-15 EN_HER_07_1(2): 49 4.9348 3.552714e-15 EN_HER_07_2: 96 4.9348 1.776357e-15 EN_HER_07_3(1): 97 4.9348 1.278977e-13 EN_HER_07_3(2): 97 4.9348 1.953993e-14 EN_HER_09_1(1): 193 4.9348 1.509903e-14 EN_HER_09_1(2): 193 4.9348 3.552714e-15 EN_HER_11_1(1): 417 4.9348 2.309264e-14 EN_HER_11_1(2): 417 4.9348 6.217249e-14 EXACT: 4.9348 N = 4 EXPON = 0 4 0 0 Degree = 4 EN_HER_05_1(1): 22 7.4022 9.769963e-15 EN_HER_05_2: 33 7.4022 2.664535e-15 EN_HER_05_3: 24 7.4022 8.881784e-16 EN_HER_05_4: 31 7.4022 2.664535e-15 EN_HER_05_5: 65 7.4022 8.881784e-16 EN_HER_07_1(1): 49 7.4022 0.000000e+00 EN_HER_07_1(2): 49 7.4022 8.881784e-16 EN_HER_07_2: 96 7.4022 8.881784e-16 EN_HER_07_3(1): 97 7.4022 1.127987e-13 EN_HER_07_3(2): 97 7.4022 8.437695e-14 EN_HER_09_1(1): 193 7.4022 4.707346e-14 EN_HER_09_1(2): 193 7.4022 3.463896e-14 EN_HER_11_1(1): 417 7.4022 7.194245e-14 EN_HER_11_1(2): 417 7.4022 4.884981e-14 EXACT: 7.4022 N = 4 EXPON = 0 0 6 0 Degree = 6 EN_HER_07_1(1): 49 18.5055 7.105427e-15 EN_HER_07_1(2): 49 18.5055 7.105427e-15 EN_HER_07_2: 96 18.5055 1.065814e-14 EN_HER_07_3(1): 97 18.5055 3.410605e-13 EN_HER_07_3(2): 97 18.5055 3.375078e-13 EN_HER_09_1(1): 193 18.5055 2.131628e-13 EN_HER_09_1(2): 193 18.5055 2.025047e-13 EN_HER_11_1(1): 417 18.5055 2.415845e-13 EN_HER_11_1(2): 417 18.5055 2.025047e-13 EXACT: 18.5055 N = 4 EXPON = 2 4 0 0 Degree = 6 EN_HER_07_1(1): 49 3.7011 0.000000e+00 EN_HER_07_1(2): 49 3.7011 0.000000e+00 EN_HER_07_2: 96 3.7011 1.332268e-15 EN_HER_07_3(1): 97 3.7011 5.861978e-14 EN_HER_07_3(2): 97 3.7011 6.128431e-14 EN_HER_09_1(1): 193 3.7011 2.531308e-14 EN_HER_09_1(2): 193 3.7011 2.087219e-14 EN_HER_11_1(1): 417 3.7011 1.820766e-14 EN_HER_11_1(2): 417 3.7011 3.863576e-14 EXACT: 3.7011 N = 4 EXPON = 0 0 0 8 Degree = 8 EN_HER_09_1(1): 193 64.7693 1.080025e-12 EN_HER_09_1(2): 193 64.7693 1.051603e-12 EN_HER_11_1(1): 417 64.7693 8.668621e-13 EN_HER_11_1(2): 417 64.7693 5.400125e-13 EXACT: 64.7693 N = 4 EXPON = 10 0 0 0 Degree = 10 EN_HER_11_1(1): 417 291.462 3.183231e-12 EN_HER_11_1(2): 417 291.462 2.046363e-12 EXACT: 291.462 N = 4 EXPON = 1 2 3 4 Degree = 10 EN_HER_11_1(1): 417 0 0.000000e+00 EN_HER_11_1(2): 417 0 0.000000e+00 EXACT: 0 N = 4 EXPON = 2 2 2 2 Degree = 8 EN_HER_09_1(1): 193 0.61685 1.232348e-14 EN_HER_09_1(2): 193 0.61685 5.551115e-16 EN_HER_11_1(1): 417 0.61685 6.661338e-16 EN_HER_11_1(2): 417 0.61685 1.443290e-14 EXACT: 0.61685 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 17.4934 7.105427e-15 EN_HER_02_XIU: 6 17.4934 1.421085e-14 GW_02_XIU: 6 17.4934 1.421085e-14 EN_HER_03_1: 10 17.4934 7.105427e-15 EN_HER_03_2: 32 17.4934 1.065814e-14 EN_HER_03_XIU: 10 17.4934 7.105427e-15 EN_HER_05_1(1): 32 17.4934 1.421085e-14 EN_HER_05_1(2): 32 17.4934 2.131628e-14 EN_HER_05_2: 51 17.4934 7.105427e-15 EN_HER_05_3: 42 17.4934 1.065814e-14 EN_HER_05_4: 63 17.4934 3.552714e-15 EN_HER_05_5: 161 17.4934 3.552714e-15 EN_HER_05_6: 192 17.4934 7.105427e-15 EN_HER_07_2: 164 17.4934 7.105427e-15 EN_HER_07_3(1): 181 17.4934 2.291500e-12 EN_HER_07_3(2): 181 17.4934 5.364598e-13 EN_HER_09_1(1): 421 17.4934 7.105427e-15 EN_HER_09_1(2): 421 17.4934 2.131628e-14 EN_HER_11_1(1): 983 17.4934 8.791901e-11 EN_HER_11_1(2): 983 17.4934 4.906298e-12 EXACT: 17.4934 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EN_HER_02_XIU: 6 8.74671 1.776357e-15 GW_02_XIU: 6 8.74671 1.776357e-15 EN_HER_03_1: 10 8.74671 1.776357e-15 EN_HER_03_2: 32 8.74671 5.329071e-15 EN_HER_03_XIU: 10 8.74671 3.552714e-15 EN_HER_05_1(1): 32 8.74671 3.357314e-13 EN_HER_05_1(2): 32 8.74671 2.664535e-14 EN_HER_05_2: 51 8.74671 1.776357e-15 EN_HER_05_3: 42 8.74671 0.000000e+00 EN_HER_05_4: 63 8.74671 5.329071e-15 EN_HER_05_5: 161 8.74671 5.329071e-15 EN_HER_05_6: 192 8.74671 3.552714e-15 EN_HER_07_2: 164 8.74671 3.552714e-15 EN_HER_07_3(1): 181 8.74671 3.925749e-13 EN_HER_07_3(2): 181 8.74671 2.842171e-14 EN_HER_09_1(1): 421 8.74671 1.065814e-14 EN_HER_09_1(2): 421 8.74671 1.776357e-15 EN_HER_11_1(1): 983 8.74671 7.338130e-12 EN_HER_11_1(2): 983 8.74671 4.636291e-13 EXACT: 8.74671 N = 5 EXPON = 0 4 0 0 0 Degree = 4 EN_HER_05_1(1): 32 13.1201 4.565237e-13 EN_HER_05_1(2): 32 13.1201 7.993606e-14 EN_HER_05_2: 51 13.1201 1.776357e-15 EN_HER_05_3: 42 13.1201 1.243450e-14 EN_HER_05_4: 63 13.1201 1.776357e-15 EN_HER_05_5: 161 13.1201 8.881784e-15 EN_HER_05_6: 192 13.1201 5.329071e-15 EN_HER_07_2: 164 13.1201 1.776357e-15 EN_HER_07_3(1): 181 13.1201 2.522427e-13 EN_HER_07_3(2): 181 13.1201 1.580958e-13 EN_HER_09_1(1): 421 13.1201 5.861978e-14 EN_HER_09_1(2): 421 13.1201 5.329071e-14 EN_HER_11_1(1): 983 13.1201 1.554312e-12 EN_HER_11_1(2): 983 13.1201 1.776357e-15 EXACT: 13.1201 N = 5 EXPON = 0 0 6 0 0 Degree = 6 EN_HER_07_2: 164 32.8002 7.105427e-15 EN_HER_07_3(1): 181 32.8002 6.110668e-13 EN_HER_07_3(2): 181 32.8002 6.323830e-13 EN_HER_09_1(1): 421 32.8002 3.197442e-13 EN_HER_09_1(2): 421 32.8002 3.410605e-13 EN_HER_11_1(1): 983 32.8002 6.608047e-13 EN_HER_11_1(2): 983 32.8002 2.771117e-13 EXACT: 32.8002 N = 5 EXPON = 2 4 0 0 0 Degree = 6 EN_HER_07_2: 164 6.56003 2.664535e-15 EN_HER_07_3(1): 181 6.56003 1.199041e-13 EN_HER_07_3(2): 181 6.56003 1.199041e-13 EN_HER_09_1(1): 421 6.56003 3.996803e-14 EN_HER_09_1(2): 421 6.56003 2.930989e-14 EN_HER_11_1(1): 983 6.56003 1.394440e-13 EN_HER_11_1(2): 983 6.56003 4.973799e-14 EXACT: 6.56003 N = 5 EXPON = 0 0 0 8 0 Degree = 8 EN_HER_09_1(1): 421 114.801 1.705303e-12 EN_HER_09_1(2): 421 114.801 1.804779e-12 EN_HER_11_1(1): 983 114.801 1.250555e-12 EN_HER_11_1(2): 983 114.801 1.080025e-12 EXACT: 114.801 N = 5 EXPON = 0 0 0 0 10 Degree = 10 EN_HER_11_1(1): 983 516.603 1.818989e-12 EN_HER_11_1(2): 983 516.603 2.273737e-12 EXACT: 516.603 N = 5 EXPON = 1 2 3 4 5 Degree = 15 EXACT: 0 N = 5 EXPON = 2 2 2 2 2 Degree = 10 EN_HER_11_1(1): 983 0.546669 3.441691e-15 EN_HER_11_1(2): 983 0.546669 3.441691e-15 EXACT: 0.546669 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 31.0063 1.776357e-14 EN_HER_02_XIU: 7 31.0063 2.842171e-14 GW_02_XIU: 7 31.0063 2.842171e-14 EN_HER_03_1: 12 31.0063 2.131628e-14 EN_HER_03_2: 64 31.0063 1.776357e-14 EN_HER_03_XIU: 12 31.0063 2.131628e-14 EN_HER_05_1(1): 44 31.0063 1.421085e-14 EN_HER_05_1(2): 44 31.0063 1.421085e-14 EN_HER_05_2: 73 31.0063 2.131628e-14 EN_HER_05_3: 76 31.0063 1.776357e-14 EN_HER_05_4: 127 31.0063 1.776357e-14 EN_HER_05_5: 385 31.0063 1.421085e-14 EN_HER_05_6: 448 31.0063 1.065814e-14 EN_HER_07_1(1): 137 31.0063 1.421085e-14 EN_HER_07_2: 272 31.0063 2.131628e-14 EN_HER_07_3(1): 305 31.0063 2.000888e-11 EN_HER_07_3(2): 305 31.0063 1.477929e-12 EN_HER_09_1(1): 825 31.0063 1.598721e-13 EN_HER_09_1(2): 825 31.0063 4.973799e-14 EXACT: 31.0063 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 7 15.5031 1.065814e-14 GW_02_XIU: 7 15.5031 1.065814e-14 EN_HER_03_1: 12 15.5031 1.065814e-14 EN_HER_03_2: 64 15.5031 5.329071e-15 EN_HER_03_XIU: 12 15.5031 8.881784e-15 EN_HER_05_1(1): 44 15.5031 6.039613e-14 EN_HER_05_1(2): 44 15.5031 1.776357e-14 EN_HER_05_2: 73 15.5031 3.552714e-15 EN_HER_05_3: 76 15.5031 5.329071e-15 EN_HER_05_4: 127 15.5031 1.065814e-14 EN_HER_05_5: 385 15.5031 1.065814e-14 EN_HER_05_6: 448 15.5031 1.776357e-14 EN_HER_07_1(1): 137 15.5031 3.552714e-15 EN_HER_07_2: 272 15.5031 8.881784e-15 EN_HER_07_3(1): 305 15.5031 2.671641e-12 EN_HER_07_3(2): 305 15.5031 2.486900e-14 EN_HER_09_1(1): 825 15.5031 2.131628e-14 EN_HER_09_1(2): 825 15.5031 5.861978e-14 EXACT: 15.5031 N = 6 EXPON = 0 4 0 0 0 0 Degree = 4 EN_HER_05_1(1): 44 23.2547 2.238210e-13 EN_HER_05_1(2): 44 23.2547 1.527667e-13 EN_HER_05_2: 73 23.2547 0.000000e+00 EN_HER_05_3: 76 23.2547 3.552714e-15 EN_HER_05_4: 127 23.2547 3.552714e-15 EN_HER_05_5: 385 23.2547 7.105427e-15 EN_HER_05_6: 448 23.2547 7.105427e-15 EN_HER_07_1(1): 137 23.2547 0.000000e+00 EN_HER_07_2: 272 23.2547 7.105427e-15 EN_HER_07_3(1): 305 23.2547 9.876544e-13 EN_HER_07_3(2): 305 23.2547 2.486900e-13 EN_HER_09_1(1): 825 23.2547 7.815970e-14 EN_HER_09_1(2): 825 23.2547 1.563194e-13 EXACT: 23.2547 N = 6 EXPON = 0 0 6 0 0 0 Degree = 6 EN_HER_07_1(1): 137 58.1368 2.842171e-14 EN_HER_07_2: 272 58.1368 4.973799e-14 EN_HER_07_3(1): 305 58.1368 1.172396e-12 EN_HER_07_3(2): 305 58.1368 1.030287e-12 EN_HER_09_1(1): 825 58.1368 5.826450e-13 EN_HER_09_1(2): 825 58.1368 6.323830e-13 EXACT: 58.1368 N = 6 EXPON = 2 4 0 0 0 0 Degree = 6 EN_HER_07_1(1): 137 11.6274 3.552714e-15 EN_HER_07_2: 272 11.6274 7.105427e-15 EN_HER_07_3(1): 305 11.6274 2.238210e-13 EN_HER_07_3(2): 305 11.6274 2.149392e-13 EN_HER_09_1(1): 825 11.6274 3.907985e-14 EN_HER_09_1(2): 825 11.6274 9.237056e-14 EXACT: 11.6274 N = 6 EXPON = 0 0 0 8 0 0 Degree = 8 EN_HER_09_1(1): 825 203.479 2.927436e-12 EN_HER_09_1(2): 825 203.479 3.325340e-12 EXACT: 203.479 N = 6 EXPON = 0 0 0 0 10 0 Degree = 10 EXACT: 915.654 N = 6 EXPON = 1 2 3 4 5 6 Degree = 21 EXACT: 0 N = 6 EXPON = 2 2 2 2 2 2 Degree = 12 EXACT: 0.484473 N = 7 EXPON = 0 0 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 54.9572 2.842171e-14 EN_HER_02_XIU: 8 54.9572 5.684342e-14 GW_02_XIU: 8 54.9572 5.684342e-14 EN_HER_03_1: 14 54.9572 2.131628e-14 EN_HER_03_2: 128 54.9572 2.842171e-14 EN_HER_03_XIU: 14 54.9572 2.131628e-14 EN_HER_05_1(1): 58 54.9572 7.105427e-15 EN_HER_05_2: 99 54.9572 2.842171e-14 EN_HER_05_3: 142 54.9572 1.421085e-14 EN_HER_05_4: 255 54.9572 2.131628e-14 EN_HER_05_5: 897 54.9572 6.394885e-14 EN_HER_05_6: 1024 54.9572 7.105427e-15 EN_HER_07_1(1): 227 54.9572 2.842171e-14 EN_HER_07_2: 452 54.9572 2.842171e-14 EXACT: 54.9572 N = 7 EXPON = 2 0 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 8 27.4786 2.131628e-14 GW_02_XIU: 8 27.4786 2.131628e-14 EN_HER_03_1: 14 27.4786 1.421085e-14 EN_HER_03_2: 128 27.4786 7.105427e-15 EN_HER_03_XIU: 14 27.4786 1.421085e-14 EN_HER_05_1(1): 58 27.4786 1.172396e-13 EN_HER_05_2: 99 27.4786 1.421085e-14 EN_HER_05_3: 142 27.4786 1.421085e-14 EN_HER_05_4: 255 27.4786 1.776357e-14 EN_HER_05_5: 897 27.4786 2.131628e-14 EN_HER_05_6: 1024 27.4786 3.197442e-14 EN_HER_07_1(1): 227 27.4786 1.065814e-14 EN_HER_07_2: 452 27.4786 2.486900e-14 EXACT: 27.4786 N = 7 EXPON = 0 4 0 0 0 0 0 Degree = 4 EN_HER_05_1(1): 58 41.2179 4.902745e-13 EN_HER_05_2: 99 41.2179 7.105427e-15 EN_HER_05_3: 142 41.2179 2.131628e-14 EN_HER_05_4: 255 41.2179 7.105427e-15 EN_HER_05_5: 897 41.2179 7.105427e-15 EN_HER_05_6: 1024 41.2179 4.263256e-14 EN_HER_07_1(1): 227 41.2179 7.105427e-15 EN_HER_07_2: 452 41.2179 2.131628e-14 EXACT: 41.2179 N = 7 EXPON = 0 0 6 0 0 0 0 Degree = 6 EN_HER_07_1(1): 227 103.045 5.684342e-14 EN_HER_07_2: 452 103.045 4.263256e-14 EXACT: 103.045 N = 7 EXPON = 2 4 0 0 0 0 0 Degree = 6 EN_HER_07_1(1): 227 20.6089 1.065814e-14 EN_HER_07_2: 452 20.6089 1.065814e-14 EXACT: 20.6089 N = 7 EXPON = 0 0 0 8 0 0 0 Degree = 8 EXACT: 360.657 N = 7 EXPON = 0 0 0 0 10 0 0 Degree = 10 EXACT: 1622.95 N = 7 EXPON = 1 2 3 4 5 6 7 Degree = 28 EXACT: 0 N = 7 EXPON = 2 2 2 2 2 2 2 Degree = 14 EXACT: 0.429353 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 = -0.500000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 1.77245 0.000000e+00 EPN_GLG_01_1: 1 1.77245 0.000000e+00 EPN_GLG_02_XIU: 2 1.77245 0.000000e+00 GW_02_XIU: 2 1.77245 0.000000e+00 EXACT: 1.77245 N = 1 ALPHA = 0.000000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 2 1 0.000000e+00 GW_02_XIU: 2 1 0.000000e+00 EXACT: 1 N = 1 ALPHA = 0.500000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 0.886227 0.000000e+00 EPN_GLG_01_1: 1 0.886227 0.000000e+00 EPN_GLG_02_XIU: 2 0.886227 0.000000e+00 GW_02_XIU: 2 0.886227 0.000000e+00 EXACT: 0.886227 N = 1 ALPHA = 1.000000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 2 1 0.000000e+00 GW_02_XIU: 2 1 0.000000e+00 EXACT: 1 N = 1 ALPHA = 2.000000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 2 0.000000e+00 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = -0.500000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 0.886227 0.000000e+00 EPN_GLG_02_XIU: 2 0.886227 2.220446e-16 GW_02_XIU: 2 0.886227 2.220446e-16 EXACT: 0.886227 N = 1 ALPHA = 0.000000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 2 1 0.000000e+00 GW_02_XIU: 2 1 0.000000e+00 EXACT: 1 N = 1 ALPHA = 0.500000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1.32934 0.000000e+00 EPN_GLG_02_XIU: 2 1.32934 0.000000e+00 GW_02_XIU: 2 1.32934 0.000000e+00 EXACT: 1.32934 N = 1 ALPHA = 1.000000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = 2.000000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 6 0.000000e+00 EPN_GLG_02_XIU: 2 6 0.000000e+00 GW_02_XIU: 2 6 0.000000e+00 EXACT: 6 N = 1 ALPHA = -0.500000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 1.32934 0.000000e+00 GW_02_XIU: 2 1.32934 0.000000e+00 EXACT: 1.32934 N = 1 ALPHA = 0.000000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 1 ALPHA = 0.500000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 3.32335 0.000000e+00 GW_02_XIU: 2 3.32335 0.000000e+00 EXACT: 3.32335 N = 1 ALPHA = 1.000000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 6 0.000000e+00 GW_02_XIU: 2 6 0.000000e+00 EXACT: 6 N = 1 ALPHA = 2.000000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 24 7.105427e-15 GW_02_XIU: 2 24 7.105427e-15 EXACT: 24 N = 2 ALPHA = -0.500000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 3.14159 0.000000e+00 EPN_GLG_01_1: 1 3.14159 0.000000e+00 EPN_GLG_02_XIU: 3 3.14159 0.000000e+00 GW_02_XIU: 3 3.14159 0.000000e+00 EXACT: 3.14159 N = 2 ALPHA = 0.000000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 3 1 0.000000e+00 GW_02_XIU: 3 1 0.000000e+00 EXACT: 1 N = 2 ALPHA = 0.500000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 0.785398 0.000000e+00 EPN_GLG_01_1: 1 0.785398 0.000000e+00 EPN_GLG_02_XIU: 3 0.785398 0.000000e+00 GW_02_XIU: 3 0.785398 0.000000e+00 EXACT: 0.785398 N = 2 ALPHA = 1.000000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 3 1 0.000000e+00 GW_02_XIU: 3 1 0.000000e+00 EXACT: 1 N = 2 ALPHA = 2.000000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 4 0.000000e+00 EPN_GLG_01_1: 1 4 0.000000e+00 EPN_GLG_02_XIU: 3 4 0.000000e+00 GW_02_XIU: 3 4 0.000000e+00 EXACT: 4 N = 2 ALPHA = -0.500000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.5708 0.000000e+00 EPN_GLG_02_XIU: 3 1.5708 2.220446e-16 GW_02_XIU: 3 1.5708 2.220446e-16 EXACT: 1.5708 N = 2 ALPHA = 0.000000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 3 1 2.220446e-16 GW_02_XIU: 3 1 2.220446e-16 EXACT: 1 N = 2 ALPHA = 0.500000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.1781 2.220446e-16 EPN_GLG_02_XIU: 3 1.1781 2.220446e-16 GW_02_XIU: 3 1.1781 2.220446e-16 EXACT: 1.1781 N = 2 ALPHA = 1.000000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 3 2 4.440892e-16 GW_02_XIU: 3 2 4.440892e-16 EXACT: 2 N = 2 ALPHA = 2.000000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 12 0.000000e+00 EPN_GLG_02_XIU: 3 12 1.776357e-15 GW_02_XIU: 3 12 1.776357e-15 EXACT: 12 N = 2 ALPHA = -0.500000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 0.785398 3.330669e-16 GW_02_XIU: 3 0.785398 3.330669e-16 EXACT: 0.785398 N = 2 ALPHA = 0.000000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1 4.440892e-16 GW_02_XIU: 3 1 4.440892e-16 EXACT: 1 N = 2 ALPHA = 0.500000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1.76715 6.661338e-16 GW_02_XIU: 3 1.76715 6.661338e-16 EXACT: 1.76715 N = 2 ALPHA = 1.000000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 4 8.881784e-16 GW_02_XIU: 3 4 8.881784e-16 EXACT: 4 N = 2 ALPHA = 2.000000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 36 0.000000e+00 GW_02_XIU: 3 36 0.000000e+00 EXACT: 36 N = 2 ALPHA = -0.500000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.35619 8.881784e-16 GW_02_XIU: 3 2.35619 8.881784e-16 EXACT: 2.35619 N = 2 ALPHA = 0.000000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2 8.881784e-16 GW_02_XIU: 3 2 8.881784e-16 EXACT: 2 N = 2 ALPHA = 0.500000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.94524 4.440892e-16 GW_02_XIU: 3 2.94524 4.440892e-16 EXACT: 2.94524 N = 2 ALPHA = 1.000000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 6 8.881784e-16 GW_02_XIU: 3 6 8.881784e-16 EXACT: 6 N = 2 ALPHA = 2.000000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 48 7.105427e-15 GW_02_XIU: 3 48 7.105427e-15 EXACT: 48 N = 3 ALPHA = -0.500000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 5.56833 0.000000e+00 EPN_GLG_01_1: 1 5.56833 0.000000e+00 EPN_GLG_02_XIU: 4 5.56833 0.000000e+00 GW_02_XIU: 4 5.56833 0.000000e+00 EXACT: 5.56833 N = 3 ALPHA = 0.000000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 4 1 0.000000e+00 GW_02_XIU: 4 1 0.000000e+00 EXACT: 1 N = 3 ALPHA = 0.500000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.696041 0.000000e+00 EPN_GLG_01_1: 1 0.696041 0.000000e+00 EPN_GLG_02_XIU: 4 0.696041 0.000000e+00 GW_02_XIU: 4 0.696041 0.000000e+00 EXACT: 0.696041 N = 3 ALPHA = 1.000000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 4 1 0.000000e+00 GW_02_XIU: 4 1 0.000000e+00 EXACT: 1 N = 3 ALPHA = 2.000000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 8 0.000000e+00 EPN_GLG_01_1: 1 8 0.000000e+00 EPN_GLG_02_XIU: 4 8 0.000000e+00 GW_02_XIU: 4 8 0.000000e+00 EXACT: 8 N = 3 ALPHA = -0.500000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.78416 0.000000e+00 EPN_GLG_02_XIU: 4 2.78416 0.000000e+00 GW_02_XIU: 4 2.78416 0.000000e+00 EXACT: 2.78416 N = 3 ALPHA = 0.000000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 4 1 0.000000e+00 GW_02_XIU: 4 1 0.000000e+00 EXACT: 1 N = 3 ALPHA = 0.500000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.04406 0.000000e+00 EPN_GLG_02_XIU: 4 1.04406 0.000000e+00 GW_02_XIU: 4 1.04406 0.000000e+00 EXACT: 1.04406 N = 3 ALPHA = 1.000000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 4 2 0.000000e+00 GW_02_XIU: 4 2 0.000000e+00 EXACT: 2 N = 3 ALPHA = 2.000000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 24 0.000000e+00 EPN_GLG_02_XIU: 4 24 0.000000e+00 GW_02_XIU: 4 24 0.000000e+00 EXACT: 24 N = 3 ALPHA = -0.500000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.39208 2.220446e-16 GW_02_XIU: 4 1.39208 2.220446e-16 EXACT: 1.39208 N = 3 ALPHA = 0.000000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1 1.110223e-16 GW_02_XIU: 4 1 1.110223e-16 EXACT: 1 N = 3 ALPHA = 0.500000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.56609 4.440892e-16 GW_02_XIU: 4 1.56609 4.440892e-16 EXACT: 1.56609 N = 3 ALPHA = 1.000000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 4 4.440892e-16 GW_02_XIU: 4 4 4.440892e-16 EXACT: 4 N = 3 ALPHA = 2.000000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 72 0.000000e+00 GW_02_XIU: 4 72 0.000000e+00 EXACT: 72 N = 3 ALPHA = -0.500000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 4.17625 2.664535e-15 GW_02_XIU: 4 4.17625 2.664535e-15 EXACT: 4.17625 N = 3 ALPHA = 0.000000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2 0.000000e+00 GW_02_XIU: 4 2 0.000000e+00 EXACT: 2 N = 3 ALPHA = 0.500000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2.61015 4.440892e-16 GW_02_XIU: 4 2.61015 4.440892e-16 EXACT: 2.61015 N = 3 ALPHA = 1.000000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 6 0.000000e+00 GW_02_XIU: 4 6 0.000000e+00 EXACT: 6 N = 3 ALPHA = 2.000000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 96 2.842171e-14 GW_02_XIU: 4 96 2.842171e-14 EXACT: 96 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 9.8696 1.776357e-15 EPN_GLG_01_1: 1 9.8696 1.776357e-15 EPN_GLG_02_XIU: 5 9.8696 0.000000e+00 GW_02_XIU: 5 9.8696 0.000000e+00 EXACT: 9.8696 N = 4 ALPHA = 0.000000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 5 1 0.000000e+00 GW_02_XIU: 5 1 0.000000e+00 EXACT: 1 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.61685 1.110223e-16 EPN_GLG_01_1: 1 0.61685 1.110223e-16 EPN_GLG_02_XIU: 5 0.61685 0.000000e+00 GW_02_XIU: 5 0.61685 0.000000e+00 EXACT: 0.61685 N = 4 ALPHA = 1.000000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 5 1 0.000000e+00 GW_02_XIU: 5 1 0.000000e+00 EXACT: 1 N = 4 ALPHA = 2.000000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 16 0.000000e+00 EPN_GLG_01_1: 1 16 0.000000e+00 EPN_GLG_02_XIU: 5 16 0.000000e+00 GW_02_XIU: 5 16 0.000000e+00 EXACT: 16 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 4.9348 8.881784e-16 EPN_GLG_02_XIU: 5 4.9348 1.776357e-15 GW_02_XIU: 5 4.9348 1.776357e-15 EXACT: 4.9348 N = 4 ALPHA = 0.000000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 5 1 1.110223e-16 GW_02_XIU: 5 1 1.110223e-16 EXACT: 1 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.925275 1.110223e-16 EPN_GLG_02_XIU: 5 0.925275 1.110223e-16 GW_02_XIU: 5 0.925275 1.110223e-16 EXACT: 0.925275 N = 4 ALPHA = 1.000000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 5 2 0.000000e+00 GW_02_XIU: 5 2 0.000000e+00 EXACT: 2 N = 4 ALPHA = 2.000000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 48 0.000000e+00 EPN_GLG_02_XIU: 5 48 0.000000e+00 GW_02_XIU: 5 48 0.000000e+00 EXACT: 48 N = 4 ALPHA = -0.500000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.4674 4.440892e-16 GW_02_XIU: 5 2.4674 4.440892e-16 EXACT: 2.4674 N = 4 ALPHA = 0.000000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1 0.000000e+00 GW_02_XIU: 5 1 0.000000e+00 EXACT: 1 N = 4 ALPHA = 0.500000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1.38791 4.440892e-16 GW_02_XIU: 5 1.38791 4.440892e-16 EXACT: 1.38791 N = 4 ALPHA = 1.000000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 4 0.000000e+00 GW_02_XIU: 5 4 0.000000e+00 EXACT: 4 N = 4 ALPHA = 2.000000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 144 0.000000e+00 GW_02_XIU: 5 144 0.000000e+00 EXACT: 144 N = 4 ALPHA = -0.500000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 7.4022 2.664535e-15 GW_02_XIU: 5 7.4022 2.664535e-15 EXACT: 7.4022 N = 4 ALPHA = 0.000000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2 0.000000e+00 GW_02_XIU: 5 2 0.000000e+00 EXACT: 2 N = 4 ALPHA = 0.500000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.31319 0.000000e+00 GW_02_XIU: 5 2.31319 0.000000e+00 EXACT: 2.31319 N = 4 ALPHA = 1.000000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 6 0.000000e+00 GW_02_XIU: 5 6 0.000000e+00 EXACT: 6 N = 4 ALPHA = 2.000000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 192 0.000000e+00 GW_02_XIU: 5 192 0.000000e+00 EXACT: 192 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 17.4934 3.552714e-15 EPN_GLG_01_1: 1 17.4934 3.552714e-15 EPN_GLG_02_XIU: 6 17.4934 3.552714e-15 GW_02_XIU: 6 17.4934 3.552714e-15 EXACT: 17.4934 N = 5 ALPHA = 0.000000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 6 1 0.000000e+00 GW_02_XIU: 6 1 0.000000e+00 EXACT: 1 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.546669 1.110223e-16 EPN_GLG_01_1: 1 0.546669 1.110223e-16 EPN_GLG_02_XIU: 6 0.546669 1.110223e-16 GW_02_XIU: 6 0.546669 1.110223e-16 EXACT: 0.546669 N = 5 ALPHA = 1.000000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 6 1 0.000000e+00 GW_02_XIU: 6 1 0.000000e+00 EXACT: 1 N = 5 ALPHA = 2.000000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 32 0.000000e+00 EPN_GLG_01_1: 1 32 0.000000e+00 EPN_GLG_02_XIU: 6 32 0.000000e+00 GW_02_XIU: 6 32 0.000000e+00 EXACT: 32 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 8.74671 1.776357e-15 EPN_GLG_02_XIU: 6 8.74671 1.776357e-15 GW_02_XIU: 6 8.74671 1.776357e-15 EXACT: 8.74671 N = 5 ALPHA = 0.000000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 6 1 0.000000e+00 GW_02_XIU: 6 1 0.000000e+00 EXACT: 1 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.820004 1.110223e-16 EPN_GLG_02_XIU: 6 0.820004 1.110223e-16 GW_02_XIU: 6 0.820004 1.110223e-16 EXACT: 0.820004 N = 5 ALPHA = 1.000000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 6 2 0.000000e+00 GW_02_XIU: 6 2 0.000000e+00 EXACT: 2 N = 5 ALPHA = 2.000000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 96 0.000000e+00 EPN_GLG_02_XIU: 6 96 1.421085e-14 GW_02_XIU: 6 96 1.421085e-14 EXACT: 96 N = 5 ALPHA = -0.500000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4.37335 0.000000e+00 GW_02_XIU: 6 4.37335 0.000000e+00 EXACT: 4.37335 N = 5 ALPHA = 0.000000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1 2.220446e-16 GW_02_XIU: 6 1 2.220446e-16 EXACT: 1 N = 5 ALPHA = 0.500000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1.23001 2.220446e-16 GW_02_XIU: 6 1.23001 2.220446e-16 EXACT: 1.23001 N = 5 ALPHA = 1.000000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4 0.000000e+00 GW_02_XIU: 6 4 0.000000e+00 EXACT: 4 N = 5 ALPHA = 2.000000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 288 0.000000e+00 GW_02_XIU: 6 288 0.000000e+00 EXACT: 288 N = 5 ALPHA = -0.500000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 13.1201 5.329071e-15 GW_02_XIU: 6 13.1201 5.329071e-15 EXACT: 13.1201 N = 5 ALPHA = 0.000000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2 0.000000e+00 GW_02_XIU: 6 2 0.000000e+00 EXACT: 2 N = 5 ALPHA = 0.500000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2.05001 0.000000e+00 GW_02_XIU: 6 2.05001 0.000000e+00 EXACT: 2.05001 N = 5 ALPHA = 1.000000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 6 0.000000e+00 GW_02_XIU: 6 6 0.000000e+00 EXACT: 6 N = 5 ALPHA = 2.000000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 384 0.000000e+00 GW_02_XIU: 6 384 0.000000e+00 EXACT: 384 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 31.0063 7.105427e-15 EPN_GLG_01_1: 1 31.0063 7.105427e-15 EPN_GLG_02_XIU: 7 31.0063 7.105427e-15 GW_02_XIU: 7 31.0063 7.105427e-15 EXACT: 31.0063 N = 6 ALPHA = 0.000000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 7 1 1.110223e-16 GW_02_XIU: 7 1 1.110223e-16 EXACT: 1 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.484473 1.110223e-16 EPN_GLG_01_1: 1 0.484473 1.110223e-16 EPN_GLG_02_XIU: 7 0.484473 1.110223e-16 GW_02_XIU: 7 0.484473 1.110223e-16 EXACT: 0.484473 N = 6 ALPHA = 1.000000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1 0.000000e+00 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 7 1 1.110223e-16 GW_02_XIU: 7 1 1.110223e-16 EXACT: 1 N = 6 ALPHA = 2.000000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 64 0.000000e+00 EPN_GLG_01_1: 1 64 0.000000e+00 EPN_GLG_02_XIU: 7 64 7.105427e-15 GW_02_XIU: 7 64 7.105427e-15 EXACT: 64 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 15.5031 3.552714e-15 EPN_GLG_02_XIU: 7 15.5031 1.776357e-15 GW_02_XIU: 7 15.5031 1.776357e-15 EXACT: 15.5031 N = 6 ALPHA = 0.000000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1 0.000000e+00 EPN_GLG_02_XIU: 7 1 0.000000e+00 GW_02_XIU: 7 1 0.000000e+00 EXACT: 1 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.72671 2.220446e-16 EPN_GLG_02_XIU: 7 0.72671 1.110223e-16 GW_02_XIU: 7 0.72671 1.110223e-16 EXACT: 0.72671 N = 6 ALPHA = 1.000000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2 0.000000e+00 EPN_GLG_02_XIU: 7 2 0.000000e+00 GW_02_XIU: 7 2 0.000000e+00 EXACT: 2 N = 6 ALPHA = 2.000000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 192 0.000000e+00 EPN_GLG_02_XIU: 7 192 0.000000e+00 GW_02_XIU: 7 192 0.000000e+00 EXACT: 192 N = 6 ALPHA = -0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 7.75157 0.000000e+00 GW_02_XIU: 7 7.75157 0.000000e+00 EXACT: 7.75157 N = 6 ALPHA = 0.000000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1 0.000000e+00 GW_02_XIU: 7 1 0.000000e+00 EXACT: 1 N = 6 ALPHA = 0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.09006 2.220446e-16 GW_02_XIU: 7 1.09006 2.220446e-16 EXACT: 1.09006 N = 6 ALPHA = 1.000000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 4 4.440892e-16 GW_02_XIU: 7 4 4.440892e-16 EXACT: 4 N = 6 ALPHA = 2.000000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 576 0.000000e+00 GW_02_XIU: 7 576 0.000000e+00 EXACT: 576 N = 6 ALPHA = -0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 23.2547 3.552714e-15 GW_02_XIU: 7 23.2547 3.552714e-15 EXACT: 23.2547 N = 6 ALPHA = 0.000000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 2 0.000000e+00 GW_02_XIU: 7 2 0.000000e+00 EXACT: 2 N = 6 ALPHA = 0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.81677 2.220446e-16 GW_02_XIU: 7 1.81677 2.220446e-16 EXACT: 1.81677 N = 6 ALPHA = 1.000000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 6 0.000000e+00 GW_02_XIU: 7 6 0.000000e+00 EXACT: 6 N = 6 ALPHA = 2.000000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 768 1.136868e-13 GW_02_XIU: 7 768 1.136868e-13 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_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 2 1 0.000000e+00 GW_02_XIU: 2 1 0.000000e+00 EXACT: 1 N = 1 EXPON = 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 2 1 0.000000e+00 GW_02_XIU: 2 1 0.000000e+00 EXACT: 1 N = 1 EXPON = 2 Degree = 2 EPN_LAG_02_XIU: 2 2 0.000000e+00 GW_02_XIU: 2 2 0.000000e+00 EXACT: 2 N = 2 EXPON = 0 0 Degree = 0 EPN_LAG_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 3 1 0.000000e+00 GW_02_XIU: 3 1 0.000000e+00 EXACT: 1 N = 2 EXPON = 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 3 1 2.220446e-16 GW_02_XIU: 3 1 2.220446e-16 EXACT: 1 N = 2 EXPON = 1 1 Degree = 2 EPN_LAG_02_XIU: 3 1 4.440892e-16 GW_02_XIU: 3 1 4.440892e-16 EXACT: 1 N = 2 EXPON = 2 0 Degree = 2 EPN_LAG_02_XIU: 3 2 8.881784e-16 GW_02_XIU: 3 2 8.881784e-16 EXACT: 2 N = 3 EXPON = 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 4 1 0.000000e+00 GW_02_XIU: 4 1 0.000000e+00 EXACT: 1 N = 3 EXPON = 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 4 1 0.000000e+00 GW_02_XIU: 4 1 0.000000e+00 EXACT: 1 N = 3 EXPON = 1 1 0 Degree = 2 EPN_LAG_02_XIU: 4 1 1.110223e-16 GW_02_XIU: 4 1 1.110223e-16 EXACT: 1 N = 3 EXPON = 2 0 0 Degree = 2 EPN_LAG_02_XIU: 4 2 0.000000e+00 GW_02_XIU: 4 2 0.000000e+00 EXACT: 2 N = 4 EXPON = 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 5 1 0.000000e+00 GW_02_XIU: 5 1 0.000000e+00 EXACT: 1 N = 4 EXPON = 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 5 1 1.110223e-16 GW_02_XIU: 5 1 1.110223e-16 EXACT: 1 N = 4 EXPON = 1 1 0 0 Degree = 2 EPN_LAG_02_XIU: 5 1 0.000000e+00 GW_02_XIU: 5 1 0.000000e+00 EXACT: 1 N = 4 EXPON = 2 0 0 0 Degree = 2 EPN_LAG_02_XIU: 5 2 0.000000e+00 GW_02_XIU: 5 2 0.000000e+00 EXACT: 2 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 6 1 0.000000e+00 GW_02_XIU: 6 1 0.000000e+00 EXACT: 1 N = 5 EXPON = 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 6 1 0.000000e+00 GW_02_XIU: 6 1 0.000000e+00 EXACT: 1 N = 5 EXPON = 1 1 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 1 2.220446e-16 GW_02_XIU: 6 1 2.220446e-16 EXACT: 1 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 2 0.000000e+00 GW_02_XIU: 6 2 0.000000e+00 EXACT: 2 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1 0.000000e+00 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 7 1 1.110223e-16 GW_02_XIU: 7 1 1.110223e-16 EXACT: 1 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1 0.000000e+00 EPN_LAG_02_XIU: 7 1 0.000000e+00 GW_02_XIU: 7 1 0.000000e+00 EXACT: 1 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 1 0.000000e+00 GW_02_XIU: 7 1 0.000000e+00 EXACT: 1 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 2 0.000000e+00 GW_02_XIU: 7 2 0.000000e+00 EXACT: 2 sandia_cubature_test(): Normal end of execution. 16-Jan-2023 06:12:47