06 April 2023 9:43:35.106 AM sandia_cubature_test(): FORTRAN90 version. 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 Gegenbauer 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 0.00000 CN_GEG_01_1: 1 3.14159 0.00000 CN_GEG_02_XIU: 2 3.14159 0.00000 GW_02_XIU: 2 3.14159 0.399680E-14 CN_GEG_03_XIU: 2 3.14159 0.00000 EXACT: 3.14159 N = 1 ALPHA = 0.00000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 2.00000 0.00000 CN_GEG_01_1: 1 2.00000 0.00000 CN_GEG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.222045E-15 CN_GEG_03_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = 0.500000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.57080 0.00000 CN_GEG_01_1: 1 1.57080 0.00000 CN_GEG_02_XIU: 2 1.57080 0.00000 GW_02_XIU: 2 1.57080 0.133227E-14 CN_GEG_03_XIU: 2 1.57080 0.00000 EXACT: 1.57080 N = 1 ALPHA = 1.00000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.33333 0.00000 CN_GEG_01_1: 1 1.33333 0.00000 CN_GEG_02_XIU: 2 1.33333 0.00000 GW_02_XIU: 2 1.33333 0.00000 CN_GEG_03_XIU: 2 1.33333 0.00000 EXACT: 1.33333 N = 1 ALPHA = 1.50000 EXPON = 0 Degree = 0 CN_GEG_00_1: 1 1.17810 0.00000 CN_GEG_01_1: 1 1.17810 0.00000 CN_GEG_02_XIU: 2 1.17810 0.00000 GW_02_XIU: 2 1.17810 0.888178E-15 CN_GEG_03_XIU: 2 1.17810 0.00000 EXACT: 1.17810 N = 1 ALPHA = -0.500000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_GEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = 0.00000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_GEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = 0.500000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_GEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = 1.00000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_GEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = 1.50000 EXPON = 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_GEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = -0.500000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 1.57080 0.666134E-15 GW_02_XIU: 2 1.57080 0.133227E-14 CN_GEG_03_XIU: 2 1.57080 0.155431E-14 EXACT: 1.57080 N = 1 ALPHA = 0.00000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.666667 0.00000 GW_02_XIU: 2 0.666667 0.111022E-15 CN_GEG_03_XIU: 2 0.666667 0.222045E-15 EXACT: 0.666667 N = 1 ALPHA = 0.500000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.392699 0.277556E-15 GW_02_XIU: 2 0.392699 0.555112E-16 CN_GEG_03_XIU: 2 0.392699 0.277556E-15 EXACT: 0.392699 N = 1 ALPHA = 1.00000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.266667 0.555112E-16 GW_02_XIU: 2 0.266667 0.555112E-16 CN_GEG_03_XIU: 2 0.266667 0.555112E-16 EXACT: 0.266667 N = 1 ALPHA = 1.50000 EXPON = 2 Degree = 2 CN_GEG_02_XIU: 2 0.196350 0.277556E-16 GW_02_XIU: 2 0.196350 0.138778E-15 CN_GEG_03_XIU: 2 0.196350 0.277556E-16 EXACT: 0.196350 N = 2 ALPHA = -0.500000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 9.86960 0.00000 CN_GEG_01_1: 1 9.86960 0.00000 CN_GEG_02_XIU: 3 9.86960 0.00000 GW_02_XIU: 3 9.86960 0.248690E-13 CN_GEG_03_XIU: 4 9.86960 0.00000 EXACT: 9.86960 N = 2 ALPHA = 0.00000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 4.00000 0.00000 CN_GEG_01_1: 1 4.00000 0.00000 CN_GEG_02_XIU: 3 4.00000 0.00000 GW_02_XIU: 3 4.00000 0.888178E-15 CN_GEG_03_XIU: 4 4.00000 0.00000 EXACT: 4.00000 N = 2 ALPHA = 0.500000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 2.46740 0.00000 CN_GEG_01_1: 1 2.46740 0.00000 CN_GEG_02_XIU: 3 2.46740 0.00000 GW_02_XIU: 3 2.46740 0.399680E-14 CN_GEG_03_XIU: 4 2.46740 0.00000 EXACT: 2.46740 N = 2 ALPHA = 1.00000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 1.77778 0.00000 CN_GEG_01_1: 1 1.77778 0.00000 CN_GEG_02_XIU: 3 1.77778 0.00000 GW_02_XIU: 3 1.77778 0.00000 CN_GEG_03_XIU: 4 1.77778 0.00000 EXACT: 1.77778 N = 2 ALPHA = 1.50000 EXPON = 0 0 Degree = 0 CN_GEG_00_1: 1 1.38791 0.00000 CN_GEG_01_1: 1 1.38791 0.00000 CN_GEG_02_XIU: 3 1.38791 0.00000 GW_02_XIU: 3 1.38791 0.222045E-14 CN_GEG_03_XIU: 4 1.38791 0.00000 EXACT: 1.38791 N = 2 ALPHA = -0.500000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 3 0.888178E-15 0.888178E-15 GW_02_XIU: 3 0.133227E-14 0.133227E-14 CN_GEG_03_XIU: 4 -0.160250E-15 0.160250E-15 EXACT: 0.00000 N = 2 ALPHA = 0.00000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 3 0.444089E-15 0.444089E-15 GW_02_XIU: 3 0.444089E-15 0.444089E-15 CN_GEG_03_XIU: 4 -0.889617E-16 0.889617E-16 EXACT: 0.00000 N = 2 ALPHA = 0.500000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 3 0.111022E-15 0.111022E-15 GW_02_XIU: 3 0.222045E-15 0.222045E-15 CN_GEG_03_XIU: 4 -0.513219E-16 0.513219E-16 EXACT: 0.00000 N = 2 ALPHA = 1.00000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 3 0.166533E-15 0.166533E-15 GW_02_XIU: 3 0.166533E-15 0.166533E-15 CN_GEG_03_XIU: 4 -0.133364E-16 0.133364E-16 EXACT: 0.00000 N = 2 ALPHA = 1.50000 EXPON = 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 3 0.555112E-16 0.555112E-16 GW_02_XIU: 3 0.555112E-16 0.555112E-16 CN_GEG_03_XIU: 4 -0.213106E-16 0.213106E-16 EXACT: 0.00000 N = 2 ALPHA = -0.500000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 0.155431E-14 0.155431E-14 GW_02_XIU: 3 0.177636E-14 0.177636E-14 CN_GEG_03_XIU: 4 -0.302169E-15 0.302169E-15 EXACT: 0.00000 N = 2 ALPHA = 0.00000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 0.277556E-15 0.277556E-15 GW_02_XIU: 3 0.333067E-15 0.333067E-15 CN_GEG_03_XIU: 4 -0.816431E-16 0.816431E-16 EXACT: 0.00000 N = 2 ALPHA = 0.500000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 0.194289E-15 0.194289E-15 GW_02_XIU: 3 0.166533E-15 0.166533E-15 CN_GEG_03_XIU: 4 -0.377712E-16 0.377712E-16 EXACT: 0.00000 N = 2 ALPHA = 1.00000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 0.971445E-16 0.971445E-16 GW_02_XIU: 3 0.971445E-16 0.971445E-16 CN_GEG_03_XIU: 4 -0.217715E-16 0.217715E-16 EXACT: 0.00000 N = 2 ALPHA = 1.50000 EXPON = 1 1 Degree = 2 CN_GEG_02_XIU: 3 0.832667E-16 0.832667E-16 GW_02_XIU: 3 0.971445E-16 0.971445E-16 CN_GEG_03_XIU: 4 -0.141642E-16 0.141642E-16 EXACT: 0.00000 N = 2 ALPHA = -0.500000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 4.93480 0.888178E-15 GW_02_XIU: 3 4.93480 0.115463E-13 CN_GEG_03_XIU: 4 4.93480 0.355271E-14 EXACT: 4.93480 N = 2 ALPHA = 0.00000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 1.33333 0.222045E-15 GW_02_XIU: 3 1.33333 0.00000 CN_GEG_03_XIU: 4 1.33333 0.444089E-15 EXACT: 1.33333 N = 2 ALPHA = 0.500000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.616850 0.777156E-15 GW_02_XIU: 3 0.616850 0.333067E-15 CN_GEG_03_XIU: 4 0.616850 0.555112E-15 EXACT: 0.616850 N = 2 ALPHA = 1.00000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.355556 0.555112E-16 GW_02_XIU: 3 0.355556 0.555112E-16 CN_GEG_03_XIU: 4 0.355556 0.555112E-16 EXACT: 0.355556 N = 2 ALPHA = 1.50000 EXPON = 2 0 Degree = 2 CN_GEG_02_XIU: 3 0.231319 0.555112E-16 GW_02_XIU: 3 0.231319 0.416334E-15 CN_GEG_03_XIU: 4 0.231319 0.277556E-16 EXACT: 0.231319 N = 3 ALPHA = -0.500000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 31.0063 0.00000 CN_GEG_01_1: 1 31.0063 0.00000 CN_GEG_02_XIU: 4 31.0063 0.00000 GW_02_XIU: 4 31.0063 0.117240E-12 CN_GEG_03_XIU: 6 31.0063 0.00000 EXACT: 31.0063 N = 3 ALPHA = 0.00000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 8.00000 0.00000 CN_GEG_01_1: 1 8.00000 0.00000 CN_GEG_02_XIU: 4 8.00000 0.00000 GW_02_XIU: 4 8.00000 0.266454E-14 CN_GEG_03_XIU: 6 8.00000 0.888178E-15 EXACT: 8.00000 N = 3 ALPHA = 0.500000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 3.87578 0.00000 CN_GEG_01_1: 1 3.87578 0.00000 CN_GEG_02_XIU: 4 3.87578 0.00000 GW_02_XIU: 4 3.87578 0.976996E-14 CN_GEG_03_XIU: 6 3.87578 0.00000 EXACT: 3.87578 N = 3 ALPHA = 1.00000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.37037 0.00000 CN_GEG_01_1: 1 2.37037 0.00000 CN_GEG_02_XIU: 4 2.37037 0.00000 GW_02_XIU: 4 2.37037 0.00000 CN_GEG_03_XIU: 6 2.37037 0.00000 EXACT: 2.37037 N = 3 ALPHA = 1.50000 EXPON = 0 0 0 Degree = 0 CN_GEG_00_1: 1 1.63510 0.00000 CN_GEG_01_1: 1 1.63510 0.00000 CN_GEG_02_XIU: 4 1.63510 0.00000 GW_02_XIU: 4 1.63510 0.377476E-14 CN_GEG_03_XIU: 6 1.63510 0.222045E-15 EXACT: 1.63510 N = 3 ALPHA = -0.500000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_GEG_03_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = 0.00000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_GEG_03_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = 0.500000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_GEG_03_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = 1.00000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_GEG_03_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = 1.50000 EXPON = 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_GEG_03_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = -0.500000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 0.949293E-15 0.949293E-15 GW_02_XIU: 4 0.949293E-15 0.949293E-15 CN_GEG_03_XIU: 6 0.665430E-16 0.665430E-16 EXACT: 0.00000 N = 3 ALPHA = 0.00000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 0.163286E-15 0.163286E-15 GW_02_XIU: 4 0.163286E-15 0.163286E-15 CN_GEG_03_XIU: 6 0.115352E-15 0.115352E-15 EXACT: 0.00000 N = 3 ALPHA = 0.500000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 0.593308E-16 0.593308E-16 GW_02_XIU: 4 0.593308E-16 0.593308E-16 CN_GEG_03_XIU: 6 0.319145E-16 0.319145E-16 EXACT: 0.00000 N = 3 ALPHA = 1.00000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 0.290287E-16 0.290287E-16 GW_02_XIU: 4 0.290287E-16 0.290287E-16 CN_GEG_03_XIU: 6 0.292848E-17 0.292848E-17 EXACT: 0.00000 N = 3 ALPHA = 1.50000 EXPON = 1 1 0 Degree = 2 CN_GEG_02_XIU: 4 0.166868E-16 0.166868E-16 GW_02_XIU: 4 0.166868E-16 0.166868E-16 CN_GEG_03_XIU: 6 -0.143238E-17 0.143238E-17 EXACT: 0.00000 N = 3 ALPHA = -0.500000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 15.5031 0.355271E-14 GW_02_XIU: 4 15.5031 0.550671E-13 CN_GEG_03_XIU: 6 15.5031 0.710543E-14 EXACT: 15.5031 N = 3 ALPHA = 0.00000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 2.66667 0.00000 GW_02_XIU: 4 2.66667 0.888178E-15 CN_GEG_03_XIU: 6 2.66667 0.133227E-14 EXACT: 2.66667 N = 3 ALPHA = 0.500000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.968946 0.999201E-15 GW_02_XIU: 4 0.968946 0.144329E-14 CN_GEG_03_XIU: 6 0.968946 0.122125E-14 EXACT: 0.968946 N = 3 ALPHA = 1.00000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.474074 0.111022E-15 GW_02_XIU: 4 0.474074 0.111022E-15 CN_GEG_03_XIU: 6 0.474074 0.111022E-15 EXACT: 0.474074 N = 3 ALPHA = 1.50000 EXPON = 2 0 0 Degree = 2 CN_GEG_02_XIU: 4 0.272516 0.00000 GW_02_XIU: 4 0.272516 0.666134E-15 CN_GEG_03_XIU: 6 0.272516 0.555112E-16 EXACT: 0.272516 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 97.4091 0.00000 CN_GEG_01_1: 1 97.4091 0.00000 CN_GEG_02_XIU: 5 97.4091 0.00000 GW_02_XIU: 5 97.4091 0.497380E-12 CN_GEG_03_XIU: 8 97.4091 0.142109E-13 EXACT: 97.4091 N = 4 ALPHA = 0.00000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 16.0000 0.00000 CN_GEG_01_1: 1 16.0000 0.00000 CN_GEG_02_XIU: 5 16.0000 0.00000 GW_02_XIU: 5 16.0000 0.710543E-14 CN_GEG_03_XIU: 8 16.0000 0.00000 EXACT: 16.0000 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 6.08807 0.00000 CN_GEG_01_1: 1 6.08807 0.00000 CN_GEG_02_XIU: 5 6.08807 0.888178E-15 GW_02_XIU: 5 6.08807 0.195399E-13 CN_GEG_03_XIU: 8 6.08807 0.888178E-15 EXACT: 6.08807 N = 4 ALPHA = 1.00000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 3.16049 0.00000 CN_GEG_01_1: 1 3.16049 0.00000 CN_GEG_02_XIU: 5 3.16049 0.00000 GW_02_XIU: 5 3.16049 0.00000 CN_GEG_03_XIU: 8 3.16049 0.00000 EXACT: 3.16049 N = 4 ALPHA = 1.50000 EXPON = 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 1.92630 0.222045E-15 CN_GEG_01_1: 1 1.92630 0.222045E-15 CN_GEG_02_XIU: 5 1.92630 0.222045E-15 GW_02_XIU: 5 1.92630 0.577316E-14 CN_GEG_03_XIU: 8 1.92630 0.444089E-15 EXACT: 1.92630 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 5 0.710543E-14 0.710543E-14 GW_02_XIU: 5 0.710543E-14 0.710543E-14 CN_GEG_03_XIU: 8 -0.178287E-13 0.178287E-13 EXACT: 0.00000 N = 4 ALPHA = 0.00000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 5 0.111022E-14 0.111022E-14 GW_02_XIU: 5 0.111022E-14 0.111022E-14 CN_GEG_03_XIU: 8 -0.253217E-14 0.253217E-14 EXACT: 0.00000 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 5 0.333067E-15 0.333067E-15 GW_02_XIU: 5 0.333067E-15 0.333067E-15 CN_GEG_03_XIU: 8 -0.783978E-15 0.783978E-15 EXACT: 0.00000 N = 4 ALPHA = 1.00000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 5 0.138778E-15 0.138778E-15 GW_02_XIU: 5 0.138778E-15 0.138778E-15 CN_GEG_03_XIU: 8 -0.377882E-15 0.377882E-15 EXACT: 0.00000 N = 4 ALPHA = 1.50000 EXPON = 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 5 0.832667E-16 0.832667E-16 GW_02_XIU: 5 0.832667E-16 0.832667E-16 CN_GEG_03_XIU: 8 -0.213172E-15 0.213172E-15 EXACT: 0.00000 N = 4 ALPHA = -0.500000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.444089E-14 0.444089E-14 GW_02_XIU: 5 0.444089E-14 0.444089E-14 CN_GEG_03_XIU: 8 0.570420E-15 0.570420E-15 EXACT: 0.00000 N = 4 ALPHA = 0.00000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.444089E-15 0.444089E-15 GW_02_XIU: 5 0.333067E-15 0.333067E-15 CN_GEG_03_XIU: 8 0.117517E-15 0.117517E-15 EXACT: 0.00000 N = 4 ALPHA = 0.500000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.194289E-15 0.194289E-15 GW_02_XIU: 5 0.194289E-15 0.194289E-15 CN_GEG_03_XIU: 8 0.178256E-16 0.178256E-16 EXACT: 0.00000 N = 4 ALPHA = 1.00000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.693889E-16 0.693889E-16 GW_02_XIU: 5 0.693889E-16 0.693889E-16 CN_GEG_03_XIU: 8 0.168063E-16 0.168063E-16 EXACT: 0.00000 N = 4 ALPHA = 1.50000 EXPON = 1 1 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.485723E-16 0.485723E-16 GW_02_XIU: 5 0.485723E-16 0.485723E-16 CN_GEG_03_XIU: 8 0.809690E-17 0.809690E-17 EXACT: 0.00000 N = 4 ALPHA = -0.500000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 48.7045 0.142109E-13 GW_02_XIU: 5 48.7045 0.234479E-12 CN_GEG_03_XIU: 8 48.7045 0.284217E-13 EXACT: 48.7045 N = 4 ALPHA = 0.00000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 5.33333 0.00000 GW_02_XIU: 5 5.33333 0.266454E-14 CN_GEG_03_XIU: 8 5.33333 0.177636E-14 EXACT: 5.33333 N = 4 ALPHA = 0.500000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 1.52202 0.111022E-14 GW_02_XIU: 5 1.52202 0.355271E-14 CN_GEG_03_XIU: 8 1.52202 0.133227E-14 EXACT: 1.52202 N = 4 ALPHA = 1.00000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.632099 0.111022E-15 GW_02_XIU: 5 0.632099 0.111022E-15 CN_GEG_03_XIU: 8 0.632099 0.111022E-15 EXACT: 0.632099 N = 4 ALPHA = 1.50000 EXPON = 2 0 0 0 Degree = 2 CN_GEG_02_XIU: 5 0.321050 0.00000 GW_02_XIU: 5 0.321050 0.999201E-15 CN_GEG_03_XIU: 8 0.321050 0.00000 EXACT: 0.321050 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 306.020 0.00000 CN_GEG_01_1: 1 306.020 0.00000 CN_GEG_02_XIU: 6 306.020 0.00000 GW_02_XIU: 6 306.020 0.193268E-11 CN_GEG_03_XIU: 10 306.020 0.00000 EXACT: 306.020 N = 5 ALPHA = 0.00000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 32.0000 0.00000 CN_GEG_01_1: 1 32.0000 0.00000 CN_GEG_02_XIU: 6 32.0000 0.355271E-14 GW_02_XIU: 6 32.0000 0.213163E-13 CN_GEG_03_XIU: 10 32.0000 0.355271E-14 EXACT: 32.0000 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 9.56312 0.00000 CN_GEG_01_1: 1 9.56312 0.00000 CN_GEG_02_XIU: 6 9.56312 0.00000 GW_02_XIU: 6 9.56312 0.390799E-13 CN_GEG_03_XIU: 10 9.56312 0.00000 EXACT: 9.56312 N = 5 ALPHA = 1.00000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 4.21399 0.00000 CN_GEG_01_1: 1 4.21399 0.00000 CN_GEG_02_XIU: 6 4.21399 0.00000 GW_02_XIU: 6 4.21399 0.00000 CN_GEG_03_XIU: 10 4.21399 0.888178E-15 EXACT: 4.21399 N = 5 ALPHA = 1.50000 EXPON = 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.26937 0.444089E-15 CN_GEG_01_1: 1 2.26937 0.444089E-15 CN_GEG_02_XIU: 6 2.26937 0.444089E-15 GW_02_XIU: 6 2.26937 0.888178E-14 CN_GEG_03_XIU: 10 2.26937 0.00000 EXACT: 2.26937 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_GEG_03_XIU: 10 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = 0.00000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_GEG_03_XIU: 10 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_GEG_03_XIU: 10 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = 1.00000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_GEG_03_XIU: 10 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = 1.50000 EXPON = 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_GEG_03_XIU: 10 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = -0.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.177636E-13 0.177636E-13 GW_02_XIU: 6 0.177636E-13 0.177636E-13 CN_GEG_03_XIU: 10 -0.389893E-15 0.389893E-15 EXACT: 0.00000 N = 5 ALPHA = 0.00000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.666134E-15 0.666134E-15 GW_02_XIU: 6 0.666134E-15 0.666134E-15 CN_GEG_03_XIU: 10 0.143618E-15 0.143618E-15 EXACT: 0.00000 N = 5 ALPHA = 0.500000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.222045E-15 0.222045E-15 GW_02_XIU: 6 0.222045E-15 0.222045E-15 CN_GEG_03_XIU: 10 -0.609208E-17 0.609208E-17 EXACT: 0.00000 N = 5 ALPHA = 1.00000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.832667E-16 0.832667E-16 GW_02_XIU: 6 0.832667E-16 0.832667E-16 CN_GEG_03_XIU: 10 -0.135296E-16 0.135296E-16 EXACT: 0.00000 N = 5 ALPHA = 1.50000 EXPON = 1 1 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.624500E-16 0.624500E-16 GW_02_XIU: 6 0.555112E-16 0.555112E-16 CN_GEG_03_XIU: 10 0.228882E-17 0.228882E-17 EXACT: 0.00000 N = 5 ALPHA = -0.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 153.010 0.00000 GW_02_XIU: 6 153.010 0.966338E-12 CN_GEG_03_XIU: 10 153.010 0.852651E-13 EXACT: 153.010 N = 5 ALPHA = 0.00000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 10.6667 0.355271E-14 GW_02_XIU: 6 10.6667 0.532907E-14 CN_GEG_03_XIU: 10 10.6667 0.532907E-14 EXACT: 10.6667 N = 5 ALPHA = 0.500000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 2.39078 0.266454E-14 GW_02_XIU: 6 2.39078 0.754952E-14 CN_GEG_03_XIU: 10 2.39078 0.222045E-14 EXACT: 2.39078 N = 5 ALPHA = 1.00000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.842798 0.222045E-15 GW_02_XIU: 6 0.842798 0.222045E-15 CN_GEG_03_XIU: 10 0.842798 0.222045E-15 EXACT: 0.842798 N = 5 ALPHA = 1.50000 EXPON = 2 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 6 0.378229 0.00000 GW_02_XIU: 6 0.378229 0.166533E-14 CN_GEG_03_XIU: 10 0.378229 0.00000 EXACT: 0.378229 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 961.389 0.00000 CN_GEG_01_1: 1 961.389 0.00000 CN_GEG_02_XIU: 7 961.389 0.113687E-12 GW_02_XIU: 7 961.389 0.727596E-11 CN_GEG_03_XIU: 12 961.389 0.113687E-12 EXACT: 961.389 N = 6 ALPHA = 0.00000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 64.0000 0.00000 CN_GEG_01_1: 1 64.0000 0.00000 CN_GEG_02_XIU: 7 64.0000 0.142109E-13 GW_02_XIU: 7 64.0000 0.355271E-13 CN_GEG_03_XIU: 12 64.0000 0.00000 EXACT: 64.0000 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 15.0217 0.177636E-14 CN_GEG_01_1: 1 15.0217 0.177636E-14 CN_GEG_02_XIU: 7 15.0217 0.00000 GW_02_XIU: 7 15.0217 0.746070E-13 CN_GEG_03_XIU: 12 15.0217 0.177636E-14 EXACT: 15.0217 N = 6 ALPHA = 1.00000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 5.61866 0.888178E-15 CN_GEG_01_1: 1 5.61866 0.888178E-15 CN_GEG_02_XIU: 7 5.61866 0.00000 GW_02_XIU: 7 5.61866 0.00000 CN_GEG_03_XIU: 12 5.61866 0.888178E-15 EXACT: 5.61866 N = 6 ALPHA = 1.50000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_GEG_00_1: 1 2.67354 0.444089E-15 CN_GEG_01_1: 1 2.67354 0.444089E-15 CN_GEG_02_XIU: 7 2.67354 0.00000 GW_02_XIU: 7 2.67354 0.128786E-13 CN_GEG_03_XIU: 12 2.67354 0.00000 EXACT: 2.67354 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 7 -0.355271E-13 0.355271E-13 GW_02_XIU: 7 -0.639488E-13 0.639488E-13 CN_GEG_03_XIU: 12 -0.261950E-12 0.261950E-12 EXACT: 0.00000 N = 6 ALPHA = 0.00000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 7 -0.355271E-14 0.355271E-14 GW_02_XIU: 7 -0.444089E-14 0.444089E-14 CN_GEG_03_XIU: 12 -0.141424E-13 0.141424E-13 EXACT: 0.00000 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 7 -0.999201E-15 0.999201E-15 GW_02_XIU: 7 -0.666134E-15 0.666134E-15 CN_GEG_03_XIU: 12 -0.272994E-14 0.272994E-14 EXACT: 0.00000 N = 6 ALPHA = 1.00000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 7 -0.249800E-15 0.249800E-15 GW_02_XIU: 7 -0.249800E-15 0.249800E-15 CN_GEG_03_XIU: 12 -0.942871E-15 0.942871E-15 EXACT: 0.00000 N = 6 ALPHA = 1.50000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_GEG_01_1: 1 0.00000 0.00000 CN_GEG_02_XIU: 7 -0.124900E-15 0.124900E-15 GW_02_XIU: 7 -0.111022E-15 0.111022E-15 CN_GEG_03_XIU: 12 -0.420227E-15 0.420227E-15 EXACT: 0.00000 N = 6 ALPHA = -0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.426326E-13 0.426326E-13 GW_02_XIU: 7 0.426326E-13 0.426326E-13 CN_GEG_03_XIU: 12 -0.196227E-13 0.196227E-13 EXACT: 0.00000 N = 6 ALPHA = 0.00000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.222045E-14 0.222045E-14 GW_02_XIU: 7 0.222045E-14 0.222045E-14 CN_GEG_03_XIU: 12 -0.648815E-15 0.648815E-15 EXACT: 0.00000 N = 6 ALPHA = 0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.222045E-15 0.222045E-15 GW_02_XIU: 7 0.333067E-15 0.333067E-15 CN_GEG_03_XIU: 12 -0.422801E-16 0.422801E-16 EXACT: 0.00000 N = 6 ALPHA = 1.00000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.555112E-16 0.555112E-16 GW_02_XIU: 7 0.555112E-16 0.555112E-16 CN_GEG_03_XIU: 12 -0.458725E-16 0.458725E-16 EXACT: 0.00000 N = 6 ALPHA = 1.50000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.277556E-16 0.277556E-16 GW_02_XIU: 7 0.208167E-16 0.208167E-16 CN_GEG_03_XIU: 12 -0.112508E-16 0.112508E-16 EXACT: 0.00000 N = 6 ALPHA = -0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 480.695 0.170530E-12 GW_02_XIU: 7 480.695 0.346745E-11 CN_GEG_03_XIU: 12 480.695 0.227374E-12 EXACT: 480.695 N = 6 ALPHA = 0.00000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 21.3333 0.00000 GW_02_XIU: 7 21.3333 0.106581E-13 CN_GEG_03_XIU: 12 21.3333 0.710543E-14 EXACT: 21.3333 N = 6 ALPHA = 0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 3.75543 0.266454E-14 GW_02_XIU: 7 3.75543 0.159872E-13 CN_GEG_03_XIU: 12 3.75543 0.266454E-14 EXACT: 3.75543 N = 6 ALPHA = 1.00000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 1.12373 0.222045E-15 GW_02_XIU: 7 1.12373 0.222045E-15 CN_GEG_03_XIU: 12 1.12373 0.444089E-15 EXACT: 1.12373 N = 6 ALPHA = 1.50000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_GEG_02_XIU: 7 0.445590 0.00000 GW_02_XIU: 7 0.445590 0.222045E-14 CN_GEG_03_XIU: 12 0.445590 0.111022E-15 EXACT: 0.445590 CN_JAC_TESTS Demonstrate the use of quadrature rules for the region CN_JAC, that is, the hypercube [-1,+1]^N, with the Jacobi 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 = 0.00000 BETA = 0.00000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2.00000 0.00000 CN_JAC_01_1: 1 2.00000 0.00000 CN_JAC_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2.00000 0.00000 CN_JAC_01_1: 1 2.00000 0.00000 CN_JAC_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 2.66667 0.00000 CN_JAC_01_1: 1 2.66667 0.00000 CN_JAC_02_XIU: 2 2.66667 0.00000 GW_02_XIU: 2 2.66667 0.444089E-15 EXACT: 2.66667 N = 1 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 Degree = 0 CN_JAC_00_1: 1 1.57080 0.00000 CN_JAC_01_1: 1 1.57080 0.00000 CN_JAC_02_XIU: 2 1.57080 0.00000 GW_02_XIU: 2 1.57080 0.444089E-15 EXACT: 1.57080 N = 1 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 -0.666667 0.00000 CN_JAC_02_XIU: 2 -0.666667 0.111022E-15 GW_02_XIU: 2 -0.666667 0.111022E-15 EXACT: -0.666667 N = 1 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 1.33333 0.00000 CN_JAC_02_XIU: 2 1.33333 0.222045E-15 GW_02_XIU: 2 1.33333 0.00000 EXACT: 1.33333 N = 1 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 Degree = 1 CN_JAC_01_1: 1 0.392699 0.555112E-16 CN_JAC_02_XIU: 2 0.392699 0.555112E-16 GW_02_XIU: 2 0.392699 0.00000 EXACT: 0.392699 N = 1 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 0.00000 GW_02_XIU: 2 0.666667 0.00000 EXACT: 0.666667 N = 1 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.666667 0.222045E-15 GW_02_XIU: 2 0.666667 0.222045E-15 EXACT: 0.666667 N = 1 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 1.06667 0.00000 GW_02_XIU: 2 1.06667 0.222045E-15 EXACT: 1.06667 N = 1 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 Degree = 2 CN_JAC_02_XIU: 2 0.392699 0.00000 GW_02_XIU: 2 0.392699 0.555112E-16 EXACT: 0.392699 N = 2 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 4.00000 0.00000 CN_JAC_01_1: 1 4.00000 0.00000 CN_JAC_02_XIU: 3 4.00000 0.00000 GW_02_XIU: 3 4.00000 0.00000 EXACT: 4.00000 N = 2 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 4.00000 0.00000 CN_JAC_01_1: 1 4.00000 0.00000 CN_JAC_02_XIU: 3 4.00000 0.00000 GW_02_XIU: 3 4.00000 0.00000 EXACT: 4.00000 N = 2 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 7.11111 0.00000 CN_JAC_01_1: 1 7.11111 0.00000 CN_JAC_02_XIU: 3 7.11111 0.00000 GW_02_XIU: 3 7.11111 0.177636E-14 EXACT: 7.11111 N = 2 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 Degree = 0 CN_JAC_00_1: 1 2.46740 0.00000 CN_JAC_01_1: 1 2.46740 0.00000 CN_JAC_02_XIU: 3 2.46740 0.00000 GW_02_XIU: 3 2.46740 0.133227E-14 EXACT: 2.46740 N = 2 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 3 0.444089E-15 0.444089E-15 GW_02_XIU: 3 0.444089E-15 0.444089E-15 EXACT: 0.00000 N = 2 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 -1.33333 0.00000 CN_JAC_02_XIU: 3 -1.33333 0.666134E-15 GW_02_XIU: 3 -1.33333 0.666134E-15 EXACT: -1.33333 N = 2 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 3.55556 0.00000 CN_JAC_02_XIU: 3 3.55556 0.444089E-15 GW_02_XIU: 3 3.55556 0.00000 EXACT: 3.55556 N = 2 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 1 Degree = 1 CN_JAC_01_1: 1 0.616850 0.00000 CN_JAC_02_XIU: 3 0.616850 0.111022E-15 GW_02_XIU: 3 0.616850 0.444089E-15 EXACT: 0.616850 N = 2 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.277556E-15 0.277556E-15 GW_02_XIU: 3 0.277556E-15 0.277556E-15 EXACT: 0.00000 N = 2 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.444444 0.555112E-16 GW_02_XIU: 3 0.444444 0.555112E-16 EXACT: 0.444444 N = 2 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 1.77778 0.888178E-15 GW_02_XIU: 3 1.77778 0.222045E-15 EXACT: 1.77778 N = 2 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 1 Degree = 2 CN_JAC_02_XIU: 3 0.154213 0.138778E-15 GW_02_XIU: 3 0.154213 0.222045E-15 EXACT: 0.154213 N = 2 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 0.222045E-15 GW_02_XIU: 3 1.33333 0.222045E-15 EXACT: 1.33333 N = 2 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 1.33333 0.222045E-15 GW_02_XIU: 3 1.33333 0.222045E-15 EXACT: 1.33333 N = 2 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 2.84444 0.00000 GW_02_XIU: 3 2.84444 0.888178E-15 EXACT: 2.84444 N = 2 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 0 Degree = 2 CN_JAC_02_XIU: 3 0.616850 0.111022E-15 GW_02_XIU: 3 0.616850 0.444089E-15 EXACT: 0.616850 N = 3 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 8.00000 0.00000 CN_JAC_01_1: 1 8.00000 0.00000 CN_JAC_02_XIU: 4 8.00000 0.00000 GW_02_XIU: 4 8.00000 0.00000 EXACT: 8.00000 N = 3 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 8.00000 0.00000 CN_JAC_01_1: 1 8.00000 0.00000 CN_JAC_02_XIU: 4 8.00000 0.00000 GW_02_XIU: 4 8.00000 0.00000 EXACT: 8.00000 N = 3 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 18.9630 0.00000 CN_JAC_01_1: 1 18.9630 0.00000 CN_JAC_02_XIU: 4 18.9630 0.00000 GW_02_XIU: 4 18.9630 0.710543E-14 EXACT: 18.9630 N = 3 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 Degree = 0 CN_JAC_00_1: 1 3.87578 0.00000 CN_JAC_01_1: 1 3.87578 0.00000 CN_JAC_02_XIU: 4 3.87578 0.00000 GW_02_XIU: 4 3.87578 0.310862E-14 EXACT: 3.87578 N = 3 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 EXACT: 0.00000 N = 3 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 -2.66667 0.00000 CN_JAC_02_XIU: 4 -2.66667 0.444089E-15 GW_02_XIU: 4 -2.66667 0.444089E-15 EXACT: -2.66667 N = 3 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 9.48148 0.00000 CN_JAC_02_XIU: 4 9.48148 0.177636E-14 GW_02_XIU: 4 9.48148 0.177636E-14 EXACT: 9.48148 N = 3 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.968946 0.111022E-15 CN_JAC_02_XIU: 4 0.968946 0.222045E-15 GW_02_XIU: 4 0.968946 0.777156E-15 EXACT: 0.968946 N = 3 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.163286E-15 0.163286E-15 GW_02_XIU: 4 0.163286E-15 0.163286E-15 EXACT: 0.00000 N = 3 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.888889 0.222045E-15 GW_02_XIU: 4 0.888889 0.222045E-15 EXACT: 0.888889 N = 3 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 4.74074 0.177636E-14 GW_02_XIU: 4 4.74074 0.00000 EXACT: 4.74074 N = 3 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 1 0 Degree = 2 CN_JAC_02_XIU: 4 0.242237 0.555112E-16 GW_02_XIU: 4 0.242237 0.277556E-15 EXACT: 0.242237 N = 3 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 0.00000 GW_02_XIU: 4 2.66667 0.00000 EXACT: 2.66667 N = 3 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 2.66667 0.888178E-15 GW_02_XIU: 4 2.66667 0.888178E-15 EXACT: 2.66667 N = 3 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 7.58519 0.888178E-15 GW_02_XIU: 4 7.58519 0.355271E-14 EXACT: 7.58519 N = 3 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 0 0 Degree = 2 CN_JAC_02_XIU: 4 0.968946 0.111022E-15 GW_02_XIU: 4 0.968946 0.888178E-15 EXACT: 0.968946 N = 4 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 16.0000 0.00000 CN_JAC_01_1: 1 16.0000 0.00000 CN_JAC_02_XIU: 5 16.0000 0.00000 GW_02_XIU: 5 16.0000 0.00000 EXACT: 16.0000 N = 4 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 16.0000 0.00000 CN_JAC_01_1: 1 16.0000 0.00000 CN_JAC_02_XIU: 5 16.0000 0.00000 GW_02_XIU: 5 16.0000 0.00000 EXACT: 16.0000 N = 4 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 50.5679 0.00000 CN_JAC_01_1: 1 50.5679 0.00000 CN_JAC_02_XIU: 5 50.5679 0.00000 GW_02_XIU: 5 50.5679 0.213163E-13 EXACT: 50.5679 N = 4 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 6.08807 0.00000 CN_JAC_01_1: 1 6.08807 0.00000 CN_JAC_02_XIU: 5 6.08807 0.888178E-15 GW_02_XIU: 5 6.08807 0.710543E-14 EXACT: 6.08807 N = 4 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 5 0.111022E-14 0.111022E-14 GW_02_XIU: 5 0.111022E-14 0.111022E-14 EXACT: 0.00000 N = 4 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -5.33333 0.00000 CN_JAC_02_XIU: 5 -5.33333 0.888178E-15 GW_02_XIU: 5 -5.33333 0.888178E-15 EXACT: -5.33333 N = 4 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 25.2840 0.00000 CN_JAC_02_XIU: 5 25.2840 0.710543E-14 GW_02_XIU: 5 25.2840 0.710543E-14 EXACT: 25.2840 N = 4 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 1.52202 0.222045E-15 CN_JAC_02_XIU: 5 1.52202 0.00000 GW_02_XIU: 5 1.52202 0.177636E-14 EXACT: 1.52202 N = 4 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 0.444089E-15 0.444089E-15 GW_02_XIU: 5 0.444089E-15 0.444089E-15 EXACT: 0.00000 N = 4 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.77778 0.00000 GW_02_XIU: 5 1.77778 0.00000 EXACT: 1.77778 N = 4 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 12.6420 0.355271E-14 GW_02_XIU: 5 12.6420 0.00000 EXACT: 12.6420 N = 4 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 1 0 0 Degree = 2 CN_JAC_02_XIU: 5 0.380504 0.166533E-15 GW_02_XIU: 5 0.380504 0.610623E-15 EXACT: 0.380504 N = 4 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 0.00000 GW_02_XIU: 5 5.33333 0.00000 EXACT: 5.33333 N = 4 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 5.33333 0.177636E-14 GW_02_XIU: 5 5.33333 0.177636E-14 EXACT: 5.33333 N = 4 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 20.2272 0.355271E-14 GW_02_XIU: 5 20.2272 0.106581E-13 EXACT: 20.2272 N = 4 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 0 0 0 Degree = 2 CN_JAC_02_XIU: 5 1.52202 0.00000 GW_02_XIU: 5 1.52202 0.199840E-14 EXACT: 1.52202 N = 5 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 32.0000 0.00000 CN_JAC_01_1: 1 32.0000 0.00000 CN_JAC_02_XIU: 6 32.0000 0.355271E-14 GW_02_XIU: 6 32.0000 0.355271E-14 EXACT: 32.0000 N = 5 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 32.0000 0.00000 CN_JAC_01_1: 1 32.0000 0.00000 CN_JAC_02_XIU: 6 32.0000 0.355271E-14 GW_02_XIU: 6 32.0000 0.355271E-14 EXACT: 32.0000 N = 5 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 134.848 0.00000 CN_JAC_01_1: 1 134.848 0.00000 CN_JAC_02_XIU: 6 134.848 0.00000 GW_02_XIU: 6 134.848 0.852651E-13 EXACT: 134.848 N = 5 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 9.56312 0.00000 CN_JAC_01_1: 1 9.56312 0.00000 CN_JAC_02_XIU: 6 9.56312 0.00000 GW_02_XIU: 6 9.56312 0.142109E-13 EXACT: 9.56312 N = 5 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 EXACT: 0.00000 N = 5 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -10.6667 0.00000 CN_JAC_02_XIU: 6 -10.6667 0.177636E-14 GW_02_XIU: 6 -10.6667 0.177636E-14 EXACT: -10.6667 N = 5 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 67.4239 0.00000 CN_JAC_02_XIU: 6 67.4239 0.142109E-13 GW_02_XIU: 6 67.4239 0.284217E-13 EXACT: 67.4239 N = 5 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 2.39078 0.00000 CN_JAC_02_XIU: 6 2.39078 0.00000 GW_02_XIU: 6 2.39078 0.266454E-14 EXACT: 2.39078 N = 5 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 0.666134E-15 0.666134E-15 GW_02_XIU: 6 0.666134E-15 0.666134E-15 EXACT: 0.00000 N = 5 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 3.55556 0.00000 GW_02_XIU: 6 3.55556 0.00000 EXACT: 3.55556 N = 5 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 33.7119 0.213163E-13 GW_02_XIU: 6 33.7119 0.00000 EXACT: 33.7119 N = 5 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 1 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 0.597695 0.111022E-15 GW_02_XIU: 6 0.597695 0.999201E-15 EXACT: 0.597695 N = 5 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 0.355271E-14 GW_02_XIU: 6 10.6667 0.355271E-14 EXACT: 10.6667 N = 5 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 10.6667 0.177636E-14 GW_02_XIU: 6 10.6667 0.177636E-14 EXACT: 10.6667 N = 5 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 53.9391 0.00000 GW_02_XIU: 6 53.9391 0.355271E-13 EXACT: 53.9391 N = 5 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 6 2.39078 0.444089E-15 GW_02_XIU: 6 2.39078 0.399680E-14 EXACT: 2.39078 N = 6 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 64.0000 0.00000 CN_JAC_01_1: 1 64.0000 0.00000 CN_JAC_02_XIU: 7 64.0000 0.142109E-13 GW_02_XIU: 7 64.0000 0.142109E-13 EXACT: 64.0000 N = 6 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 64.0000 0.00000 CN_JAC_01_1: 1 64.0000 0.00000 CN_JAC_02_XIU: 7 64.0000 0.142109E-13 GW_02_XIU: 7 64.0000 0.142109E-13 EXACT: 64.0000 N = 6 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 359.594 0.00000 CN_JAC_01_1: 1 359.594 0.00000 CN_JAC_02_XIU: 7 359.594 0.00000 GW_02_XIU: 7 359.594 0.284217E-12 EXACT: 359.594 N = 6 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 0 0 0 Degree = 0 CN_JAC_00_1: 1 15.0217 0.177636E-14 CN_JAC_01_1: 1 15.0217 0.177636E-14 CN_JAC_02_XIU: 7 15.0217 0.177636E-14 GW_02_XIU: 7 15.0217 0.266454E-13 EXACT: 15.0217 N = 6 ALPHA = 0.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 0.00000 0.00000 CN_JAC_02_XIU: 7 -0.355271E-14 0.355271E-14 GW_02_XIU: 7 -0.355271E-14 0.355271E-14 EXACT: 0.00000 N = 6 ALPHA = 1.00000 BETA = 0.00000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 -21.3333 0.00000 CN_JAC_02_XIU: 7 -21.3333 0.355271E-14 GW_02_XIU: 7 -21.3333 0.355271E-14 EXACT: -21.3333 N = 6 ALPHA = 0.00000 BETA = 2.00000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 179.797 0.00000 CN_JAC_02_XIU: 7 179.797 0.284217E-13 GW_02_XIU: 7 179.797 0.113687E-12 EXACT: 179.797 N = 6 ALPHA = 0.500000 BETA = 1.50000 EXPON = 0 0 0 0 0 1 Degree = 1 CN_JAC_01_1: 1 3.75543 0.888178E-15 CN_JAC_02_XIU: 7 3.75543 0.888178E-15 GW_02_XIU: 7 3.75543 0.488498E-14 EXACT: 3.75543 N = 6 ALPHA = 0.00000 BETA = 0.00000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 0.222045E-14 0.222045E-14 GW_02_XIU: 7 0.222045E-14 0.222045E-14 EXACT: 0.00000 N = 6 ALPHA = 1.00000 BETA = 0.00000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 7.11111 0.00000 GW_02_XIU: 7 7.11111 0.00000 EXACT: 7.11111 N = 6 ALPHA = 0.00000 BETA = 2.00000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 89.8985 0.284217E-13 GW_02_XIU: 7 89.8985 0.426326E-13 EXACT: 89.8985 N = 6 ALPHA = 0.500000 BETA = 1.50000 EXPON = 1 1 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 0.938857 0.00000 GW_02_XIU: 7 0.938857 0.155431E-14 EXACT: 0.938857 N = 6 ALPHA = 0.00000 BETA = 0.00000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 0.00000 GW_02_XIU: 7 21.3333 0.00000 EXACT: 21.3333 N = 6 ALPHA = 1.00000 BETA = 0.00000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 21.3333 0.355271E-14 GW_02_XIU: 7 21.3333 0.355271E-14 EXACT: 21.3333 N = 6 ALPHA = 0.00000 BETA = 2.00000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 143.838 0.284217E-13 GW_02_XIU: 7 143.838 0.142109E-12 EXACT: 143.838 N = 6 ALPHA = 0.500000 BETA = 1.50000 EXPON = 2 0 0 0 0 0 Degree = 2 CN_JAC_02_XIU: 7 3.75543 0.444089E-15 GW_02_XIU: 7 3.75543 0.577316E-14 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 2.00000 0.00000 CN_LEG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 CN_LEG_03_1: 2 2.00000 0.00000 CN_LEG_03_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 EXPON = 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 2 0.00000 0.00000 GW_02_XIU: 2 0.00000 0.00000 CN_LEG_03_1: 2 0.00000 0.00000 CN_LEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 EXPON = 2 Degree = 2 CN_LEG_02_XIU: 2 0.666667 0.00000 GW_02_XIU: 2 0.666667 0.00000 CN_LEG_03_1: 2 0.666667 0.222045E-15 CN_LEG_03_XIU: 2 0.666667 0.222045E-15 EXACT: 0.666667 N = 1 EXPON = 3 Degree = 3 CN_LEG_03_1: 2 0.00000 0.00000 CN_LEG_03_XIU: 2 0.00000 0.00000 EXACT: 0.00000 N = 1 EXPON = 4 Degree = 4 EXACT: 0.400000 N = 2 EXPON = 0 0 Degree = 0 CN_LEG_01_1: 1 4.00000 0.00000 CN_LEG_02_XIU: 3 4.00000 0.00000 GW_02_XIU: 3 4.00000 0.00000 CN_LEG_03_1: 4 4.00000 0.00000 CN_LEG_03_XIU: 4 4.00000 0.00000 CN_LEG_05_2: 9 4.00000 0.00000 EXACT: 4.00000 N = 2 EXPON = 0 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 3 0.444089E-15 0.444089E-15 GW_02_XIU: 3 0.444089E-15 0.444089E-15 CN_LEG_03_1: 4 -0.111022E-15 0.111022E-15 CN_LEG_03_XIU: 4 -0.889617E-16 0.889617E-16 CN_LEG_05_2: 9 0.00000 0.00000 EXACT: 0.00000 N = 2 EXPON = 1 1 Degree = 2 CN_LEG_02_XIU: 3 0.277556E-15 0.277556E-15 GW_02_XIU: 3 0.277556E-15 0.277556E-15 CN_LEG_03_1: 4 0.816431E-16 0.816431E-16 CN_LEG_03_XIU: 4 -0.816431E-16 0.816431E-16 CN_LEG_05_2: 9 0.00000 0.00000 EXACT: 0.00000 N = 2 EXPON = 2 0 Degree = 2 CN_LEG_02_XIU: 3 1.33333 0.222045E-15 GW_02_XIU: 3 1.33333 0.222045E-15 CN_LEG_03_1: 4 1.33333 0.444089E-15 CN_LEG_03_XIU: 4 1.33333 0.444089E-15 CN_LEG_05_2: 9 1.33333 0.222045E-15 EXACT: 1.33333 N = 2 EXPON = 0 3 Degree = 3 CN_LEG_03_1: 4 0.00000 0.00000 CN_LEG_03_XIU: 4 -0.799808E-47 0.799808E-47 CN_LEG_05_2: 9 0.00000 0.00000 EXACT: 0.00000 N = 2 EXPON = 0 4 Degree = 4 CN_LEG_05_2: 9 0.800000 0.222045E-15 EXACT: 0.800000 N = 2 EXPON = 2 3 Degree = 5 CN_LEG_05_2: 9 0.00000 0.00000 EXACT: 0.00000 N = 3 EXPON = 0 0 0 Degree = 0 CN_LEG_01_1: 1 8.00000 0.00000 CN_LEG_02_XIU: 4 8.00000 0.00000 GW_02_XIU: 4 8.00000 0.00000 CN_LEG_03_1: 6 8.00000 0.888178E-15 CN_LEG_03_XIU: 6 8.00000 0.888178E-15 CN_LEG_05_2: 19 8.00000 0.00000 EXACT: 8.00000 N = 3 EXPON = 0 0 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 4 0.00000 0.00000 GW_02_XIU: 4 0.00000 0.00000 CN_LEG_03_1: 6 0.00000 0.00000 CN_LEG_03_XIU: 6 0.00000 0.00000 CN_LEG_05_2: 19 0.00000 0.00000 EXACT: 0.00000 N = 3 EXPON = 1 1 0 Degree = 2 CN_LEG_02_XIU: 4 0.163286E-15 0.163286E-15 GW_02_XIU: 4 0.163286E-15 0.163286E-15 CN_LEG_03_1: 6 0.277556E-15 0.277556E-15 CN_LEG_03_XIU: 6 0.115352E-15 0.115352E-15 CN_LEG_05_2: 19 0.00000 0.00000 EXACT: 0.00000 N = 3 EXPON = 2 0 0 Degree = 2 CN_LEG_02_XIU: 4 2.66667 0.00000 GW_02_XIU: 4 2.66667 0.00000 CN_LEG_03_1: 6 2.66667 0.177636E-14 CN_LEG_03_XIU: 6 2.66667 0.133227E-14 CN_LEG_05_2: 19 2.66667 0.444089E-15 EXACT: 2.66667 N = 3 EXPON = 0 0 3 Degree = 3 CN_LEG_03_1: 6 0.00000 0.00000 CN_LEG_03_XIU: 6 0.00000 0.00000 CN_LEG_05_2: 19 0.00000 0.00000 EXACT: 0.00000 N = 3 EXPON = 0 0 4 Degree = 4 CN_LEG_05_2: 19 1.60000 0.444089E-15 EXACT: 1.60000 N = 3 EXPON = 2 0 3 Degree = 5 CN_LEG_05_2: 19 0.00000 0.00000 EXACT: 0.00000 N = 4 EXPON = 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 16.0000 0.00000 CN_LEG_02_XIU: 5 16.0000 0.00000 GW_02_XIU: 5 16.0000 0.00000 CN_LEG_03_1: 8 16.0000 0.00000 CN_LEG_03_XIU: 8 16.0000 0.00000 CN_LEG_05_1(1): 22 16.0000 0.106581E-13 CN_LEG_05_1(2): 22 16.0000 0.177636E-13 CN_LEG_05_2: 33 16.0000 0.355271E-14 EXACT: 16.0000 N = 4 EXPON = 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 5 0.111022E-14 0.111022E-14 GW_02_XIU: 5 0.111022E-14 0.111022E-14 CN_LEG_03_1: 8 -0.666134E-15 0.666134E-15 CN_LEG_03_XIU: 8 -0.253217E-14 0.253217E-14 CN_LEG_05_1(1): 22 0.00000 0.00000 CN_LEG_05_1(2): 22 0.832667E-16 0.832667E-16 CN_LEG_05_2: 33 0.00000 0.00000 EXACT: 0.00000 N = 4 EXPON = 1 1 0 0 Degree = 2 CN_LEG_02_XIU: 5 0.444089E-15 0.444089E-15 GW_02_XIU: 5 0.444089E-15 0.444089E-15 CN_LEG_03_1: 8 -0.111022E-15 0.111022E-15 CN_LEG_03_XIU: 8 0.117517E-15 0.117517E-15 CN_LEG_05_1(1): 22 -0.115186E-14 0.115186E-14 CN_LEG_05_1(2): 22 -0.194289E-15 0.194289E-15 CN_LEG_05_2: 33 0.00000 0.00000 EXACT: 0.00000 N = 4 EXPON = 2 0 0 0 Degree = 2 CN_LEG_02_XIU: 5 5.33333 0.00000 GW_02_XIU: 5 5.33333 0.00000 CN_LEG_03_1: 8 5.33333 0.177636E-14 CN_LEG_03_XIU: 8 5.33333 0.177636E-14 CN_LEG_05_1(1): 22 5.33333 0.444089E-14 CN_LEG_05_1(2): 22 5.33333 0.444089E-14 CN_LEG_05_2: 33 5.33333 0.888178E-15 EXACT: 5.33333 N = 4 EXPON = 0 0 0 3 Degree = 3 CN_LEG_03_1: 8 -0.166533E-15 0.166533E-15 CN_LEG_03_XIU: 8 -0.199840E-14 0.199840E-14 CN_LEG_05_1(1): 22 0.00000 0.00000 CN_LEG_05_1(2): 22 -0.117961E-15 0.117961E-15 CN_LEG_05_2: 33 0.00000 0.00000 EXACT: 0.00000 N = 4 EXPON = 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 22 3.20000 0.310862E-14 CN_LEG_05_1(2): 22 3.20000 0.621725E-14 CN_LEG_05_2: 33 3.20000 0.888178E-15 EXACT: 3.20000 N = 4 EXPON = 2 0 0 3 Degree = 5 CN_LEG_05_1(1): 22 -0.138778E-16 0.138778E-16 CN_LEG_05_1(2): 22 -0.277556E-16 0.277556E-16 CN_LEG_05_2: 33 0.00000 0.00000 EXACT: 0.00000 N = 5 EXPON = 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 32.0000 0.00000 CN_LEG_02_XIU: 6 32.0000 0.355271E-14 GW_02_XIU: 6 32.0000 0.355271E-14 CN_LEG_03_1: 10 32.0000 0.355271E-14 CN_LEG_03_XIU: 10 32.0000 0.355271E-14 CN_LEG_05_1(1): 32 32.0000 0.426326E-13 CN_LEG_05_1(2): 32 32.0000 0.568434E-13 CN_LEG_05_2: 51 32.0000 0.319744E-13 EXACT: 32.0000 N = 5 EXPON = 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 6 0.00000 0.00000 GW_02_XIU: 6 0.00000 0.00000 CN_LEG_03_1: 10 0.00000 0.00000 CN_LEG_03_XIU: 10 0.00000 0.00000 CN_LEG_05_1(1): 32 -0.111022E-15 0.111022E-15 CN_LEG_05_1(2): 32 0.333067E-15 0.333067E-15 CN_LEG_05_2: 51 0.00000 0.00000 EXACT: 0.00000 N = 5 EXPON = 1 1 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 0.666134E-15 0.666134E-15 GW_02_XIU: 6 0.666134E-15 0.666134E-15 CN_LEG_03_1: 10 -0.666134E-15 0.666134E-15 CN_LEG_03_XIU: 10 0.143618E-15 0.143618E-15 CN_LEG_05_1(1): 32 0.999201E-15 0.999201E-15 CN_LEG_05_1(2): 32 -0.693889E-16 0.693889E-16 CN_LEG_05_2: 51 0.00000 0.00000 EXACT: 0.00000 N = 5 EXPON = 2 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 6 10.6667 0.355271E-14 GW_02_XIU: 6 10.6667 0.355271E-14 CN_LEG_03_1: 10 10.6667 0.710543E-14 CN_LEG_03_XIU: 10 10.6667 0.532907E-14 CN_LEG_05_1(1): 32 10.6667 0.106581E-13 CN_LEG_05_1(2): 32 10.6667 0.00000 CN_LEG_05_2: 51 10.6667 0.177636E-14 EXACT: 10.6667 N = 5 EXPON = 0 0 0 0 3 Degree = 3 CN_LEG_03_1: 10 0.00000 0.00000 CN_LEG_03_XIU: 10 0.00000 0.00000 CN_LEG_05_1(1): 32 0.416334E-15 0.416334E-15 CN_LEG_05_1(2): 32 0.00000 0.00000 CN_LEG_05_2: 51 0.00000 0.00000 EXACT: 0.00000 N = 5 EXPON = 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 32 6.40000 0.799361E-14 CN_LEG_05_1(2): 32 6.40000 0.133227E-13 CN_LEG_05_2: 51 6.40000 0.177636E-14 EXACT: 6.40000 N = 5 EXPON = 2 0 0 0 3 Degree = 5 CN_LEG_05_1(1): 32 -0.152656E-15 0.152656E-15 CN_LEG_05_1(2): 32 0.111022E-15 0.111022E-15 CN_LEG_05_2: 51 0.00000 0.00000 EXACT: 0.00000 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 CN_LEG_01_1: 1 64.0000 0.00000 CN_LEG_02_XIU: 7 64.0000 0.142109E-13 GW_02_XIU: 7 64.0000 0.142109E-13 CN_LEG_03_1: 12 64.0000 0.00000 CN_LEG_03_XIU: 12 64.0000 0.00000 CN_LEG_05_1(1): 44 64.0000 0.284217E-13 CN_LEG_05_2: 73 64.0000 0.994760E-13 EXACT: 64.0000 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 CN_LEG_01_1: 1 0.00000 0.00000 CN_LEG_02_XIU: 7 -0.355271E-14 0.355271E-14 GW_02_XIU: 7 -0.355271E-14 0.355271E-14 CN_LEG_03_1: 12 -0.119904E-13 0.119904E-13 CN_LEG_03_XIU: 12 -0.141424E-13 0.141424E-13 CN_LEG_05_1(1): 44 0.666134E-15 0.666134E-15 CN_LEG_05_2: 73 0.00000 0.00000 EXACT: 0.00000 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 0.222045E-14 0.222045E-14 GW_02_XIU: 7 0.222045E-14 0.222045E-14 CN_LEG_03_1: 12 0.00000 0.00000 CN_LEG_03_XIU: 12 -0.648815E-15 0.648815E-15 CN_LEG_05_1(1): 44 0.00000 0.00000 CN_LEG_05_2: 73 0.00000 0.00000 EXACT: 0.00000 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 CN_LEG_02_XIU: 7 21.3333 0.00000 GW_02_XIU: 7 21.3333 0.00000 CN_LEG_03_1: 12 21.3333 0.710543E-14 CN_LEG_03_XIU: 12 21.3333 0.710543E-14 CN_LEG_05_1(1): 44 21.3333 0.213163E-13 CN_LEG_05_2: 73 21.3333 0.710543E-14 EXACT: 21.3333 N = 6 EXPON = 0 0 0 0 0 3 Degree = 3 CN_LEG_03_1: 12 0.777156E-15 0.777156E-15 CN_LEG_03_XIU: 12 -0.666134E-15 0.666134E-15 CN_LEG_05_1(1): 44 0.111022E-15 0.111022E-15 CN_LEG_05_2: 73 0.00000 0.00000 EXACT: 0.00000 N = 6 EXPON = 0 0 0 0 0 4 Degree = 4 CN_LEG_05_1(1): 44 12.8000 0.213163E-13 CN_LEG_05_2: 73 12.8000 0.710543E-14 EXACT: 12.8000 N = 6 EXPON = 2 0 0 0 0 3 Degree = 5 CN_LEG_05_1(1): 44 0.00000 0.00000 CN_LEG_05_2: 73 0.00000 0.00000 EXACT: 0.00000 EN_HER_TESTS Demonstrate the use of Stroud rules for the region EN_HER, that is, all of N-dimensional space, with the Hermite weight function W(X) = product ( 1 <= i <= N ) exp ( - X(I)^2 ) 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 EN_HER_01_1: 1 1.77245 0.222045E-15 EN_HER_02_XIU: 2 1.77245 0.222045E-15 GW_02_XIU: 2 1.77245 0.222045E-15 EN_HER_03_1: 2 1.77245 0.222045E-15 EN_HER_03_2: 2 1.77245 0.222045E-15 EN_HER_03_XIU: 2 1.77245 0.222045E-15 EN_HER_05_2: 3 1.77245 0.222045E-15 EN_HER_05_4: 3 1.77245 0.222045E-15 EN_HER_05_5: 3 1.77245 0.444089E-15 EXACT: 1.77245 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 0.111022E-15 GW_02_XIU: 2 0.886227 0.111022E-15 EN_HER_03_1: 2 0.886227 0.111022E-15 EN_HER_03_2: 2 0.886227 0.111022E-15 EN_HER_03_XIU: 2 0.886227 0.333067E-15 EN_HER_05_2: 3 0.886227 0.111022E-15 EN_HER_05_4: 3 0.886227 0.333067E-15 EN_HER_05_5: 3 0.886227 0.333067E-15 EXACT: 0.886227 N = 1 EXPON = 0 Degree = 0 EN_HER_01_1: 1 1.77245 0.222045E-15 EN_HER_02_XIU: 2 1.77245 0.222045E-15 GW_02_XIU: 2 1.77245 0.222045E-15 EN_HER_03_1: 2 1.77245 0.222045E-15 EN_HER_03_2: 2 1.77245 0.222045E-15 EN_HER_03_XIU: 2 1.77245 0.222045E-15 EN_HER_05_2: 3 1.77245 0.222045E-15 EN_HER_05_4: 3 1.77245 0.222045E-15 EN_HER_05_5: 3 1.77245 0.444089E-15 EXACT: 1.77245 N = 1 EXPON = 6 Degree = 6 EXACT: 3.32335 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 0.111022E-15 GW_02_XIU: 2 0.886227 0.111022E-15 EN_HER_03_1: 2 0.886227 0.111022E-15 EN_HER_03_2: 2 0.886227 0.111022E-15 EN_HER_03_XIU: 2 0.886227 0.333067E-15 EN_HER_05_2: 3 0.886227 0.111022E-15 EN_HER_05_4: 3 0.886227 0.333067E-15 EN_HER_05_5: 3 0.886227 0.333067E-15 EXACT: 0.886227 N = 1 EXPON = 8 Degree = 8 EXACT: 11.6317 N = 1 EXPON = 10 Degree = 10 EXACT: 52.3428 N = 1 EXPON = 0 Degree = 0 EN_HER_01_1: 1 1.77245 0.222045E-15 EN_HER_02_XIU: 2 1.77245 0.222045E-15 GW_02_XIU: 2 1.77245 0.222045E-15 EN_HER_03_1: 2 1.77245 0.222045E-15 EN_HER_03_2: 2 1.77245 0.222045E-15 EN_HER_03_XIU: 2 1.77245 0.222045E-15 EN_HER_05_2: 3 1.77245 0.222045E-15 EN_HER_05_4: 3 1.77245 0.222045E-15 EN_HER_05_5: 3 1.77245 0.444089E-15 EXACT: 1.77245 N = 1 EXPON = 2 Degree = 2 EN_HER_02_XIU: 2 0.886227 0.111022E-15 GW_02_XIU: 2 0.886227 0.111022E-15 EN_HER_03_1: 2 0.886227 0.111022E-15 EN_HER_03_2: 2 0.886227 0.111022E-15 EN_HER_03_XIU: 2 0.886227 0.333067E-15 EN_HER_05_2: 3 0.886227 0.111022E-15 EN_HER_05_4: 3 0.886227 0.333067E-15 EN_HER_05_5: 3 0.886227 0.333067E-15 EXACT: 0.886227 N = 2 EXPON = 0 0 Degree = 0 EN_HER_01_1: 1 3.14159 0.888178E-15 EN_HER_02_XIU: 3 3.14159 0.444089E-15 GW_02_XIU: 3 3.14159 0.444089E-15 EN_HER_03_1: 4 3.14159 0.888178E-15 EN_HER_03_2: 4 3.14159 0.888178E-15 EN_HER_03_XIU: 4 3.14159 0.888178E-15 EN_HER_05_1(1): 8 3.14159 0.177636E-14 EN_HER_05_2: 9 3.14159 0.177636E-14 EN_HER_05_4: 7 3.14159 0.888178E-15 EN_HER_05_5: 9 3.14159 0.177636E-14 EXACT: 3.14159 N = 2 EXPON = 2 0 Degree = 2 EN_HER_02_XIU: 3 1.57080 0.666134E-15 GW_02_XIU: 3 1.57080 0.666134E-15 EN_HER_03_1: 4 1.57080 0.444089E-15 EN_HER_03_2: 4 1.57080 0.00000 EN_HER_03_XIU: 4 1.57080 0.444089E-15 EN_HER_05_1(1): 8 1.57080 0.177636E-14 EN_HER_05_2: 9 1.57080 0.222045E-15 EN_HER_05_4: 7 1.57080 0.666134E-15 EN_HER_05_5: 9 1.57080 0.666134E-15 EXACT: 1.57080 N = 2 EXPON = 0 4 Degree = 4 EN_HER_05_1(1): 8 2.35619 0.666134E-14 EN_HER_05_2: 9 2.35619 0.00000 EN_HER_05_4: 7 2.35619 0.888178E-15 EN_HER_05_5: 9 2.35619 0.444089E-15 EXACT: 2.35619 N = 2 EXPON = 6 0 Degree = 6 EXACT: 5.89049 N = 2 EXPON = 2 4 Degree = 6 EXACT: 1.17810 N = 2 EXPON = 0 8 Degree = 8 EXACT: 20.6167 N = 2 EXPON = 10 0 Degree = 10 EXACT: 92.7752 N = 2 EXPON = 0 1 Degree = 1 EN_HER_01_1: 1 0.00000 0.00000 EN_HER_02_XIU: 3 0.333067E-15 0.333067E-15 GW_02_XIU: 3 0.333067E-15 0.333067E-15 EN_HER_03_1: 4 0.00000 0.00000 EN_HER_03_2: 4 0.00000 0.00000 EN_HER_03_XIU: 4 -0.813448E-16 0.813448E-16 EN_HER_05_1(1): 8 0.00000 0.00000 EN_HER_05_2: 9 0.00000 0.00000 EN_HER_05_4: 7 0.00000 0.00000 EN_HER_05_5: 9 0.00000 0.00000 EXACT: 0.00000 N = 2 EXPON = 2 2 Degree = 4 EN_HER_05_1(1): 8 0.785398 0.122125E-14 EN_HER_05_2: 9 0.785398 0.222045E-15 EN_HER_05_4: 7 0.785398 0.111022E-15 EN_HER_05_5: 9 0.785398 0.333067E-15 EXACT: 0.785398 N = 3 EXPON = 0 0 0 Degree = 0 EN_HER_01_1: 1 5.56833 0.266454E-14 EN_HER_02_XIU: 4 5.56833 0.266454E-14 GW_02_XIU: 4 5.56833 0.266454E-14 EN_HER_03_1: 6 5.56833 0.266454E-14 EN_HER_03_2: 8 5.56833 0.266454E-14 EN_HER_03_XIU: 6 5.56833 0.266454E-14 EN_HER_05_1(1): 14 5.56833 0.355271E-14 EN_HER_05_1(2): 14 5.56833 0.355271E-14 EN_HER_05_2: 19 5.56833 0.888178E-15 EN_HER_05_3: 14 5.56833 0.266454E-14 EN_HER_05_4: 15 5.56833 0.355271E-14 EN_HER_05_5: 25 5.56833 0.888178E-15 EN_HER_07_1(1): 27 5.56833 0.266454E-14 EN_HER_07_1(2): 27 5.56833 0.266454E-14 EN_HER_07_2: 52 5.56833 0.888178E-15 EN_HER_07_3(1): 45 5.56833 0.156319E-12 EN_HER_07_3(2): 45 5.56833 0.337508E-13 EN_HER_09_1(1): 77 5.56833 0.532907E-14 EN_HER_09_1(2): 77 5.56833 0.532907E-14 EN_HER_11_1(1): 151 5.56833 0.710543E-14 EN_HER_11_1(2): 151 5.56833 0.230926E-13 EXACT: 5.56833 N = 3 EXPON = 2 0 0 Degree = 2 EN_HER_02_XIU: 4 2.78416 0.00000 GW_02_XIU: 4 2.78416 0.00000 EN_HER_03_1: 6 2.78416 0.177636E-14 EN_HER_03_2: 8 2.78416 0.133227E-14 EN_HER_03_XIU: 6 2.78416 0.888178E-15 EN_HER_05_1(1): 14 2.78416 0.266454E-14 EN_HER_05_1(2): 14 2.78416 0.444089E-14 EN_HER_05_2: 19 2.78416 0.133227E-14 EN_HER_05_3: 14 2.78416 0.444089E-15 EN_HER_05_4: 15 2.78416 0.177636E-14 EN_HER_05_5: 25 2.78416 0.444089E-15 EN_HER_07_1(1): 27 2.78416 0.888178E-15 EN_HER_07_1(2): 27 2.78416 0.00000 EN_HER_07_2: 52 2.78416 0.266454E-14 EN_HER_07_3(1): 45 2.78416 0.142109E-13 EN_HER_07_3(2): 45 2.78416 0.159872E-13 EN_HER_09_1(1): 77 2.78416 0.266454E-14 EN_HER_09_1(2): 77 2.78416 0.266454E-14 EN_HER_11_1(1): 151 2.78416 0.444089E-15 EN_HER_11_1(2): 151 2.78416 0.124345E-13 EXACT: 2.78416 N = 3 EXPON = 0 4 0 Degree = 4 EN_HER_05_1(1): 14 4.17625 0.888178E-15 EN_HER_05_1(2): 14 4.17625 0.186517E-13 EN_HER_05_2: 19 4.17625 0.177636E-14 EN_HER_05_3: 14 4.17625 0.888178E-15 EN_HER_05_4: 15 4.17625 0.888178E-15 EN_HER_05_5: 25 4.17625 0.177636E-14 EN_HER_07_1(1): 27 4.17625 0.888178E-15 EN_HER_07_1(2): 27 4.17625 0.888178E-15 EN_HER_07_2: 52 4.17625 0.266454E-14 EN_HER_07_3(1): 45 4.17625 0.461853E-13 EN_HER_07_3(2): 45 4.17625 0.417444E-13 EN_HER_09_1(1): 77 4.17625 0.248690E-13 EN_HER_09_1(2): 77 4.17625 0.248690E-13 EN_HER_11_1(1): 151 4.17625 0.301981E-13 EN_HER_11_1(2): 151 4.17625 0.310862E-13 EXACT: 4.17625 N = 3 EXPON = 0 0 6 Degree = 6 EN_HER_07_1(1): 27 10.4406 0.532907E-14 EN_HER_07_1(2): 27 10.4406 0.710543E-14 EN_HER_07_2: 52 10.4406 0.888178E-14 EN_HER_07_3(1): 45 10.4406 0.197176E-12 EN_HER_07_3(2): 45 10.4406 0.168754E-12 EN_HER_09_1(1): 77 10.4406 0.122569E-12 EN_HER_09_1(2): 77 10.4406 0.122569E-12 EN_HER_11_1(1): 151 10.4406 0.213163E-13 EN_HER_11_1(2): 151 10.4406 0.621725E-13 EXACT: 10.4406 N = 3 EXPON = 2 4 0 Degree = 6 EN_HER_07_1(1): 27 2.08812 0.444089E-15 EN_HER_07_1(2): 27 2.08812 0.444089E-15 EN_HER_07_2: 52 2.08812 0.222045E-14 EN_HER_07_3(1): 45 2.08812 0.377476E-13 EN_HER_07_3(2): 45 2.08812 0.328626E-13 EN_HER_09_1(1): 77 2.08812 0.128786E-13 EN_HER_09_1(2): 77 2.08812 0.128786E-13 EN_HER_11_1(1): 151 2.08812 0.230926E-13 EN_HER_11_1(2): 151 2.08812 0.235367E-13 EXACT: 2.08812 N = 3 EXPON = 8 0 0 Degree = 8 EN_HER_09_1(1): 77 36.5422 0.653699E-12 EN_HER_09_1(2): 77 36.5422 0.653699E-12 EN_HER_11_1(1): 151 36.5422 0.163425E-12 EN_HER_11_1(2): 151 36.5422 0.355271E-13 EXACT: 36.5422 N = 3 EXPON = 0 10 0 Degree = 10 EN_HER_11_1(1): 151 164.440 0.426326E-12 EN_HER_11_1(2): 151 164.440 0.105160E-11 EXACT: 164.440 N = 3 EXPON = 0 1 2 Degree = 3 EN_HER_03_1: 6 0.00000 0.00000 EN_HER_03_2: 8 0.00000 0.00000 EN_HER_03_XIU: 6 0.216781E-15 0.216781E-15 EN_HER_05_1(1): 14 0.00000 0.00000 EN_HER_05_1(2): 14 0.00000 0.00000 EN_HER_05_2: 19 0.00000 0.00000 EN_HER_05_3: 14 0.00000 0.00000 EN_HER_05_4: 15 0.00000 0.00000 EN_HER_05_5: 25 0.00000 0.00000 EN_HER_07_1(1): 27 0.00000 0.00000 EN_HER_07_1(2): 27 0.00000 0.00000 EN_HER_07_2: 52 0.00000 0.00000 EN_HER_07_3(1): 45 0.00000 0.00000 EN_HER_07_3(2): 45 0.00000 0.00000 EN_HER_09_1(1): 77 0.00000 0.00000 EN_HER_09_1(2): 77 0.00000 0.00000 EN_HER_11_1(1): 151 0.00000 0.00000 EN_HER_11_1(2): 151 0.00000 0.00000 EXACT: 0.00000 N = 3 EXPON = 2 2 2 Degree = 6 EN_HER_07_1(1): 27 0.696041 0.333067E-15 EN_HER_07_1(2): 27 0.696041 0.333067E-15 EN_HER_07_2: 52 0.696041 0.111022E-14 EN_HER_07_3(1): 45 0.696041 0.555112E-15 EN_HER_07_3(2): 45 0.696041 0.117684E-13 EN_HER_09_1(1): 77 0.696041 0.155431E-14 EN_HER_09_1(2): 77 0.696041 0.155431E-14 EN_HER_11_1(1): 151 0.696041 0.666134E-14 EN_HER_11_1(2): 151 0.696041 0.732747E-14 EXACT: 0.696041 N = 4 EXPON = 0 0 0 0 Degree = 0 EN_HER_01_1: 1 9.86960 0.710543E-14 EN_HER_02_XIU: 5 9.86960 0.710543E-14 GW_02_XIU: 5 9.86960 0.710543E-14 EN_HER_03_1: 8 9.86960 0.710543E-14 EN_HER_03_2: 16 9.86960 0.355271E-14 EN_HER_03_XIU: 8 9.86960 0.710543E-14 EN_HER_05_1(1): 22 9.86960 0.177636E-14 EN_HER_05_2: 33 9.86960 0.710543E-14 EN_HER_05_3: 24 9.86960 0.00000 EN_HER_05_4: 31 9.86960 0.106581E-13 EN_HER_05_5: 65 9.86960 0.532907E-14 EN_HER_07_1(1): 49 9.86960 0.177636E-14 EN_HER_07_1(2): 49 9.86960 0.00000 EN_HER_07_2: 96 9.86960 0.195399E-13 EN_HER_07_3(1): 97 9.86960 0.131806E-11 EN_HER_07_3(2): 97 9.86960 0.213163E-13 EN_HER_09_1(1): 193 9.86960 0.159872E-13 EN_HER_09_1(2): 193 9.86960 0.337508E-13 EN_HER_11_1(1): 417 9.86960 0.600409E-11 EN_HER_11_1(2): 417 9.86960 0.131450E-12 EXACT: 9.86960 N = 4 EXPON = 2 0 0 0 Degree = 2 EN_HER_02_XIU: 5 4.93480 0.888178E-15 GW_02_XIU: 5 4.93480 0.888178E-15 EN_HER_03_1: 8 4.93480 0.266454E-14 EN_HER_03_2: 16 4.93480 0.177636E-14 EN_HER_03_XIU: 8 4.93480 0.355271E-14 EN_HER_05_1(1): 22 4.93480 0.177636E-14 EN_HER_05_2: 33 4.93480 0.444089E-14 EN_HER_05_3: 24 4.93480 0.710543E-14 EN_HER_05_4: 31 4.93480 0.444089E-14 EN_HER_05_5: 65 4.93480 0.710543E-14 EN_HER_07_1(1): 49 4.93480 0.621725E-14 EN_HER_07_1(2): 49 4.93480 0.355271E-14 EN_HER_07_2: 96 4.93480 0.799361E-14 EN_HER_07_3(1): 97 4.93480 0.104805E-12 EN_HER_07_3(2): 97 4.93480 0.310862E-13 EN_HER_09_1(1): 193 4.93480 0.888178E-14 EN_HER_09_1(2): 193 4.93480 0.355271E-14 EN_HER_11_1(1): 417 4.93480 0.380140E-12 EN_HER_11_1(2): 417 4.93480 0.117240E-12 EXACT: 4.93480 N = 4 EXPON = 0 4 0 0 Degree = 4 EN_HER_05_1(1): 22 7.40220 0.142109E-13 EN_HER_05_2: 33 7.40220 0.532907E-14 EN_HER_05_3: 24 7.40220 0.177636E-14 EN_HER_05_4: 31 7.40220 0.888178E-15 EN_HER_05_5: 65 7.40220 0.266454E-14 EN_HER_07_1(1): 49 7.40220 0.888178E-15 EN_HER_07_1(2): 49 7.40220 0.621725E-14 EN_HER_07_2: 96 7.40220 0.888178E-14 EN_HER_07_3(1): 97 7.40220 0.116351E-12 EN_HER_07_3(2): 97 7.40220 0.968114E-13 EN_HER_09_1(1): 193 7.40220 0.541789E-13 EN_HER_09_1(2): 193 7.40220 0.337508E-13 EN_HER_11_1(1): 417 7.40220 0.116351E-12 EN_HER_11_1(2): 417 7.40220 0.621725E-13 EXACT: 7.40220 N = 4 EXPON = 0 0 6 0 Degree = 6 EN_HER_07_1(1): 49 18.5055 0.355271E-14 EN_HER_07_1(2): 49 18.5055 0.355271E-14 EN_HER_07_2: 96 18.5055 0.177636E-13 EN_HER_07_3(1): 97 18.5055 0.312639E-12 EN_HER_07_3(2): 97 18.5055 0.323297E-12 EN_HER_09_1(1): 193 18.5055 0.216716E-12 EN_HER_09_1(2): 193 18.5055 0.262901E-12 EN_HER_11_1(1): 417 18.5055 0.184741E-12 EN_HER_11_1(2): 417 18.5055 0.213163E-13 EXACT: 18.5055 N = 4 EXPON = 2 4 0 0 Degree = 6 EN_HER_07_1(1): 49 3.70110 0.888178E-15 EN_HER_07_1(2): 49 3.70110 0.888178E-15 EN_HER_07_2: 96 3.70110 0.399680E-14 EN_HER_07_3(1): 97 3.70110 0.599520E-13 EN_HER_07_3(2): 97 3.70110 0.635048E-13 EN_HER_09_1(1): 193 3.70110 0.235367E-13 EN_HER_09_1(2): 193 3.70110 0.177636E-13 EN_HER_11_1(1): 417 3.70110 0.208722E-13 EN_HER_11_1(2): 417 3.70110 0.386358E-13 EXACT: 3.70110 N = 4 EXPON = 0 0 0 8 Degree = 8 EN_HER_09_1(1): 193 64.7693 0.112266E-11 EN_HER_09_1(2): 193 64.7693 0.108002E-11 EN_HER_11_1(1): 417 64.7693 0.966338E-12 EN_HER_11_1(2): 417 64.7693 0.190425E-11 EXACT: 64.7693 N = 4 EXPON = 10 0 0 0 Degree = 10 EN_HER_11_1(1): 417 291.462 0.420641E-11 EN_HER_11_1(2): 417 291.462 0.159162E-11 EXACT: 291.462 N = 4 EXPON = 0 1 2 3 Degree = 6 EN_HER_07_1(1): 49 0.00000 0.00000 EN_HER_07_1(2): 49 0.00000 0.00000 EN_HER_07_2: 96 0.00000 0.00000 EN_HER_07_3(1): 97 0.00000 0.00000 EN_HER_07_3(2): 97 0.00000 0.00000 EN_HER_09_1(1): 193 0.00000 0.00000 EN_HER_09_1(2): 193 0.00000 0.00000 EN_HER_11_1(1): 417 0.00000 0.00000 EN_HER_11_1(2): 417 0.00000 0.00000 EXACT: 0.00000 N = 4 EXPON = 2 2 2 2 Degree = 8 EN_HER_09_1(1): 193 0.616850 0.123235E-13 EN_HER_09_1(2): 193 0.616850 0.555112E-15 EN_HER_11_1(1): 417 0.616850 0.666134E-15 EN_HER_11_1(2): 417 0.616850 0.145439E-13 EXACT: 0.616850 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 17.4934 0.142109E-13 EN_HER_02_XIU: 6 17.4934 0.142109E-13 GW_02_XIU: 6 17.4934 0.142109E-13 EN_HER_03_1: 10 17.4934 0.142109E-13 EN_HER_03_2: 32 17.4934 0.106581E-13 EN_HER_03_XIU: 10 17.4934 0.142109E-13 EN_HER_05_1(1): 32 17.4934 0.710543E-14 EN_HER_05_1(2): 32 17.4934 0.710543E-14 EN_HER_05_2: 51 17.4934 0.284217E-13 EN_HER_05_3: 42 17.4934 0.106581E-13 EN_HER_05_4: 63 17.4934 0.142109E-13 EN_HER_05_5: 161 17.4934 0.568434E-13 EN_HER_05_6: 192 17.4934 0.568434E-13 EN_HER_07_2: 164 17.4934 0.319744E-13 EN_HER_07_3(1): 181 17.4934 0.742517E-12 EN_HER_07_3(2): 181 17.4934 0.166622E-11 EN_HER_09_1(1): 421 17.4934 0.213163E-13 EN_HER_09_1(2): 421 17.4934 0.461853E-13 EN_HER_11_1(1): 983 17.4935 0.795467E-04 EN_HER_11_1(2): 983 17.4934 0.117844E-10 EXACT: 17.4934 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EN_HER_02_XIU: 6 8.74671 0.177636E-14 GW_02_XIU: 6 8.74671 0.177636E-14 EN_HER_03_1: 10 8.74671 0.532907E-14 EN_HER_03_2: 32 8.74671 0.532907E-14 EN_HER_03_XIU: 10 8.74671 0.710543E-14 EN_HER_05_1(1): 32 8.74671 0.341061E-12 EN_HER_05_1(2): 32 8.74671 0.355271E-13 EN_HER_05_2: 51 8.74671 0.888178E-14 EN_HER_05_3: 42 8.74671 0.195399E-13 EN_HER_05_4: 63 8.74671 0.532907E-14 EN_HER_05_5: 161 8.74671 0.444089E-13 EN_HER_05_6: 192 8.74671 0.319744E-13 EN_HER_07_2: 164 8.74671 0.355271E-14 EN_HER_07_3(1): 181 8.74671 0.467182E-12 EN_HER_07_3(2): 181 8.74671 0.444089E-13 EN_HER_09_1(1): 421 8.74671 0.479616E-13 EN_HER_09_1(2): 421 8.74671 0.266454E-13 EN_HER_11_1(1): 983 8.74671 0.400819E-06 EN_HER_11_1(2): 983 8.74671 0.129674E-12 EXACT: 8.74671 N = 5 EXPON = 0 4 0 0 0 Degree = 4 EN_HER_05_1(1): 32 13.1201 0.456524E-12 EN_HER_05_1(2): 32 13.1201 0.817124E-13 EN_HER_05_2: 51 13.1201 0.532907E-14 EN_HER_05_3: 42 13.1201 0.195399E-13 EN_HER_05_4: 63 13.1201 0.532907E-14 EN_HER_05_5: 161 13.1201 0.319744E-13 EN_HER_05_6: 192 13.1201 0.177636E-13 EN_HER_07_2: 164 13.1201 0.195399E-13 EN_HER_07_3(1): 181 13.1201 0.298428E-12 EN_HER_07_3(2): 181 13.1201 0.159872E-12 EN_HER_09_1(1): 421 13.1201 0.888178E-14 EN_HER_09_1(2): 421 13.1201 0.710543E-13 EN_HER_11_1(1): 983 13.1201 0.762219E-07 EN_HER_11_1(2): 983 13.1201 0.817124E-13 EXACT: 13.1201 N = 5 EXPON = 0 0 6 0 0 Degree = 6 EN_HER_07_2: 164 32.8002 0.568434E-13 EN_HER_07_3(1): 181 32.8002 0.632383E-12 EN_HER_07_3(2): 181 32.8002 0.575540E-12 EN_HER_09_1(1): 421 32.8002 0.369482E-12 EN_HER_09_1(2): 421 32.8002 0.348166E-12 EN_HER_11_1(1): 983 32.8002 0.144940E-07 EN_HER_11_1(2): 983 32.8002 0.426326E-12 EXACT: 32.8002 N = 5 EXPON = 2 4 0 0 0 Degree = 6 EN_HER_07_2: 164 6.56003 0.888178E-15 EN_HER_07_3(1): 181 6.56003 0.117240E-12 EN_HER_07_3(2): 181 6.56003 0.122569E-12 EN_HER_09_1(1): 421 6.56003 0.479616E-13 EN_HER_09_1(2): 421 6.56003 0.417444E-13 EN_HER_11_1(1): 983 6.56003 0.162537E-12 EN_HER_11_1(2): 983 6.56003 0.808242E-13 EXACT: 6.56003 N = 5 EXPON = 0 0 0 8 0 Degree = 8 EN_HER_09_1(1): 421 114.801 0.150635E-11 EN_HER_09_1(2): 421 114.801 0.153477E-11 EN_HER_11_1(1): 983 114.801 0.275533E-08 EN_HER_11_1(2): 983 114.801 0.190425E-11 EXACT: 114.801 N = 5 EXPON = 0 0 0 0 10 Degree = 10 EN_HER_11_1(1): 983 516.603 0.522050E-09 EN_HER_11_1(2): 983 516.603 0.341061E-12 EXACT: 516.603 N = 5 EXPON = 0 1 2 3 4 Degree = 10 EN_HER_11_1(1): 983 0.00000 0.00000 EN_HER_11_1(2): 983 0.00000 0.00000 EXACT: 0.00000 N = 5 EXPON = 2 2 2 2 2 Degree = 10 EN_HER_11_1(1): 983 0.546669 0.355271E-14 EN_HER_11_1(2): 983 0.546669 0.355271E-14 EXACT: 0.546669 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EN_HER_01_1: 1 31.0063 0.319744E-13 EN_HER_02_XIU: 7 31.0063 0.284217E-13 GW_02_XIU: 7 31.0063 0.284217E-13 EN_HER_03_1: 12 31.0063 0.319744E-13 EN_HER_03_2: 64 31.0063 0.106581E-13 EN_HER_03_XIU: 12 31.0063 0.319744E-13 EN_HER_05_1(1): 44 31.0063 0.284217E-13 EN_HER_05_1(2): 44 31.0063 0.284217E-13 EN_HER_05_2: 73 31.0063 0.106581E-13 EN_HER_05_3: 76 31.0063 0.142109E-12 EN_HER_05_4: 127 31.0063 0.675016E-13 EN_HER_05_5: 385 31.0063 0.959233E-13 EN_HER_05_6: 448 31.0063 0.355271E-14 EN_HER_07_1(1): 137 31.0063 0.163425E-12 EN_HER_07_2: 272 31.0063 0.177636E-13 EN_HER_07_3(1): 305 31.0062 0.112129E-03 EN_HER_07_3(2): 305 31.0063 0.246914E-11 EN_HER_09_1(1): 825 31.0063 0.891731E-12 EN_HER_09_1(2): 825 31.0063 0.579092E-12 EXACT: 31.0063 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 7 15.5031 0.106581E-13 GW_02_XIU: 7 15.5031 0.106581E-13 EN_HER_03_1: 12 15.5031 0.195399E-13 EN_HER_03_2: 64 15.5031 0.177636E-14 EN_HER_03_XIU: 12 15.5031 0.159872E-13 EN_HER_05_1(1): 44 15.5031 0.639488E-13 EN_HER_05_1(2): 44 15.5031 0.319744E-13 EN_HER_05_2: 73 15.5031 0.710543E-14 EN_HER_05_3: 76 15.5031 0.710543E-14 EN_HER_05_4: 127 15.5031 0.710543E-14 EN_HER_05_5: 385 15.5031 0.110134E-12 EN_HER_05_6: 448 15.5031 0.639488E-13 EN_HER_07_1(1): 137 15.5031 0.124345E-13 EN_HER_07_2: 272 15.5031 0.390799E-13 EN_HER_07_3(1): 305 15.5031 0.307665E-11 EN_HER_07_3(2): 305 15.5031 0.692779E-13 EN_HER_09_1(1): 825 15.5031 0.181188E-12 EN_HER_09_1(2): 825 15.5031 0.248690E-13 EXACT: 15.5031 N = 6 EXPON = 0 4 0 0 0 0 Degree = 4 EN_HER_05_1(1): 44 23.2547 0.230926E-12 EN_HER_05_1(2): 44 23.2547 0.131450E-12 EN_HER_05_2: 73 23.2547 0.00000 EN_HER_05_3: 76 23.2547 0.106581E-12 EN_HER_05_4: 127 23.2547 0.710543E-14 EN_HER_05_5: 385 23.2547 0.206057E-12 EN_HER_05_6: 448 23.2547 0.355271E-14 EN_HER_07_1(1): 137 23.2547 0.603961E-13 EN_HER_07_2: 272 23.2547 0.284217E-13 EN_HER_07_3(1): 305 23.2547 0.120437E-11 EN_HER_07_3(2): 305 23.2547 0.291323E-12 EN_HER_09_1(1): 825 23.2547 0.230926E-12 EN_HER_09_1(2): 825 23.2547 0.461853E-13 EXACT: 23.2547 N = 6 EXPON = 0 0 6 0 0 0 Degree = 6 EN_HER_07_1(1): 137 58.1368 0.142109E-13 EN_HER_07_2: 272 58.1368 0.177636E-12 EN_HER_07_3(1): 305 58.1368 0.112266E-11 EN_HER_07_3(2): 305 58.1368 0.930811E-12 EN_HER_09_1(1): 825 58.1368 0.220268E-12 EN_HER_09_1(2): 825 58.1368 0.412115E-12 EXACT: 58.1368 N = 6 EXPON = 2 4 0 0 0 0 Degree = 6 EN_HER_07_1(1): 137 11.6274 0.532907E-14 EN_HER_07_2: 272 11.6274 0.888178E-14 EN_HER_07_3(1): 305 11.6274 0.216716E-12 EN_HER_07_3(2): 305 11.6274 0.220268E-12 EN_HER_09_1(1): 825 11.6274 0.122569E-12 EN_HER_09_1(2): 825 11.6274 0.781597E-13 EXACT: 11.6274 N = 6 EXPON = 0 0 0 8 0 0 Degree = 8 EN_HER_09_1(1): 825 203.479 0.503064E-11 EN_HER_09_1(2): 825 203.479 0.443379E-11 EXACT: 203.479 N = 6 EXPON = 0 0 0 0 10 0 Degree = 10 EXACT: 915.654 N = 6 EXPON = 0 1 2 3 4 5 Degree = 15 EXACT: 0.00000 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 0.639488E-13 EN_HER_02_XIU: 8 54.9572 0.639488E-13 GW_02_XIU: 8 54.9572 0.639488E-13 EN_HER_03_1: 14 54.9572 0.852651E-13 EN_HER_03_2: 128 54.9572 0.184741E-12 EN_HER_03_XIU: 14 54.9572 0.852651E-13 EN_HER_05_1(1): 58 54.9572 0.213163E-13 EN_HER_05_2: 99 54.9572 0.170530E-12 EN_HER_05_3: 142 54.9572 0.262901E-12 EN_HER_05_4: 255 54.9572 0.113687E-12 EN_HER_05_5: 897 54.9572 0.319744E-12 EN_HER_05_6: 1024 54.9572 0.916600E-12 EN_HER_07_1(1): 227 54.9572 0.170530E-12 EN_HER_07_2: 452 54.9572 0.142109E-12 EXACT: 54.9572 N = 7 EXPON = 2 0 0 0 0 0 0 Degree = 2 EN_HER_02_XIU: 8 27.4786 0.213163E-13 GW_02_XIU: 8 27.4786 0.213163E-13 EN_HER_03_1: 14 27.4786 0.319744E-13 EN_HER_03_2: 128 27.4786 0.746070E-13 EN_HER_03_XIU: 14 27.4786 0.355271E-13 EN_HER_05_1(1): 58 27.4786 0.149214E-12 EN_HER_05_2: 99 27.4786 0.213163E-13 EN_HER_05_3: 142 27.4786 0.124345E-12 EN_HER_05_4: 255 27.4786 0.923706E-13 EN_HER_05_5: 897 27.4786 0.532907E-12 EN_HER_05_6: 1024 27.4786 0.270006E-12 EN_HER_07_1(1): 227 27.4786 0.120792E-12 EN_HER_07_2: 452 27.4786 0.355271E-14 EXACT: 27.4786 N = 7 EXPON = 0 4 0 0 0 0 0 Degree = 4 EN_HER_05_1(1): 58 41.2179 0.490274E-12 EN_HER_05_2: 99 41.2179 0.213163E-13 EN_HER_05_3: 142 41.2179 0.177636E-12 EN_HER_05_4: 255 41.2179 0.355271E-13 EN_HER_05_5: 897 41.2179 0.326850E-12 EN_HER_05_6: 1024 41.2179 0.540012E-12 EN_HER_07_1(1): 227 41.2179 0.127898E-12 EN_HER_07_2: 452 41.2179 0.710543E-14 EXACT: 41.2179 N = 7 EXPON = 0 0 6 0 0 0 0 Degree = 6 EN_HER_07_1(1): 227 103.045 0.710543E-13 EN_HER_07_2: 452 103.045 0.568434E-13 EXACT: 103.045 N = 7 EXPON = 2 4 0 0 0 0 0 Degree = 6 EN_HER_07_1(1): 227 20.6089 0.355271E-13 EN_HER_07_2: 452 20.6089 0.461853E-13 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 = 0 1 2 3 4 5 6 Degree = 21 EXACT: 0.00000 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 Generalized Laguerre 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 0.00000 EPN_GLG_01_1: 1 1.77245 0.00000 EPN_GLG_02_XIU: 2 1.77245 0.00000 GW_02_XIU: 2 1.77245 0.00000 EXACT: 1.77245 N = 1 ALPHA = 0.00000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 2 1.00000 0.00000 GW_02_XIU: 2 1.00000 0.00000 EXACT: 1.00000 N = 1 ALPHA = 0.500000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 0.886227 0.00000 EPN_GLG_01_1: 1 0.886227 0.00000 EPN_GLG_02_XIU: 2 0.886227 0.00000 GW_02_XIU: 2 0.886227 0.00000 EXACT: 0.886227 N = 1 ALPHA = 1.00000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 2 1.00000 0.00000 GW_02_XIU: 2 1.00000 0.00000 EXACT: 1.00000 N = 1 ALPHA = 2.00000 EXPON = 0 Degree = 0 EPN_GLG_00_1: 1 2.00000 0.00000 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = -0.500000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 0.886227 0.00000 EPN_GLG_02_XIU: 2 0.886227 0.222045E-15 GW_02_XIU: 2 0.886227 0.222045E-15 EXACT: 0.886227 N = 1 ALPHA = 0.00000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 2 1.00000 0.00000 GW_02_XIU: 2 1.00000 0.00000 EXACT: 1.00000 N = 1 ALPHA = 0.500000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 1.32934 0.00000 EPN_GLG_02_XIU: 2 1.32934 0.00000 GW_02_XIU: 2 1.32934 0.00000 EXACT: 1.32934 N = 1 ALPHA = 1.00000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = 2.00000 EXPON = 1 Degree = 1 EPN_GLG_01_1: 1 6.00000 0.00000 EPN_GLG_02_XIU: 2 6.00000 0.00000 GW_02_XIU: 2 6.00000 0.00000 EXACT: 6.00000 N = 1 ALPHA = -0.500000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 1.32934 0.00000 GW_02_XIU: 2 1.32934 0.00000 EXACT: 1.32934 N = 1 ALPHA = 0.00000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 1 ALPHA = 0.500000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 3.32335 0.00000 GW_02_XIU: 2 3.32335 0.00000 EXACT: 3.32335 N = 1 ALPHA = 1.00000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 6.00000 0.00000 GW_02_XIU: 2 6.00000 0.00000 EXACT: 6.00000 N = 1 ALPHA = 2.00000 EXPON = 2 Degree = 2 EPN_GLG_02_XIU: 2 24.0000 0.710543E-14 GW_02_XIU: 2 24.0000 0.710543E-14 EXACT: 24.0000 N = 2 ALPHA = -0.500000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 3.14159 0.00000 EPN_GLG_01_1: 1 3.14159 0.00000 EPN_GLG_02_XIU: 3 3.14159 0.00000 GW_02_XIU: 3 3.14159 0.00000 EXACT: 3.14159 N = 2 ALPHA = 0.00000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 3 1.00000 0.00000 GW_02_XIU: 3 1.00000 0.00000 EXACT: 1.00000 N = 2 ALPHA = 0.500000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 0.785398 0.00000 EPN_GLG_01_1: 1 0.785398 0.00000 EPN_GLG_02_XIU: 3 0.785398 0.00000 GW_02_XIU: 3 0.785398 0.00000 EXACT: 0.785398 N = 2 ALPHA = 1.00000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 3 1.00000 0.00000 GW_02_XIU: 3 1.00000 0.00000 EXACT: 1.00000 N = 2 ALPHA = 2.00000 EXPON = 0 0 Degree = 0 EPN_GLG_00_1: 1 4.00000 0.00000 EPN_GLG_01_1: 1 4.00000 0.00000 EPN_GLG_02_XIU: 3 4.00000 0.00000 GW_02_XIU: 3 4.00000 0.00000 EXACT: 4.00000 N = 2 ALPHA = -0.500000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.57080 0.00000 EPN_GLG_02_XIU: 3 1.57080 0.444089E-15 GW_02_XIU: 3 1.57080 0.444089E-15 EXACT: 1.57080 N = 2 ALPHA = 0.00000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 3 1.00000 0.222045E-15 GW_02_XIU: 3 1.00000 0.222045E-15 EXACT: 1.00000 N = 2 ALPHA = 0.500000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 1.17810 0.222045E-15 EPN_GLG_02_XIU: 3 1.17810 0.00000 GW_02_XIU: 3 1.17810 0.00000 EXACT: 1.17810 N = 2 ALPHA = 1.00000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 3 2.00000 0.444089E-15 GW_02_XIU: 3 2.00000 0.444089E-15 EXACT: 2.00000 N = 2 ALPHA = 2.00000 EXPON = 0 1 Degree = 1 EPN_GLG_01_1: 1 12.0000 0.00000 EPN_GLG_02_XIU: 3 12.0000 0.177636E-14 GW_02_XIU: 3 12.0000 0.177636E-14 EXACT: 12.0000 N = 2 ALPHA = -0.500000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 0.785398 0.111022E-15 GW_02_XIU: 3 0.785398 0.111022E-15 EXACT: 0.785398 N = 2 ALPHA = 0.00000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1.00000 0.222045E-15 GW_02_XIU: 3 1.00000 0.222045E-15 EXACT: 1.00000 N = 2 ALPHA = 0.500000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 1.76715 0.444089E-15 GW_02_XIU: 3 1.76715 0.444089E-15 EXACT: 1.76715 N = 2 ALPHA = 1.00000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 4.00000 0.444089E-15 GW_02_XIU: 3 4.00000 0.444089E-15 EXACT: 4.00000 N = 2 ALPHA = 2.00000 EXPON = 1 1 Degree = 2 EPN_GLG_02_XIU: 3 36.0000 0.00000 GW_02_XIU: 3 36.0000 0.00000 EXACT: 36.0000 N = 2 ALPHA = -0.500000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.35619 0.888178E-15 GW_02_XIU: 3 2.35619 0.888178E-15 EXACT: 2.35619 N = 2 ALPHA = 0.00000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.00000 0.888178E-15 GW_02_XIU: 3 2.00000 0.888178E-15 EXACT: 2.00000 N = 2 ALPHA = 0.500000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 2.94524 0.444089E-15 GW_02_XIU: 3 2.94524 0.444089E-15 EXACT: 2.94524 N = 2 ALPHA = 1.00000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 6.00000 0.888178E-15 GW_02_XIU: 3 6.00000 0.888178E-15 EXACT: 6.00000 N = 2 ALPHA = 2.00000 EXPON = 2 0 Degree = 2 EPN_GLG_02_XIU: 3 48.0000 0.00000 GW_02_XIU: 3 48.0000 0.00000 EXACT: 48.0000 N = 3 ALPHA = -0.500000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 5.56833 0.00000 EPN_GLG_01_1: 1 5.56833 0.00000 EPN_GLG_02_XIU: 4 5.56833 0.00000 GW_02_XIU: 4 5.56833 0.00000 EXACT: 5.56833 N = 3 ALPHA = 0.00000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 4 1.00000 0.00000 GW_02_XIU: 4 1.00000 0.00000 EXACT: 1.00000 N = 3 ALPHA = 0.500000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.696041 0.00000 EPN_GLG_01_1: 1 0.696041 0.00000 EPN_GLG_02_XIU: 4 0.696041 0.00000 GW_02_XIU: 4 0.696041 0.00000 EXACT: 0.696041 N = 3 ALPHA = 1.00000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 4 1.00000 0.00000 GW_02_XIU: 4 1.00000 0.00000 EXACT: 1.00000 N = 3 ALPHA = 2.00000 EXPON = 0 0 0 Degree = 0 EPN_GLG_00_1: 1 8.00000 0.00000 EPN_GLG_01_1: 1 8.00000 0.00000 EPN_GLG_02_XIU: 4 8.00000 0.00000 GW_02_XIU: 4 8.00000 0.00000 EXACT: 8.00000 N = 3 ALPHA = -0.500000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.78416 0.00000 EPN_GLG_02_XIU: 4 2.78416 0.00000 GW_02_XIU: 4 2.78416 0.00000 EXACT: 2.78416 N = 3 ALPHA = 0.00000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 4 1.00000 0.00000 GW_02_XIU: 4 1.00000 0.00000 EXACT: 1.00000 N = 3 ALPHA = 0.500000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.04406 0.00000 EPN_GLG_02_XIU: 4 1.04406 0.00000 GW_02_XIU: 4 1.04406 0.00000 EXACT: 1.04406 N = 3 ALPHA = 1.00000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 4 2.00000 0.00000 GW_02_XIU: 4 2.00000 0.00000 EXACT: 2.00000 N = 3 ALPHA = 2.00000 EXPON = 0 0 1 Degree = 1 EPN_GLG_01_1: 1 24.0000 0.00000 EPN_GLG_02_XIU: 4 24.0000 0.00000 GW_02_XIU: 4 24.0000 0.00000 EXACT: 24.0000 N = 3 ALPHA = -0.500000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.39208 0.222045E-15 GW_02_XIU: 4 1.39208 0.222045E-15 EXACT: 1.39208 N = 3 ALPHA = 0.00000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.00000 0.111022E-15 GW_02_XIU: 4 1.00000 0.111022E-15 EXACT: 1.00000 N = 3 ALPHA = 0.500000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 1.56609 0.444089E-15 GW_02_XIU: 4 1.56609 0.444089E-15 EXACT: 1.56609 N = 3 ALPHA = 1.00000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 4.00000 0.00000 GW_02_XIU: 4 4.00000 0.00000 EXACT: 4.00000 N = 3 ALPHA = 2.00000 EXPON = 1 1 0 Degree = 2 EPN_GLG_02_XIU: 4 72.0000 0.00000 GW_02_XIU: 4 72.0000 0.00000 EXACT: 72.0000 N = 3 ALPHA = -0.500000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 4.17625 0.266454E-14 GW_02_XIU: 4 4.17625 0.266454E-14 EXACT: 4.17625 N = 3 ALPHA = 0.00000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2.00000 0.00000 GW_02_XIU: 4 2.00000 0.00000 EXACT: 2.00000 N = 3 ALPHA = 0.500000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 2.61015 0.444089E-15 GW_02_XIU: 4 2.61015 0.444089E-15 EXACT: 2.61015 N = 3 ALPHA = 1.00000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 6.00000 0.00000 GW_02_XIU: 4 6.00000 0.00000 EXACT: 6.00000 N = 3 ALPHA = 2.00000 EXPON = 2 0 0 Degree = 2 EPN_GLG_02_XIU: 4 96.0000 0.284217E-13 GW_02_XIU: 4 96.0000 0.284217E-13 EXACT: 96.0000 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 9.86960 0.177636E-14 EPN_GLG_01_1: 1 9.86960 0.177636E-14 EPN_GLG_02_XIU: 5 9.86960 0.177636E-14 GW_02_XIU: 5 9.86960 0.177636E-14 EXACT: 9.86960 N = 4 ALPHA = 0.00000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 5 1.00000 0.00000 GW_02_XIU: 5 1.00000 0.00000 EXACT: 1.00000 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.616850 0.111022E-15 EPN_GLG_01_1: 1 0.616850 0.111022E-15 EPN_GLG_02_XIU: 5 0.616850 0.111022E-15 GW_02_XIU: 5 0.616850 0.111022E-15 EXACT: 0.616850 N = 4 ALPHA = 1.00000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 5 1.00000 0.00000 GW_02_XIU: 5 1.00000 0.00000 EXACT: 1.00000 N = 4 ALPHA = 2.00000 EXPON = 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 16.0000 0.00000 EPN_GLG_01_1: 1 16.0000 0.00000 EPN_GLG_02_XIU: 5 16.0000 0.00000 GW_02_XIU: 5 16.0000 0.00000 EXACT: 16.0000 N = 4 ALPHA = -0.500000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 4.93480 0.888178E-15 EPN_GLG_02_XIU: 5 4.93480 0.177636E-14 GW_02_XIU: 5 4.93480 0.177636E-14 EXACT: 4.93480 N = 4 ALPHA = 0.00000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 5 1.00000 0.00000 GW_02_XIU: 5 1.00000 0.00000 EXACT: 1.00000 N = 4 ALPHA = 0.500000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.925275 0.111022E-15 EPN_GLG_02_XIU: 5 0.925275 0.111022E-15 GW_02_XIU: 5 0.925275 0.111022E-15 EXACT: 0.925275 N = 4 ALPHA = 1.00000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 5 2.00000 0.00000 GW_02_XIU: 5 2.00000 0.00000 EXACT: 2.00000 N = 4 ALPHA = 2.00000 EXPON = 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 48.0000 0.00000 EPN_GLG_02_XIU: 5 48.0000 0.00000 GW_02_XIU: 5 48.0000 0.00000 EXACT: 48.0000 N = 4 ALPHA = -0.500000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.46740 0.444089E-15 GW_02_XIU: 5 2.46740 0.444089E-15 EXACT: 2.46740 N = 4 ALPHA = 0.00000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1.00000 0.222045E-15 GW_02_XIU: 5 1.00000 0.222045E-15 EXACT: 1.00000 N = 4 ALPHA = 0.500000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 1.38791 0.444089E-15 GW_02_XIU: 5 1.38791 0.444089E-15 EXACT: 1.38791 N = 4 ALPHA = 1.00000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 4.00000 0.00000 GW_02_XIU: 5 4.00000 0.00000 EXACT: 4.00000 N = 4 ALPHA = 2.00000 EXPON = 1 1 0 0 Degree = 2 EPN_GLG_02_XIU: 5 144.000 0.00000 GW_02_XIU: 5 144.000 0.00000 EXACT: 144.000 N = 4 ALPHA = -0.500000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 7.40220 0.266454E-14 GW_02_XIU: 5 7.40220 0.266454E-14 EXACT: 7.40220 N = 4 ALPHA = 0.00000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.00000 0.444089E-15 GW_02_XIU: 5 2.00000 0.444089E-15 EXACT: 2.00000 N = 4 ALPHA = 0.500000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 2.31319 0.444089E-15 GW_02_XIU: 5 2.31319 0.444089E-15 EXACT: 2.31319 N = 4 ALPHA = 1.00000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 6.00000 0.888178E-15 GW_02_XIU: 5 6.00000 0.888178E-15 EXACT: 6.00000 N = 4 ALPHA = 2.00000 EXPON = 2 0 0 0 Degree = 2 EPN_GLG_02_XIU: 5 192.000 0.284217E-13 GW_02_XIU: 5 192.000 0.284217E-13 EXACT: 192.000 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 17.4934 0.355271E-14 EPN_GLG_01_1: 1 17.4934 0.355271E-14 EPN_GLG_02_XIU: 6 17.4934 0.355271E-14 GW_02_XIU: 6 17.4934 0.355271E-14 EXACT: 17.4934 N = 5 ALPHA = 0.00000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 6 1.00000 0.111022E-15 GW_02_XIU: 6 1.00000 0.111022E-15 EXACT: 1.00000 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.546669 0.111022E-15 EPN_GLG_01_1: 1 0.546669 0.111022E-15 EPN_GLG_02_XIU: 6 0.546669 0.111022E-15 GW_02_XIU: 6 0.546669 0.111022E-15 EXACT: 0.546669 N = 5 ALPHA = 1.00000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 6 1.00000 0.111022E-15 GW_02_XIU: 6 1.00000 0.111022E-15 EXACT: 1.00000 N = 5 ALPHA = 2.00000 EXPON = 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 32.0000 0.00000 EPN_GLG_01_1: 1 32.0000 0.00000 EPN_GLG_02_XIU: 6 32.0000 0.355271E-14 GW_02_XIU: 6 32.0000 0.355271E-14 EXACT: 32.0000 N = 5 ALPHA = -0.500000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 8.74671 0.177636E-14 EPN_GLG_02_XIU: 6 8.74671 0.355271E-14 GW_02_XIU: 6 8.74671 0.355271E-14 EXACT: 8.74671 N = 5 ALPHA = 0.00000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 6 1.00000 0.00000 GW_02_XIU: 6 1.00000 0.00000 EXACT: 1.00000 N = 5 ALPHA = 0.500000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.820004 0.111022E-15 EPN_GLG_02_XIU: 6 0.820004 0.111022E-15 GW_02_XIU: 6 0.820004 0.111022E-15 EXACT: 0.820004 N = 5 ALPHA = 1.00000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 6 2.00000 0.00000 GW_02_XIU: 6 2.00000 0.00000 EXACT: 2.00000 N = 5 ALPHA = 2.00000 EXPON = 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 96.0000 0.00000 EPN_GLG_02_XIU: 6 96.0000 0.142109E-13 GW_02_XIU: 6 96.0000 0.142109E-13 EXACT: 96.0000 N = 5 ALPHA = -0.500000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4.37335 0.00000 GW_02_XIU: 6 4.37335 0.00000 EXACT: 4.37335 N = 5 ALPHA = 0.00000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1.00000 0.00000 GW_02_XIU: 6 1.00000 0.00000 EXACT: 1.00000 N = 5 ALPHA = 0.500000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 1.23001 0.222045E-15 GW_02_XIU: 6 1.23001 0.222045E-15 EXACT: 1.23001 N = 5 ALPHA = 1.00000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 4.00000 0.888178E-15 GW_02_XIU: 6 4.00000 0.888178E-15 EXACT: 4.00000 N = 5 ALPHA = 2.00000 EXPON = 1 1 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 288.000 0.00000 GW_02_XIU: 6 288.000 0.00000 EXACT: 288.000 N = 5 ALPHA = -0.500000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 13.1201 0.532907E-14 GW_02_XIU: 6 13.1201 0.532907E-14 EXACT: 13.1201 N = 5 ALPHA = 0.00000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2.00000 0.00000 GW_02_XIU: 6 2.00000 0.00000 EXACT: 2.00000 N = 5 ALPHA = 0.500000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 2.05001 0.00000 GW_02_XIU: 6 2.05001 0.00000 EXACT: 2.05001 N = 5 ALPHA = 1.00000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 6.00000 0.00000 GW_02_XIU: 6 6.00000 0.00000 EXACT: 6.00000 N = 5 ALPHA = 2.00000 EXPON = 2 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 6 384.000 0.00000 GW_02_XIU: 6 384.000 0.00000 EXACT: 384.000 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 31.0063 0.710543E-14 EPN_GLG_01_1: 1 31.0063 0.710543E-14 EPN_GLG_02_XIU: 7 31.0063 0.355271E-14 GW_02_XIU: 7 31.0063 0.355271E-14 EXACT: 31.0063 N = 6 ALPHA = 0.00000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 7 1.00000 0.222045E-15 GW_02_XIU: 7 1.00000 0.222045E-15 EXACT: 1.00000 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 0.484473 0.111022E-15 EPN_GLG_01_1: 1 0.484473 0.111022E-15 EPN_GLG_02_XIU: 7 0.484473 0.555112E-16 GW_02_XIU: 7 0.484473 0.555112E-16 EXACT: 0.484473 N = 6 ALPHA = 1.00000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 1.00000 0.00000 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 7 1.00000 0.222045E-15 GW_02_XIU: 7 1.00000 0.222045E-15 EXACT: 1.00000 N = 6 ALPHA = 2.00000 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_GLG_00_1: 1 64.0000 0.00000 EPN_GLG_01_1: 1 64.0000 0.00000 EPN_GLG_02_XIU: 7 64.0000 0.142109E-13 GW_02_XIU: 7 64.0000 0.142109E-13 EXACT: 64.0000 N = 6 ALPHA = -0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 15.5031 0.355271E-14 EPN_GLG_02_XIU: 7 15.5031 0.355271E-14 GW_02_XIU: 7 15.5031 0.355271E-14 EXACT: 15.5031 N = 6 ALPHA = 0.00000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 1.00000 0.00000 EPN_GLG_02_XIU: 7 1.00000 0.00000 GW_02_XIU: 7 1.00000 0.00000 EXACT: 1.00000 N = 6 ALPHA = 0.500000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 0.726710 0.222045E-15 EPN_GLG_02_XIU: 7 0.726710 0.222045E-15 GW_02_XIU: 7 0.726710 0.222045E-15 EXACT: 0.726710 N = 6 ALPHA = 1.00000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 2.00000 0.00000 EPN_GLG_02_XIU: 7 2.00000 0.00000 GW_02_XIU: 7 2.00000 0.00000 EXACT: 2.00000 N = 6 ALPHA = 2.00000 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_GLG_01_1: 1 192.000 0.00000 EPN_GLG_02_XIU: 7 192.000 0.00000 GW_02_XIU: 7 192.000 0.00000 EXACT: 192.000 N = 6 ALPHA = -0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 7.75157 0.888178E-15 GW_02_XIU: 7 7.75157 0.888178E-15 EXACT: 7.75157 N = 6 ALPHA = 0.00000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.00000 0.00000 GW_02_XIU: 7 1.00000 0.00000 EXACT: 1.00000 N = 6 ALPHA = 0.500000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.09006 0.222045E-15 GW_02_XIU: 7 1.09006 0.222045E-15 EXACT: 1.09006 N = 6 ALPHA = 1.00000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 4.00000 0.00000 GW_02_XIU: 7 4.00000 0.00000 EXACT: 4.00000 N = 6 ALPHA = 2.00000 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 576.000 0.00000 GW_02_XIU: 7 576.000 0.00000 EXACT: 576.000 N = 6 ALPHA = -0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 23.2547 0.710543E-14 GW_02_XIU: 7 23.2547 0.710543E-14 EXACT: 23.2547 N = 6 ALPHA = 0.00000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 2.00000 0.00000 GW_02_XIU: 7 2.00000 0.00000 EXACT: 2.00000 N = 6 ALPHA = 0.500000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 1.81677 0.222045E-15 GW_02_XIU: 7 1.81677 0.222045E-15 EXACT: 1.81677 N = 6 ALPHA = 1.00000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 6.00000 0.888178E-15 GW_02_XIU: 7 6.00000 0.888178E-15 EXACT: 6.00000 N = 6 ALPHA = 2.00000 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_GLG_02_XIU: 7 768.000 0.00000 GW_02_XIU: 7 768.000 0.00000 EXACT: 768.000 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 Laguerre 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 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 2 1.00000 0.00000 GW_02_XIU: 2 1.00000 0.00000 EXACT: 1.00000 N = 1 EXPON = 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 2 1.00000 0.00000 GW_02_XIU: 2 1.00000 0.00000 EXACT: 1.00000 N = 1 EXPON = 2 Degree = 2 EPN_LAG_02_XIU: 2 2.00000 0.00000 GW_02_XIU: 2 2.00000 0.00000 EXACT: 2.00000 N = 2 EXPON = 0 0 Degree = 0 EPN_LAG_00_1: 1 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 3 1.00000 0.00000 GW_02_XIU: 3 1.00000 0.00000 EXACT: 1.00000 N = 2 EXPON = 0 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 3 1.00000 0.222045E-15 GW_02_XIU: 3 1.00000 0.222045E-15 EXACT: 1.00000 N = 2 EXPON = 1 1 Degree = 2 EPN_LAG_02_XIU: 3 1.00000 0.222045E-15 GW_02_XIU: 3 1.00000 0.222045E-15 EXACT: 1.00000 N = 2 EXPON = 2 0 Degree = 2 EPN_LAG_02_XIU: 3 2.00000 0.888178E-15 GW_02_XIU: 3 2.00000 0.888178E-15 EXACT: 2.00000 N = 3 EXPON = 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 4 1.00000 0.00000 GW_02_XIU: 4 1.00000 0.00000 EXACT: 1.00000 N = 3 EXPON = 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 4 1.00000 0.00000 GW_02_XIU: 4 1.00000 0.00000 EXACT: 1.00000 N = 3 EXPON = 1 1 0 Degree = 2 EPN_LAG_02_XIU: 4 1.00000 0.111022E-15 GW_02_XIU: 4 1.00000 0.111022E-15 EXACT: 1.00000 N = 3 EXPON = 2 0 0 Degree = 2 EPN_LAG_02_XIU: 4 2.00000 0.00000 GW_02_XIU: 4 2.00000 0.00000 EXACT: 2.00000 N = 4 EXPON = 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 5 1.00000 0.00000 GW_02_XIU: 5 1.00000 0.00000 EXACT: 1.00000 N = 4 EXPON = 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 5 1.00000 0.00000 GW_02_XIU: 5 1.00000 0.00000 EXACT: 1.00000 N = 4 EXPON = 1 1 0 0 Degree = 2 EPN_LAG_02_XIU: 5 1.00000 0.222045E-15 GW_02_XIU: 5 1.00000 0.222045E-15 EXACT: 1.00000 N = 4 EXPON = 2 0 0 0 Degree = 2 EPN_LAG_02_XIU: 5 2.00000 0.444089E-15 GW_02_XIU: 5 2.00000 0.444089E-15 EXACT: 2.00000 N = 5 EXPON = 0 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 6 1.00000 0.111022E-15 GW_02_XIU: 6 1.00000 0.111022E-15 EXACT: 1.00000 N = 5 EXPON = 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 6 1.00000 0.00000 GW_02_XIU: 6 1.00000 0.00000 EXACT: 1.00000 N = 5 EXPON = 1 1 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 1.00000 0.00000 GW_02_XIU: 6 1.00000 0.00000 EXACT: 1.00000 N = 5 EXPON = 2 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 6 2.00000 0.00000 GW_02_XIU: 6 2.00000 0.00000 EXACT: 2.00000 N = 6 EXPON = 0 0 0 0 0 0 Degree = 0 EPN_LAG_00_1: 1 1.00000 0.00000 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 7 1.00000 0.222045E-15 GW_02_XIU: 7 1.00000 0.222045E-15 EXACT: 1.00000 N = 6 EXPON = 0 0 0 0 0 1 Degree = 1 EPN_LAG_01_1: 1 1.00000 0.00000 EPN_LAG_02_XIU: 7 1.00000 0.00000 GW_02_XIU: 7 1.00000 0.00000 EXACT: 1.00000 N = 6 EXPON = 1 1 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 1.00000 0.00000 GW_02_XIU: 7 1.00000 0.00000 EXACT: 1.00000 N = 6 EXPON = 2 0 0 0 0 0 Degree = 2 EPN_LAG_02_XIU: 7 2.00000 0.00000 GW_02_XIU: 7 2.00000 0.00000 EXACT: 2.00000 sandia_cubature_test(): Normal end of execution. 06 April 2023 9:43:35.115 AM