6 March 2017 7:46:54.924 AM SIMPLEX_GM_RULE_PRB FORTRAN90 version Test the SIMPLEX_GM_RULE library. TEST01 SIMPLEX_UNIT_TO_GENERAL maps points in the unit simplex to a general simplex. Here we consider a simplex in 2D, a triangle. The vertices of the general triangle are: 1.0000 1.0000 3.0000 1.0000 2.0000 5.0000 ( XSI ETA ) ( X Y ) 0.0000 0.0000 1.0000 1.0000 1.0000 0.0000 3.0000 1.0000 0.0000 1.0000 2.0000 5.0000 0.8679 0.0255 2.7613 1.1019 0.1383 0.2106 1.4872 1.8425 0.2027 0.3299 1.7353 2.3197 0.1128 0.6893 1.9149 3.7572 0.6425 0.1981 2.4831 1.7923 0.8450 0.0145 2.7044 1.0580 0.3465 0.6312 2.3242 3.5247 0.0242 0.2926 1.3410 2.1704 0.3726 0.0254 1.7706 1.1014 0.4083 0.0761 1.8926 1.3046 TEST02 SIMPLEX_UNIT_TO_GENERAL maps points in the unit simplex to a general simplex. Here we consider a simplex in 3D, a tetrahedron. The vertices of the general tetrahedron are: 1.0000 1.0000 1.0000 3.0000 1.0000 1.0000 1.0000 4.0000 1.0000 1.0000 1.0000 5.0000 ( XSI ETA MU ) ( X Y Z ) 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 3.0000 1.0000 1.0000 0.0000 1.0000 0.0000 1.0000 4.0000 1.0000 0.0000 0.0000 1.0000 1.0000 1.0000 5.0000 0.6530 0.0192 0.0802 2.3060 1.0575 1.3209 0.1227 0.3794 0.1895 1.2455 2.1383 1.7579 0.4363 0.0636 0.3885 1.8726 1.1908 2.5542 0.1183 0.0365 0.0293 1.2365 1.1094 1.1174 0.0138 0.1341 0.3020 1.0277 1.4024 2.2079 0.0208 0.0237 0.2865 1.0415 1.0711 2.1460 0.2890 0.0197 0.4669 1.5780 1.0590 2.8677 0.0792 0.5366 0.1496 1.1585 2.6099 1.5985 0.0966 0.5111 0.0596 1.1933 2.5332 1.2384 0.3663 0.0599 0.2031 1.7327 1.1797 1.8125 TEST03 GM_RULE_SIZE returns N, the number of points associated with a Grundmann-Moeller quadrature rule for the unit simplex of dimension M with rule index RULE and degree of exactness DEGREE = 2*RULE+1. M RULE DEGREE N 2 0 1 1 2 1 3 4 2 2 5 10 2 3 7 20 2 4 9 35 2 5 11 56 3 0 1 1 3 1 3 5 3 2 5 15 3 3 7 35 3 4 9 70 3 5 11 126 5 0 1 1 5 1 3 7 5 2 5 28 5 3 7 84 5 4 9 210 5 5 11 462 10 0 1 1 10 1 3 12 10 2 5 78 10 3 7 364 10 4 9 1365 10 5 11 4368 TEST04 GM_UNIT_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional unit simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. Here we use M = 3 RULE = 2 DEGREE = 5 POINT W X Y Z 1 0.050794 0.125000 0.125000 0.125000 2 0.050794 0.375000 0.125000 0.125000 3 0.050794 0.625000 0.125000 0.125000 4 0.050794 0.125000 0.375000 0.125000 5 0.050794 0.375000 0.375000 0.125000 6 0.050794 0.125000 0.625000 0.125000 7 0.050794 0.125000 0.125000 0.375000 8 0.050794 0.375000 0.125000 0.375000 9 0.050794 0.125000 0.375000 0.375000 10 0.050794 0.125000 0.125000 0.625000 11 -0.096429 0.166667 0.166667 0.166667 12 -0.096429 0.500000 0.166667 0.166667 13 -0.096429 0.166667 0.500000 0.166667 14 -0.096429 0.166667 0.166667 0.500000 15 0.044444 0.250000 0.250000 0.250000 TEST05 GM_UNIT_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional unit simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. In this test, we compute various rules, and simply report the number of points, and the sum of weights. M RULE N WEIGHT SUM 2 0 1 0.5000000000000000 2 1 4 0.4999999999999999 2 2 10 0.4999999999999999 2 3 20 0.5000000000000006 2 4 35 0.4999999999999999 2 5 56 0.5000000000000028 3 0 1 0.1666666666666667 3 1 5 0.1666666666666667 3 2 15 0.1666666666666667 3 3 35 0.1666666666666670 3 4 70 0.1666666666666664 3 5 126 0.1666666666666647 5 0 1 0.8333333333333333E-02 5 1 7 0.8333333333333331E-02 5 2 28 0.8333333333333331E-02 5 3 84 0.8333333333333283E-02 5 4 210 0.8333333333333585E-02 5 5 462 0.8333333333332863E-02 10 0 1 0.2755731922398589E-06 10 1 12 0.2755731922398589E-06 10 2 78 0.2755731922398579E-06 10 3 364 0.2755731922398308E-06 10 4 1365 0.2755731922397991E-06 10 5 4368 0.2755731922406156E-06 TEST06 GM_UNIT_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional unit simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. In this test, we write a rule to a file. Here we use M = 3 RULE = 2 DEGREE = 5 Wrote rule 2 to "gm2_3d_w.txt" and "gm2_3d_x.txt". TEST07 GM_UNIT_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional unit simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. In this test, look at all the monomials up to some maximum degree, choose a few low order rules and determine the quadrature error for each. Here we use M = 5 Rule Order Quad_Error F(X) = X1^0 * X2^0 * X3^0 * X4^0 * X5^0 0 1 0.00000 1 7 0.222045E-15 2 28 0.222045E-15 3 84 0.599520E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^0 * X5^0 0 1 0.111022E-15 1 7 0.333067E-15 2 28 0.444089E-15 3 84 0.688338E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^0 * X5^0 0 1 0.111022E-15 1 7 0.333067E-15 2 28 0.111022E-15 3 84 0.754952E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^0 * X5^0 0 1 0.111022E-15 1 7 0.333067E-15 2 28 0.888178E-15 3 84 0.688338E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^1 * X5^0 0 1 0.111022E-15 1 7 0.333067E-15 2 28 0.222045E-15 3 84 0.466294E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^0 * X5^1 0 1 0.111022E-15 1 7 0.00000 2 28 0.199840E-14 3 84 0.444089E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^0 * X5^0 0 1 0.416667 1 7 0.444089E-15 2 28 0.377476E-14 3 84 0.710543E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^0 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.888178E-15 3 84 0.155431E-14 F(X) = X1^0 * X2^2 * X3^0 * X4^0 * X5^0 0 1 0.416667 1 7 0.222045E-15 2 28 0.444089E-14 3 84 0.865974E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^0 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.888178E-15 3 84 0.266454E-14 F(X) = X1^0 * X2^1 * X3^1 * X4^0 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.111022E-14 3 84 0.266454E-14 F(X) = X1^0 * X2^0 * X3^2 * X4^0 * X5^0 0 1 0.416667 1 7 0.222045E-15 2 28 0.377476E-14 3 84 0.106581E-13 F(X) = X1^1 * X2^0 * X3^0 * X4^1 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.888178E-15 3 84 0.444089E-15 F(X) = X1^0 * X2^1 * X3^0 * X4^1 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.111022E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^1 * X4^1 * X5^0 0 1 0.166667 1 7 0.00000 2 28 0.133227E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^2 * X5^0 0 1 0.416667 1 7 0.111022E-15 2 28 0.244249E-14 3 84 0.108802E-13 F(X) = X1^1 * X2^0 * X3^0 * X4^0 * X5^1 0 1 0.166667 1 7 0.00000 2 28 0.666134E-15 3 84 0.155431E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^0 * X5^1 0 1 0.166667 1 7 0.00000 2 28 0.888178E-15 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^1 * X4^0 * X5^1 0 1 0.166667 1 7 0.00000 2 28 0.133227E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^1 * X5^1 0 1 0.166667 1 7 0.00000 2 28 0.155431E-14 3 84 0.666134E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^0 * X5^2 0 1 0.416667 1 7 0.111022E-15 2 28 0.133227E-14 3 84 0.111022E-13 F(X) = X1^3 * X2^0 * X3^0 * X4^0 * X5^0 0 1 0.740741 1 7 0.222045E-15 2 28 0.444089E-15 3 84 0.954792E-14 F(X) = X1^2 * X2^1 * X3^0 * X4^0 * X5^0 0 1 0.222222 1 7 0.222045E-15 2 28 0.666134E-15 3 84 0.111022E-15 F(X) = X1^1 * X2^2 * X3^0 * X4^0 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.122125E-14 F(X) = X1^0 * X2^3 * X3^0 * X4^0 * X5^0 0 1 0.740741 1 7 0.222045E-15 2 28 0.222045E-15 3 84 0.888178E-14 F(X) = X1^2 * X2^0 * X3^1 * X4^0 * X5^0 0 1 0.222222 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.888178E-15 F(X) = X1^1 * X2^1 * X3^1 * X4^0 * X5^0 0 1 0.555556 1 7 0.222045E-15 2 28 0.155431E-14 3 84 0.466294E-14 F(X) = X1^0 * X2^2 * X3^1 * X4^0 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.222045E-15 3 84 0.444089E-15 F(X) = X1^1 * X2^0 * X3^2 * X4^0 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.111022E-15 F(X) = X1^0 * X2^1 * X3^2 * X4^0 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.111022E-14 3 84 0.111022E-14 F(X) = X1^0 * X2^0 * X3^3 * X4^0 * X5^0 0 1 0.740741 1 7 0.222045E-15 2 28 0.222045E-15 3 84 0.643929E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^1 * X5^0 0 1 0.222222 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.288658E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^1 * X5^0 0 1 0.555556 1 7 0.222045E-15 2 28 0.133227E-14 3 84 0.355271E-14 F(X) = X1^0 * X2^2 * X3^0 * X4^1 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.166533E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^1 * X5^0 0 1 0.555556 1 7 0.222045E-15 2 28 0.155431E-14 3 84 0.133227E-14 F(X) = X1^0 * X2^1 * X3^1 * X4^1 * X5^0 0 1 0.555556 1 7 0.222045E-15 2 28 0.155431E-14 3 84 0.222045E-15 F(X) = X1^0 * X2^0 * X3^2 * X4^1 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.111022E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^2 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.666134E-15 3 84 0.666134E-15 F(X) = X1^0 * X2^1 * X3^0 * X4^2 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.133227E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^1 * X4^2 * X5^0 0 1 0.222222 1 7 0.00000 2 28 0.666134E-15 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^3 * X5^0 0 1 0.740741 1 7 0.222045E-15 2 28 0.222045E-15 3 84 0.244249E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^0 * X5^1 0 1 0.222222 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.344169E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^0 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.133227E-14 3 84 0.133227E-14 F(X) = X1^0 * X2^2 * X3^0 * X4^0 * X5^1 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.377476E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^0 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.155431E-14 3 84 0.222045E-15 F(X) = X1^0 * X2^1 * X3^1 * X4^0 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.155431E-14 3 84 0.222045E-15 F(X) = X1^0 * X2^0 * X3^2 * X4^0 * X5^1 0 1 0.222222 1 7 0.00000 2 28 0.444089E-15 3 84 0.277556E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^1 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.199840E-14 3 84 0.310862E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^1 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.199840E-14 3 84 0.310862E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^1 * X5^1 0 1 0.555556 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.510703E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^2 * X5^1 0 1 0.222222 1 7 0.222045E-15 2 28 0.444089E-15 3 84 0.277556E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^0 * X5^2 0 1 0.222222 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.444089E-15 F(X) = X1^0 * X2^1 * X3^0 * X4^0 * X5^2 0 1 0.222222 1 7 0.222045E-15 2 28 0.133227E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^1 * X4^0 * X5^2 0 1 0.222222 1 7 0.222045E-15 2 28 0.888178E-15 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^1 * X5^2 0 1 0.222222 1 7 0.222045E-15 2 28 0.111022E-14 3 84 0.444089E-15 F(X) = X1^0 * X2^0 * X3^0 * X4^0 * X5^3 0 1 0.740741 1 7 0.222045E-15 2 28 0.222045E-15 3 84 0.277556E-14 F(X) = X1^4 * X2^0 * X3^0 * X4^0 * X5^0 0 1 0.902778 1 7 0.117188 2 28 0.155431E-14 3 84 0.102141E-13 F(X) = X1^3 * X2^1 * X3^0 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.00000 3 84 0.821565E-14 F(X) = X1^2 * X2^2 * X3^0 * X4^0 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.222045E-15 3 84 0.510703E-14 F(X) = X1^1 * X2^3 * X3^0 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.00000 3 84 0.888178E-14 F(X) = X1^0 * X2^4 * X3^0 * X4^0 * X5^0 0 1 0.902778 1 7 0.117188 2 28 0.133227E-14 3 84 0.921485E-14 F(X) = X1^3 * X2^0 * X3^1 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.888178E-15 3 84 0.621725E-14 F(X) = X1^2 * X2^1 * X3^1 * X4^0 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.111022E-15 3 84 0.954792E-14 F(X) = X1^1 * X2^2 * X3^1 * X4^0 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.444089E-15 3 84 0.108802E-13 F(X) = X1^0 * X2^3 * X3^1 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.732747E-14 F(X) = X1^2 * X2^0 * X3^2 * X4^0 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.222045E-15 3 84 0.321965E-14 F(X) = X1^1 * X2^1 * X3^2 * X4^0 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.777156E-15 3 84 0.108802E-13 F(X) = X1^0 * X2^2 * X3^2 * X4^0 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.00000 3 84 0.388578E-14 F(X) = X1^1 * X2^0 * X3^3 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.799361E-14 F(X) = X1^0 * X2^1 * X3^3 * X4^0 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.843769E-14 F(X) = X1^0 * X2^0 * X3^4 * X4^0 * X5^0 0 1 0.902778 1 7 0.117188 2 28 0.155431E-14 3 84 0.699441E-14 F(X) = X1^3 * X2^0 * X3^0 * X4^1 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.00000 3 84 0.244249E-14 F(X) = X1^2 * X2^1 * X3^0 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.444089E-15 3 84 0.588418E-14 F(X) = X1^1 * X2^2 * X3^0 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.721645E-14 F(X) = X1^0 * X2^3 * X3^0 * X4^1 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.399680E-14 F(X) = X1^2 * X2^0 * X3^1 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.00000 3 84 0.710543E-14 F(X) = X1^1 * X2^1 * X3^1 * X4^1 * X5^0 0 1 1.33333 1 7 0.625000E-01 2 28 0.122125E-14 3 84 0.277556E-14 F(X) = X1^0 * X2^2 * X3^1 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.00000 3 84 0.688338E-14 F(X) = X1^1 * X2^0 * X3^2 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.888178E-15 3 84 0.910383E-14 F(X) = X1^0 * X2^1 * X3^2 * X4^1 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.222045E-15 3 84 0.754952E-14 F(X) = X1^0 * X2^0 * X3^3 * X4^1 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.444089E-15 3 84 0.555112E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^2 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.888178E-15 3 84 0.166533E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^2 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.103251E-13 F(X) = X1^0 * X2^2 * X3^0 * X4^2 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.00000 3 84 0.199840E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^2 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.888178E-15 3 84 0.910383E-14 F(X) = X1^0 * X2^1 * X3^1 * X4^2 * X5^0 0 1 0.166667 1 7 0.312500E-01 2 28 0.222045E-15 3 84 0.106581E-13 F(X) = X1^0 * X2^0 * X3^2 * X4^2 * X5^0 0 1 0.416667 1 7 0.203125 2 28 0.333067E-15 3 84 0.111022E-15 F(X) = X1^1 * X2^0 * X3^0 * X4^3 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.444089E-15 3 84 0.599520E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^3 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.444089E-15 3 84 0.643929E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^3 * X5^0 0 1 0.611111 1 7 0.937500E-01 2 28 0.444089E-15 3 84 0.666134E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^4 * X5^0 0 1 0.902778 1 7 0.117188 2 28 0.133227E-14 3 84 0.188738E-14 F(X) = X1^3 * X2^0 * X3^0 * X4^0 * X5^1 0 1 0.611111 1 7 0.937500E-01 2 28 0.444089E-15 3 84 0.444089E-15 F(X) = X1^2 * X2^1 * X3^0 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.444089E-15 3 84 0.888178E-15 F(X) = X1^1 * X2^2 * X3^0 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.111022E-14 F(X) = X1^0 * X2^3 * X3^0 * X4^0 * X5^1 0 1 0.611111 1 7 0.937500E-01 2 28 0.666134E-15 3 84 0.133227E-14 F(X) = X1^2 * X2^0 * X3^1 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.00000 3 84 0.210942E-14 F(X) = X1^1 * X2^1 * X3^1 * X4^0 * X5^1 0 1 1.33333 1 7 0.625000E-01 2 28 0.133227E-14 3 84 0.277556E-14 F(X) = X1^0 * X2^2 * X3^1 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.199840E-14 F(X) = X1^1 * X2^0 * X3^2 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.888178E-15 3 84 0.288658E-14 F(X) = X1^0 * X2^1 * X3^2 * X4^0 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.155431E-14 3 84 0.266454E-14 F(X) = X1^0 * X2^0 * X3^3 * X4^0 * X5^1 0 1 0.611111 1 7 0.937500E-01 2 28 0.00000 3 84 0.177636E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^1 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.155431E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^1 * X5^1 0 1 1.33333 1 7 0.625000E-01 2 28 0.133227E-14 3 84 0.399680E-14 F(X) = X1^0 * X2^2 * X3^0 * X4^1 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.321965E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^1 * X5^1 0 1 1.33333 1 7 0.625000E-01 2 28 0.155431E-14 3 84 0.277556E-14 F(X) = X1^0 * X2^1 * X3^1 * X4^1 * X5^1 0 1 1.33333 1 7 0.625000E-01 2 28 0.155431E-14 3 84 0.244249E-14 F(X) = X1^0 * X2^0 * X3^2 * X4^1 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.666134E-15 3 84 0.432987E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^2 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.111022E-14 3 84 0.477396E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^2 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.444089E-15 3 84 0.444089E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^2 * X5^1 0 1 0.166667 1 7 0.312500E-01 2 28 0.111022E-14 3 84 0.432987E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^3 * X5^1 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.333067E-14 F(X) = X1^2 * X2^0 * X3^0 * X4^0 * X5^2 0 1 0.416667 1 7 0.203125 2 28 0.888178E-15 3 84 0.510703E-14 F(X) = X1^1 * X2^1 * X3^0 * X4^0 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.199840E-14 3 84 0.599520E-14 F(X) = X1^0 * X2^2 * X3^0 * X4^0 * X5^2 0 1 0.416667 1 7 0.203125 2 28 0.666134E-15 3 84 0.310862E-14 F(X) = X1^1 * X2^0 * X3^1 * X4^0 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.222045E-14 3 84 0.599520E-14 F(X) = X1^0 * X2^1 * X3^1 * X4^0 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.177636E-14 3 84 0.566214E-14 F(X) = X1^0 * X2^0 * X3^2 * X4^0 * X5^2 0 1 0.416667 1 7 0.203125 2 28 0.222045E-15 3 84 0.111022E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^1 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.222045E-14 3 84 0.788258E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^1 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.177636E-14 3 84 0.754952E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^1 * X5^2 0 1 0.166667 1 7 0.312500E-01 2 28 0.222045E-14 3 84 0.732747E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^2 * X5^2 0 1 0.416667 1 7 0.203125 2 28 0.00000 3 84 0.333067E-14 F(X) = X1^1 * X2^0 * X3^0 * X4^0 * X5^3 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.244249E-14 F(X) = X1^0 * X2^1 * X3^0 * X4^0 * X5^3 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.288658E-14 F(X) = X1^0 * X2^0 * X3^1 * X4^0 * X5^3 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.333067E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^1 * X5^3 0 1 0.611111 1 7 0.937500E-01 2 28 0.222045E-15 3 84 0.377476E-14 F(X) = X1^0 * X2^0 * X3^0 * X4^0 * X5^4 0 1 0.902778 1 7 0.117188 2 28 0.133227E-14 3 84 0.532907E-14 TEST08 GM_GENERAL_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional general simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. Here we use M = 3 RULE = 2 DEGREE = 5 Simplex vertices: 1.00000 0.00000 0.00000 2.00000 0.00000 0.00000 1.00000 2.00000 0.00000 1.00000 0.00000 3.00000 POINT W X Y Z 1 0.304762 1.125000 0.250000 0.375000 2 0.304762 1.375000 0.250000 0.375000 3 0.304762 1.625000 0.250000 0.375000 4 0.304762 1.125000 0.750000 0.375000 5 0.304762 1.375000 0.750000 0.375000 6 0.304762 1.125000 1.250000 0.375000 7 0.304762 1.125000 0.250000 1.125000 8 0.304762 1.375000 0.250000 1.125000 9 0.304762 1.125000 0.750000 1.125000 10 0.304762 1.125000 0.250000 1.875000 11 -0.578571 1.166667 0.333333 0.500000 12 -0.578571 1.500000 0.333333 0.500000 13 -0.578571 1.166667 1.000000 0.500000 14 -0.578571 1.166667 0.333333 1.500000 15 0.266667 1.250000 0.500000 0.750000 TEST09 GM_UNIT_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional unit simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. In this test, look at all the monomials up to some maximum degree, choose a few low order rules and determine the quadrature error for each. Simplex volume = 0.166667 N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.104167E-01 0.104167E-01 0.104167E-01 0.104167E-01 0.104167E-01 0.104167E-01 5 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.166667E-01 0.833333E-02 0.833333E-02 0.166667E-01 0.833333E-02 0.166667E-01 15 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.166667E-01 0.833333E-02 0.833333E-02 0.166667E-01 0.833333E-02 0.166667E-01 35 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.166667E-01 0.833333E-02 0.833333E-02 0.166667E-01 0.833333E-02 0.166667E-01 70 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.166667E-01 0.833333E-02 0.833333E-02 0.166667E-01 0.833333E-02 0.166667E-01 126 0.166667 0.416667E-01 0.416667E-01 0.416667E-01 0.166667E-01 0.833333E-02 0.833333E-02 0.166667E-01 0.833333E-02 0.166667E-01 TEST10 GM_GENERAL_RULE_SET determines the weights and abscissas of a Grundmann-Moeller quadrature rule for the M dimensional general simplex, using a rule of index RULE, which will have degree of exactness 2*RULE+1. In this test, look at all the monomials up to some maximum degree, choose a few low order rules and determine the quadrature error for each. Simplex vertices: 1.00000 0.00000 0.00000 2.00000 0.00000 0.00000 1.00000 2.00000 0.00000 1.00000 0.00000 3.00000 Simplex volume = 1.00000 N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 1.00000 1.25000 0.500000 0.750000 1.56250 0.625000 0.937500 0.250000 0.375000 0.562500 5 1.00000 1.25000 0.500000 0.750000 1.60000 0.600000 0.900000 0.400000 0.300000 0.900000 15 1.00000 1.25000 0.500000 0.750000 1.60000 0.600000 0.900000 0.400000 0.300000 0.900000 35 1.00000 1.25000 0.500000 0.750000 1.60000 0.600000 0.900000 0.400000 0.300000 0.900000 70 1.00000 1.25000 0.500000 0.750000 1.60000 0.600000 0.900000 0.400000 0.300000 0.900000 126 1.00000 1.25000 0.500000 0.750000 1.60000 0.600000 0.900000 0.400000 0.300000 0.900000 SIMPLEX_GM_RULE_PRB Normal end of execution. 6 March 2017 7:46:54.927 AM