16 November 2024 1:11:02.389 PM sphere_design_rule_test(): Fortran90 version Test sphere_design_rule(). TEST01 DESIGN_QUAD returns the average value of a function F(X,Y,Z) at the points of a spherical design. For this test, we will use single polynomial terms. F(x,y,z) = x^ 0y^ 0z^ 0 Order Size Quad Integral Exact: 12.5664 1 2 1.00000 12.5664 2 4 1.00000 12.5664 3 6 1.00000 12.5664 4 14 1.00000 12.5664 5 12 1.00000 12.5664 6 26 1.00000 12.5664 7 24 1.00000 12.5664 8 36 1.00000 12.5664 9 48 1.00000 12.5664 10 60 1.00000 12.5664 11 70 1.00000 12.5664 12 84 1.00000 12.5664 13 94 1.00000 12.5664 14 108 1.00000 12.5664 15 120 1.00000 12.5664 16 144 1.00000 12.5664 17 156 1.00000 12.5664 18 180 1.00000 12.5664 19 204 1.00000 12.5664 20 216 1.00000 12.5664 21 240 1.00000 12.5664 F(x,y,z) = x^ 1y^ 0z^ 0 Order Size Quad Integral Exact: 0.00000 1 2 0.00000 0.00000 2 4 0.00000 0.00000 3 6 0.00000 0.00000 4 14 0.00000 0.00000 5 12 0.00000 0.00000 6 26 0.811317E-16 0.101953E-14 7 24 0.925186E-17 0.116262E-15 8 36 0.231296E-16 0.290656E-15 9 48 -0.462593E-17 -0.581311E-16 10 60 -0.471845E-16 -0.592938E-15 11 70 0.426246E-16 0.535637E-15 12 84 -0.991271E-16 -0.124567E-14 13 94 0.334396E-15 0.420214E-14 14 108 -0.165505E-15 -0.207980E-14 15 120 0.274642E-10 0.345125E-09 16 144 -0.298792E-10 -0.375474E-09 17 156 -0.951018E-11 -0.119508E-09 18 180 0.357122E-15 0.448772E-14 19 204 0.108845E-17 0.136779E-16 20 216 0.169617E-16 0.213148E-15 21 240 0.705917E-15 0.887081E-14 F(x,y,z) = x^ 0y^ 1z^ 0 Order Size Quad Integral Exact: 0.00000 1 2 0.00000 0.00000 2 4 0.00000 0.00000 3 6 0.00000 0.00000 4 14 0.158603E-16 0.199307E-15 5 12 0.00000 0.00000 6 26 -0.122765E-15 -0.154271E-14 7 24 0.925186E-17 0.116262E-15 8 36 0.616791E-17 0.775082E-16 9 48 -0.462593E-17 -0.581311E-16 10 60 -0.166533E-16 -0.209272E-15 11 70 0.269626E-16 0.338822E-15 12 84 -0.350249E-15 -0.440136E-14 13 94 -0.270617E-15 -0.340067E-14 14 108 -0.400914E-16 -0.503803E-15 15 120 0.383147E-11 0.481477E-10 16 144 0.112370E-10 0.141209E-09 17 156 0.124044E-10 0.155879E-09 18 180 0.197373E-16 0.248026E-15 19 204 0.683005E-16 0.858289E-15 20 216 -0.709309E-16 -0.891344E-15 21 240 0.132440E-14 0.166429E-13 F(x,y,z) = x^ 0y^ 0z^ 1 Order Size Quad Integral Exact: 0.00000 1 2 0.00000 0.00000 2 4 0.00000 0.00000 3 6 0.00000 0.00000 4 14 0.00000 0.00000 5 12 0.00000 0.00000 6 26 -0.170804E-16 -0.214638E-15 7 24 0.925186E-17 0.116262E-15 8 36 0.578241E-17 0.726639E-16 9 48 -0.462593E-17 -0.581311E-16 10 60 -0.115648E-16 -0.145328E-15 11 70 -0.888178E-16 -0.111612E-14 12 84 -0.553459E-16 -0.695498E-15 13 94 -0.449995E-15 -0.565480E-14 14 108 -0.303255E-16 -0.381082E-15 15 120 0.724611E-10 0.910573E-09 16 144 0.209881E-10 0.263744E-09 17 156 0.534762E-11 0.672002E-10 18 180 -0.641154E-15 -0.805698E-14 19 204 0.952397E-18 0.119682E-16 20 216 0.371841E-16 0.467269E-15 21 240 0.148284E-14 0.186339E-13 F(x,y,z) = x^ 2y^ 0z^ 0 Order Size Quad Integral Exact: 4.18879 1 2 1.00000 12.5664 2 4 0.333333 4.18879 3 6 0.333333 4.18879 4 14 0.333333 4.18879 5 12 0.333333 4.18879 6 26 0.333333 4.18879 7 24 0.333333 4.18879 8 36 0.333333 4.18879 9 48 0.333333 4.18879 10 60 0.333333 4.18879 11 70 0.333333 4.18879 12 84 0.333333 4.18879 13 94 0.333333 4.18879 14 108 0.333333 4.18879 15 120 0.333333 4.18879 16 144 0.333333 4.18879 17 156 0.333333 4.18879 18 180 0.333333 4.18879 19 204 0.333333 4.18879 20 216 0.333333 4.18879 21 240 0.333333 4.18879 F(x,y,z) = x^ 0y^ 2z^ 2 Order Size Quad Integral Exact: 0.837758 1 2 0.00000 0.00000 2 4 0.111111 1.39626 3 6 0.00000 0.00000 4 14 0.666667E-01 0.837758 5 12 0.666667E-01 0.837758 6 26 0.666667E-01 0.837758 7 24 0.666667E-01 0.837758 8 36 0.666667E-01 0.837758 9 48 0.666667E-01 0.837758 10 60 0.666667E-01 0.837758 11 70 0.666667E-01 0.837758 12 84 0.666667E-01 0.837758 13 94 0.666667E-01 0.837758 14 108 0.666667E-01 0.837758 15 120 0.666667E-01 0.837758 16 144 0.666667E-01 0.837758 17 156 0.666667E-01 0.837758 18 180 0.666667E-01 0.837758 19 204 0.666667E-01 0.837758 20 216 0.666667E-01 0.837758 21 240 0.666667E-01 0.837758 F(x,y,z) = x^ 2y^ 2z^ 2 Order Size Quad Integral Exact: 0.119680 1 2 0.00000 0.00000 2 4 0.370370E-01 0.465421 3 6 0.00000 0.00000 4 14 0.119342E-01 0.149969 5 12 0.00000 0.00000 6 26 0.952381E-02 0.119680 7 24 0.952381E-02 0.119680 8 36 0.952381E-02 0.119680 9 48 0.952381E-02 0.119680 10 60 0.952381E-02 0.119680 11 70 0.952381E-02 0.119680 12 84 0.952381E-02 0.119680 13 94 0.952381E-02 0.119680 14 108 0.952381E-02 0.119680 15 120 0.952381E-02 0.119680 16 144 0.952381E-02 0.119680 17 156 0.952381E-02 0.119680 18 180 0.952381E-02 0.119680 19 204 0.952381E-02 0.119680 20 216 0.952381E-02 0.119680 21 240 0.952381E-02 0.119680 F(x,y,z) = x^ 0y^ 2z^ 4 Order Size Quad Integral Exact: 0.359039 1 2 0.00000 0.00000 2 4 0.370370E-01 0.465421 3 6 0.00000 0.00000 4 14 0.192387E-01 0.241760 5 12 0.482405E-01 0.606207 6 26 0.285714E-01 0.359039 7 24 0.285714E-01 0.359039 8 36 0.285714E-01 0.359039 9 48 0.285714E-01 0.359039 10 60 0.285714E-01 0.359039 11 70 0.285714E-01 0.359039 12 84 0.285714E-01 0.359039 13 94 0.285714E-01 0.359039 14 108 0.285714E-01 0.359039 15 120 0.285714E-01 0.359039 16 144 0.285714E-01 0.359039 17 156 0.285714E-01 0.359039 18 180 0.285714E-01 0.359039 19 204 0.285714E-01 0.359039 20 216 0.285714E-01 0.359039 21 240 0.285714E-01 0.359039 F(x,y,z) = x^ 0y^ 0z^ 6 Order Size Quad Integral Exact: 1.79520 1 2 0.00000 0.00000 2 4 0.370370E-01 0.465421 3 6 0.333333 4.18879 4 14 0.144959 1.82161 5 12 0.133333 1.67552 6 26 0.142857 1.79520 7 24 0.142857 1.79520 8 36 0.142857 1.79520 9 48 0.142857 1.79520 10 60 0.142857 1.79520 11 70 0.142857 1.79520 12 84 0.142857 1.79520 13 94 0.142857 1.79520 14 108 0.142857 1.79520 15 120 0.142857 1.79520 16 144 0.142857 1.79520 17 156 0.142857 1.79520 18 180 0.142857 1.79520 19 204 0.142857 1.79520 20 216 0.142857 1.79520 21 240 0.142857 1.79520 F(x,y,z) = x^ 1y^ 2z^ 4 Order Size Quad Integral Exact: 0.00000 1 2 0.00000 0.00000 2 4 0.00000 0.00000 3 6 0.00000 0.00000 4 14 0.00000 0.00000 5 12 0.00000 0.00000 6 26 -0.135609E-16 -0.170411E-15 7 24 0.00000 0.00000 8 36 0.421740E-18 0.529974E-17 9 48 -0.722801E-19 -0.908299E-18 10 60 0.355054E-17 0.446174E-16 11 70 0.433681E-17 0.544979E-16 12 84 -0.212178E-17 -0.266630E-16 13 94 -0.139144E-16 -0.174854E-15 14 108 -0.245752E-17 -0.308822E-16 15 120 0.167301E-12 0.210237E-11 16 144 0.373556E-12 0.469424E-11 17 156 0.147008E-11 0.184735E-10 18 180 0.251955E-12 0.316615E-11 19 204 0.711670E-17 0.894311E-16 20 216 0.321929E-17 0.404548E-16 21 240 0.186125E-12 0.233892E-11 F(x,y,z) = x^ 2y^ 4z^ 2 Order Size Quad Integral Exact: 0.398932E-01 1 2 0.00000 0.00000 2 4 0.123457E-01 0.155140 3 6 0.00000 0.00000 4 14 0.534294E-02 0.671413E-01 5 12 0.00000 0.00000 6 26 0.334450E-02 0.420282E-01 7 24 0.317460E-02 0.398932E-01 8 36 0.317460E-02 0.398932E-01 9 48 0.317460E-02 0.398932E-01 10 60 0.317460E-02 0.398932E-01 11 70 0.317460E-02 0.398932E-01 12 84 0.317460E-02 0.398932E-01 13 94 0.317460E-02 0.398932E-01 14 108 0.317460E-02 0.398932E-01 15 120 0.317460E-02 0.398932E-01 16 144 0.317460E-02 0.398932E-01 17 156 0.317460E-02 0.398932E-01 18 180 0.317460E-02 0.398932E-01 19 204 0.317460E-02 0.398932E-01 20 216 0.317460E-02 0.398932E-01 21 240 0.317460E-02 0.398932E-01 F(x,y,z) = x^ 6y^ 2z^ 0 Order Size Quad Integral Exact: 0.199466 1 2 0.00000 0.00000 2 4 0.123457E-01 0.155140 3 6 0.00000 0.00000 4 14 0.627343E-02 0.788343E-01 5 12 0.509288E-02 0.639990E-01 6 26 0.163429E-01 0.205371 7 24 0.184127E-01 0.231381 8 36 0.158730E-01 0.199466 9 48 0.158730E-01 0.199466 10 60 0.158730E-01 0.199466 11 70 0.158730E-01 0.199466 12 84 0.158730E-01 0.199466 13 94 0.158730E-01 0.199466 14 108 0.158730E-01 0.199466 15 120 0.158730E-01 0.199466 16 144 0.158730E-01 0.199466 17 156 0.158730E-01 0.199466 18 180 0.158730E-01 0.199466 19 204 0.158730E-01 0.199466 20 216 0.158730E-01 0.199466 21 240 0.158730E-01 0.199466 F(x,y,z) = x^ 0y^ 0z^ 8 Order Size Quad Integral Exact: 1.39626 1 2 0.00000 0.00000 2 4 0.123457E-01 0.155140 3 6 0.333333 4.18879 4 14 0.114882 1.44365 5 12 0.933333E-01 1.17286 6 26 0.114065 1.43339 7 24 0.106032 1.33243 8 36 0.111111 1.39626 9 48 0.111111 1.39626 10 60 0.111111 1.39626 11 70 0.111111 1.39626 12 84 0.111111 1.39626 13 94 0.111111 1.39626 14 108 0.111111 1.39626 15 120 0.111111 1.39626 16 144 0.111111 1.39626 17 156 0.111111 1.39626 18 180 0.111111 1.39626 19 204 0.111111 1.39626 20 216 0.111111 1.39626 21 240 0.111111 1.39626 F(x,y,z) = x^ 6y^ 0z^ 4 Order Size Quad Integral Exact: 0.543999E-01 1 2 0.00000 0.00000 2 4 0.411523E-02 0.517135E-01 3 6 0.00000 0.00000 4 14 0.306965E-02 0.385744E-01 5 12 0.964809E-02 0.121241 6 26 0.502197E-02 0.631079E-01 7 24 0.317460E-02 0.398932E-01 8 36 0.373054E-02 0.468794E-01 9 48 0.431197E-02 0.541859E-01 10 60 0.432900E-02 0.543999E-01 11 70 0.432900E-02 0.543999E-01 12 84 0.432900E-02 0.543999E-01 13 94 0.432900E-02 0.543999E-01 14 108 0.432900E-02 0.543999E-01 15 120 0.432900E-02 0.543999E-01 16 144 0.432900E-02 0.543999E-01 17 156 0.432900E-02 0.543999E-01 18 180 0.432900E-02 0.543999E-01 19 204 0.432900E-02 0.543999E-01 20 216 0.432900E-02 0.543999E-01 21 240 0.432900E-02 0.543999E-01 F(x,y,z) = x^ 4y^ 6z^ 2 Order Size Quad Integral Exact: 0.418461E-02 1 2 0.00000 0.00000 2 4 0.137174E-02 0.172378E-01 3 6 0.00000 0.00000 4 14 0.582000E-03 0.731362E-02 5 12 0.00000 0.00000 6 26 0.267207E-03 0.335783E-02 7 24 0.272109E-03 0.341942E-02 8 36 0.295523E-03 0.371366E-02 9 48 0.363121E-03 0.456312E-02 10 60 0.320098E-03 0.402248E-02 11 70 0.349753E-03 0.439512E-02 12 84 0.333000E-03 0.418461E-02 13 94 0.333000E-03 0.418461E-02 14 108 0.333000E-03 0.418461E-02 15 120 0.333000E-03 0.418461E-02 16 144 0.333000E-03 0.418461E-02 17 156 0.333000E-03 0.418461E-02 18 180 0.333000E-03 0.418461E-02 19 204 0.333000E-03 0.418461E-02 20 216 0.333000E-03 0.418461E-02 21 240 0.333000E-03 0.418461E-02 F(x,y,z) = x^ 2y^ 4z^ 8 Order Size Quad Integral Exact: 0.195282E-02 1 2 0.00000 0.00000 2 4 0.457247E-03 0.574594E-02 3 6 0.00000 0.00000 4 14 0.113222E-03 0.142279E-02 5 12 0.00000 0.00000 6 26 0.261349E-03 0.328421E-02 7 24 0.175359E-03 0.220363E-02 8 36 0.126167E-03 0.158546E-02 9 48 0.163846E-03 0.205895E-02 10 60 0.149294E-03 0.187608E-02 11 70 0.160835E-03 0.202111E-02 12 84 0.155122E-03 0.194932E-02 13 94 0.154462E-03 0.194102E-02 14 108 0.155400E-03 0.195282E-02 15 120 0.155400E-03 0.195282E-02 16 144 0.155400E-03 0.195282E-02 17 156 0.155400E-03 0.195282E-02 18 180 0.155400E-03 0.195282E-02 19 204 0.155400E-03 0.195282E-02 20 216 0.155400E-03 0.195282E-02 21 240 0.155400E-03 0.195282E-02 F(x,y,z) = x^16y^ 0z^ 0 Order Size Quad Integral Exact: 0.739198 1 2 1.00000 12.5664 2 4 0.152416E-03 0.191531E-02 3 6 0.333333 4.18879 4 14 0.142962 1.79651 5 12 0.250667E-01 0.314997 6 26 0.618135E-01 0.776771 7 24 0.335081E-01 0.421075 8 36 0.595666E-01 0.748536 9 48 0.560714E-01 0.704614 10 60 0.582032E-01 0.731402 11 70 0.589471E-01 0.740752 12 84 0.588362E-01 0.739357 13 94 0.587710E-01 0.738539 14 108 0.588201E-01 0.739155 15 120 0.588206E-01 0.739161 16 144 0.588235E-01 0.739198 17 156 0.588235E-01 0.739198 18 180 0.588235E-01 0.739198 19 204 0.588235E-01 0.739198 20 216 0.588235E-01 0.739198 21 240 0.588235E-01 0.739198 TEST02 DESIGN_QUAD returns the average value of a function F(X,Y,Z) at the points of a spherical design. For this test, we will use single polynomial terms. F(x,y,z) = x^ 0y^ 0z^ 0 Order Size Quad Integral 1 2 4.00000 201.062 2 4 4.00000 201.062 3 6 4.00000 201.062 4 14 4.00000 201.062 5 12 4.00000 201.062 6 26 4.00000 201.062 7 24 4.00000 201.062 8 36 4.00000 201.062 9 48 4.00000 201.062 10 60 4.00000 201.062 11 70 4.00000 201.062 12 84 4.00000 201.062 13 94 4.00000 201.062 14 108 4.00000 201.062 15 120 4.00000 201.062 16 144 4.00000 201.062 17 156 4.00000 201.062 18 180 4.00000 201.062 19 204 4.00000 201.062 20 216 4.00000 201.062 21 240 4.00000 201.062 F(x,y,z) = x^ 1y^ 0z^ 0 Order Size Quad Integral 1 2 4.00000 201.062 2 4 4.00000 201.062 3 6 4.00000 201.062 4 14 4.00000 201.062 5 12 4.00000 201.062 6 26 4.00000 201.062 7 24 4.00000 201.062 8 36 4.00000 201.062 9 48 4.00000 201.062 10 60 4.00000 201.062 11 70 4.00000 201.062 12 84 4.00000 201.062 13 94 4.00000 201.062 14 108 4.00000 201.062 15 120 4.00000 201.062 16 144 4.00000 201.062 17 156 4.00000 201.062 18 180 4.00000 201.062 19 204 4.00000 201.062 20 216 4.00000 201.062 21 240 4.00000 201.062 F(x,y,z) = x^ 0y^ 1z^ 0 Order Size Quad Integral 1 2 8.00000 402.124 2 4 8.00000 402.124 3 6 8.00000 402.124 4 14 8.00000 402.124 5 12 8.00000 402.124 6 26 8.00000 402.124 7 24 8.00000 402.124 8 36 8.00000 402.124 9 48 8.00000 402.124 10 60 8.00000 402.124 11 70 8.00000 402.124 12 84 8.00000 402.124 13 94 8.00000 402.124 14 108 8.00000 402.124 15 120 8.00000 402.124 16 144 8.00000 402.124 17 156 8.00000 402.124 18 180 8.00000 402.124 19 204 8.00000 402.124 20 216 8.00000 402.124 21 240 8.00000 402.124 F(x,y,z) = x^ 0y^ 0z^ 1 Order Size Quad Integral 1 2 12.0000 603.186 2 4 12.0000 603.186 3 6 12.0000 603.186 4 14 12.0000 603.186 5 12 12.0000 603.186 6 26 12.0000 603.186 7 24 12.0000 603.186 8 36 12.0000 603.186 9 48 12.0000 603.186 10 60 12.0000 603.186 11 70 12.0000 603.186 12 84 12.0000 603.186 13 94 12.0000 603.186 14 108 12.0000 603.186 15 120 12.0000 603.186 16 144 12.0000 603.186 17 156 12.0000 603.186 18 180 12.0000 603.186 19 204 12.0000 603.186 20 216 12.0000 603.186 21 240 12.0000 603.186 F(x,y,z) = x^ 2y^ 0z^ 0 Order Size Quad Integral 1 2 20.0000 1005.31 2 4 9.33333 469.145 3 6 9.33333 469.145 4 14 9.33333 469.145 5 12 9.33333 469.145 6 26 9.33333 469.145 7 24 9.33333 469.145 8 36 9.33333 469.145 9 48 9.33333 469.145 10 60 9.33333 469.145 11 70 9.33333 469.145 12 84 9.33333 469.145 13 94 9.33333 469.145 14 108 9.33333 469.145 15 120 9.33333 469.145 16 144 9.33333 469.145 17 156 9.33333 469.145 18 180 9.33333 469.145 19 204 9.33333 469.145 20 216 9.33333 469.145 21 240 9.33333 469.145 F(x,y,z) = x^ 0y^ 2z^ 2 Order Size Quad Integral 1 2 144.000 7238.23 2 4 220.444 11080.7 3 6 213.333 10723.3 4 14 217.600 10937.8 5 12 217.600 10937.8 6 26 217.600 10937.8 7 24 217.600 10937.8 8 36 217.600 10937.8 9 48 217.600 10937.8 10 60 217.600 10937.8 11 70 217.600 10937.8 12 84 217.600 10937.8 13 94 217.600 10937.8 14 108 217.600 10937.8 15 120 217.600 10937.8 16 144 217.600 10937.8 17 156 217.600 10937.8 18 180 217.600 10937.8 19 204 217.600 10937.8 20 216 217.600 10937.8 21 240 217.600 10937.8 F(x,y,z) = x^ 2y^ 2z^ 2 Order Size Quad Integral 1 2 720.000 36191.1 2 4 809.974 40713.7 3 6 405.333 20374.3 4 14 472.767 23763.8 5 12 465.067 23376.8 6 26 467.505 23499.4 7 24 467.505 23499.4 8 36 467.505 23499.4 9 48 467.505 23499.4 10 60 467.505 23499.4 11 70 467.505 23499.4 12 84 467.505 23499.4 13 94 467.505 23499.4 14 108 467.505 23499.4 15 120 467.505 23499.4 16 144 467.505 23499.4 17 156 467.505 23499.4 18 180 467.505 23499.4 19 204 467.505 23499.4 20 216 467.505 23499.4 21 240 467.505 23499.4 F(x,y,z) = x^ 0y^ 2z^ 4 Order Size Quad Integral 1 2 1296.00 65144.1 2 4 3301.93 165973. 3 6 2965.33 149054. 4 14 3163.04 158992. 5 12 3173.95 159540. 6 26 3168.91 159287. 7 24 3168.91 159287. 8 36 3168.91 159287. 9 48 3168.91 159287. 10 60 3168.91 159287. 11 70 3168.91 159287. 12 84 3168.91 159287. 13 94 3168.91 159287. 14 108 3168.91 159287. 15 120 3168.91 159287. 16 144 3168.91 159287. 17 156 3168.91 159287. 18 180 3168.91 159287. 19 204 3168.91 159287. 20 216 3168.91 159287. 21 240 3168.91 159287. F(x,y,z) = x^ 0y^ 0z^ 6 Order Size Quad Integral 1 2 2916.00 146574. 2 4 10365.5 521026. 3 6 12361.3 621348. 4 14 11161.1 561019. 5 12 11158.1 560869. 6 26 11160.6 560992. 7 24 11160.6 560992. 8 36 11160.6 560992. 9 48 11160.6 560992. 10 60 11160.6 560992. 11 70 11160.6 560992. 12 84 11160.6 560992. 13 94 11160.6 560992. 14 108 11160.6 560992. 15 120 11160.6 560992. 16 144 11160.6 560992. 17 156 11160.6 560992. 18 180 11160.6 560992. 19 204 11160.6 560992. 20 216 11160.6 560992. 21 240 11160.6 560992. F(x,y,z) = x^ 1y^ 2z^ 4 Order Size Quad Integral 1 2 1296.00 65144.1 2 4 6356.49 319512. 3 6 2965.33 149054. 4 14 3168.29 159256. 5 12 3173.95 159540. 6 26 3168.91 159287. 7 24 3168.91 159287. 8 36 3168.91 159287. 9 48 3168.91 159287. 10 60 3168.91 159287. 11 70 3168.91 159287. 12 84 3168.91 159287. 13 94 3168.91 159287. 14 108 3168.91 159287. 15 120 3168.91 159287. 16 144 3168.91 159287. 17 156 3168.91 159287. 18 180 3168.91 159287. 19 204 3168.91 159287. 20 216 3168.91 159287. 21 240 3168.91 159287. F(x,y,z) = x^ 2y^ 4z^ 2 Order Size Quad Integral 1 2 2880.00 144765. 2 4 7953.89 399806. 3 6 2773.33 139403. 4 14 3931.30 197609. 5 12 3904.66 196270. 6 26 3921.55 197118. 7 24 3923.71 197227. 8 36 3923.71 197227. 9 48 3923.71 197227. 10 60 3923.71 197227. 11 70 3923.71 197227. 12 84 3923.71 197227. 13 94 3923.71 197227. 14 108 3923.71 197227. 15 120 3923.71 197227. 16 144 3923.71 197227. 17 156 3923.71 197227. 18 180 3923.71 197227. 19 204 3923.71 197227. 20 216 3923.71 197227. 21 240 3923.71 197227. F(x,y,z) = x^ 6y^ 2z^ 0 Order Size Quad Integral 1 2 5840.00 293550. 2 4 1067.46 53656.2 3 6 1962.67 98654.4 4 14 1418.48 71300.6 5 12 1385.84 69659.8 6 26 1448.69 72819.3 7 24 1448.19 72793.9 8 36 1445.59 72663.1 9 48 1445.59 72663.1 10 60 1445.59 72663.1 11 70 1445.59 72663.1 12 84 1445.59 72663.1 13 94 1445.59 72663.1 14 108 1445.59 72663.1 15 120 1445.59 72663.1 16 144 1445.59 72663.1 17 156 1445.59 72663.1 18 180 1445.59 72663.1 19 204 1445.59 72663.1 20 216 1445.59 72663.1 21 240 1445.59 72663.1 F(x,y,z) = x^ 0y^ 0z^ 8 Order Size Quad Integral 1 2 26244.0 0.131917E+07 2 4 177830. 0.893871E+07 3 6 277913. 0.139694E+08 4 14 217153. 0.109153E+08 5 12 216381. 0.108765E+08 6 26 217017. 0.109085E+08 7 24 217009. 0.109080E+08 8 36 217014. 0.109083E+08 9 48 217014. 0.109083E+08 10 60 217014. 0.109083E+08 11 70 217014. 0.109083E+08 12 84 217014. 0.109083E+08 13 94 217014. 0.109083E+08 14 108 217014. 0.109083E+08 15 120 217014. 0.109083E+08 16 144 217014. 0.109083E+08 17 156 217014. 0.109083E+08 18 180 217014. 0.109083E+08 19 204 217014. 0.109083E+08 20 216 217014. 0.109083E+08 21 240 217014. 0.109083E+08 F(x,y,z) = x^ 6y^ 0z^ 4 Order Size Quad Integral 1 2 118260. 0.594440E+07 2 4 30978.5 0.155715E+07 3 6 39945.3 0.200787E+07 4 14 34686.6 0.174354E+07 5 12 41126.0 0.206722E+07 6 26 36246.7 0.182196E+07 7 24 36247.8 0.182201E+07 8 36 36148.7 0.181703E+07 9 48 36151.0 0.181715E+07 10 60 36151.1 0.181715E+07 11 70 36151.1 0.181715E+07 12 84 36151.1 0.181715E+07 13 94 36151.1 0.181715E+07 14 108 36151.1 0.181715E+07 15 120 36151.1 0.181715E+07 16 144 36151.1 0.181715E+07 17 156 36151.1 0.181715E+07 18 180 36151.1 0.181715E+07 19 204 36151.1 0.181715E+07 20 216 36151.1 0.181715E+07 21 240 36151.1 0.181715E+07 F(x,y,z) = x^ 4y^ 6z^ 2 Order Size Quad Integral 1 2 94464.0 0.474828E+07 2 4 366784. 0.184366E+08 3 6 57173.3 0.287385E+07 4 14 136036. 0.683789E+07 5 12 166087. 0.834842E+07 6 26 156158. 0.784936E+07 7 24 155858. 0.783428E+07 8 36 157705. 0.792710E+07 9 48 157615. 0.792261E+07 10 60 157608. 0.792226E+07 11 70 157609. 0.792229E+07 12 84 157609. 0.792228E+07 13 94 157609. 0.792228E+07 14 108 157609. 0.792228E+07 15 120 157609. 0.792228E+07 16 144 157609. 0.792228E+07 17 156 157609. 0.792228E+07 18 180 157609. 0.792228E+07 19 204 157609. 0.792228E+07 20 216 157609. 0.792228E+07 21 240 157609. 0.792228E+07 F(x,y,z) = x^ 2y^ 4z^ 8 Order Size Quad Integral 1 2 0.209952E+07 0.105533E+09 2 4 0.408265E+08 0.205217E+10 3 6 0.598626E+07 0.300902E+09 4 14 0.141220E+08 0.709848E+09 5 12 0.117143E+08 0.588825E+09 6 26 0.132315E+08 0.665086E+09 7 24 0.129345E+08 0.650160E+09 8 36 0.129643E+08 0.651658E+09 9 48 0.129527E+08 0.651073E+09 10 60 0.129534E+08 0.651110E+09 11 70 0.129535E+08 0.651116E+09 12 84 0.129535E+08 0.651114E+09 13 94 0.129535E+08 0.651114E+09 14 108 0.129535E+08 0.651114E+09 15 120 0.129535E+08 0.651114E+09 16 144 0.129535E+08 0.651114E+09 17 156 0.129535E+08 0.651114E+09 18 180 0.129535E+08 0.651114E+09 19 204 0.129535E+08 0.651114E+09 20 216 0.129535E+08 0.651114E+09 21 240 0.129535E+08 0.651114E+09 F(x,y,z) = x^16y^ 0z^ 0 Order Size Quad Integral 1 2 0.860934E+08 0.432753E+10 2 4 431738. 0.217015E+08 3 6 0.286978E+08 0.144251E+10 4 14 0.125397E+08 0.630313E+09 5 12 0.542453E+07 0.272667E+09 6 26 0.767432E+07 0.385753E+09 7 24 0.645219E+07 0.324322E+09 8 36 0.762338E+07 0.383193E+09 9 48 0.755715E+07 0.379864E+09 10 60 0.759237E+07 0.381634E+09 11 70 0.759729E+07 0.381882E+09 12 84 0.759650E+07 0.381842E+09 13 94 0.759636E+07 0.381835E+09 14 108 0.759648E+07 0.381841E+09 15 120 0.759648E+07 0.381841E+09 16 144 0.759648E+07 0.381841E+09 17 156 0.759648E+07 0.381841E+09 18 180 0.759648E+07 0.381841E+09 19 204 0.759648E+07 0.381841E+09 20 216 0.759648E+07 0.381841E+09 21 240 0.759648E+07 0.381841E+09 TEST03 R8MAT_WRITE can write a sphere design rule to a file. Sphere design rule of 180 points written to "sphere_design_rule_18.txt". sphere_design_rule_test(): Normal end of execution. 16 November 2024 1:11:02.392 PM