September 27 2010 11:00:11.183 AM SPHERE_QUAD_PRB FORTRAN90 version Test the SPHERE_QUAD library. TEST01 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_MC uses a Monte Carlo method. SPHERE01_QUAD_LLC uses centroids of spherical triangles. SPHERE01_QUAD_LLM uses midsides of spherical triangles. SPHERE01_QUAD_LLV uses vertices of spherical triangles. H QUAD_MC QUAD_LLC QUAD_LLM QUAD_LLV EXACT Point counts per method: 1.00000 12 36 108 108 0.100000 1256 3844 11532 11532 0.100000E-01 125663 394384 1183152 1183152 P(X,Y,Z) = 1 1.00000 12.5664 12.5664 12.5664 12.5664 12.5664 0.100000 12.5664 12.5664 12.5664 12.5664 12.5664 0.100000E-01 12.5664 12.5664 12.5664 12.5664 12.5664 P(X,Y,Z) = X 1.00000 -0.589665 -0.638378E-15 -0.416334E-15 -0.444089E-15 0.00000 0.100000 -0.164461 -0.340666E-14 -0.332411E-14 -0.347445E-14 0.00000 0.100000E-01 0.444155E-01 -0.101395E-12 -0.101604E-12 -0.101240E-12 0.00000 P(X,Y,Z) = Y 1.00000 -1.17619 0.777156E-15 0.385109E-15 0.650431E-15 0.00000 0.100000 0.200868 0.756622E-14 0.752949E-14 0.757090E-14 0.00000 0.100000E-01 -0.614701E-02 -0.349532E-12 -0.349962E-12 -0.349845E-12 0.00000 P(X,Y,Z) = Z 1.00000 1.48610 -0.555112E-15 0.568989E-15 0.179023E-14 0.00000 0.100000 0.439399 -0.573478E-14 -0.381748E-14 -0.328562E-13 0.00000 0.100000E-01 -0.301076E-01 -0.459566E-11 -0.489151E-11 -0.423805E-11 0.00000 P(X,Y,Z) = X^2 1.00000 4.91170 4.20106 4.18085 4.11426 4.18879 0.100000 4.22987 4.18943 4.18879 4.18686 4.18879 0.100000E-01 4.18427 4.18880 4.18879 4.18877 4.18879 P(X,Y,Z) = Y^2 Z^2 1.00000 0.351093 0.863669 0.846232 0.812460 0.837758 0.100000 0.813288 0.838051 0.837759 0.836889 0.837758 0.100000E-01 0.839271 0.837761 0.837758 0.837749 0.837758 P(X,Y,Z) = X^2 Y^2 Z^2 1.00000 0.199044 0.129578 0.124238 0.101557 0.119680 0.100000 0.121300 0.119712 0.119680 0.119584 0.119680 0.100000E-01 0.119616 0.119680 0.119680 0.119679 0.119680 P(X,Y,Z) = Y^2 Z^4 1.00000 0.255397 0.345359 0.349282 0.406230 0.359039 0.100000 0.367814 0.359204 0.359039 0.358553 0.359039 0.100000E-01 0.357071 0.359041 0.359039 0.359034 0.359039 P(X,Y,Z) = Z^6 1.00000 0.314945 1.74619 1.81365 1.90048 1.79520 0.100000 1.87683 1.79299 1.79520 1.80177 1.79520 0.100000E-01 1.80312 1.79517 1.79520 1.79527 1.79520 P(X,Y,Z) = X Y^2 Z^4 1.00000 -0.347930E-02 0.303577E-17 0.433681E-17 0.173472E-17 0.00000 0.100000 -0.218956E-02 0.761654E-16 0.762270E-16 0.704450E-16 0.00000 0.100000E-01 0.260920E-03 0.508682E-14 0.508682E-14 0.509027E-14 0.00000 P(X,Y,Z) = X^2 Y^4 Z^2 1.00000 0.511243E-01 0.376728E-01 0.416209E-01 0.380841E-01 0.398932E-01 0.100000 0.435338E-01 0.399019E-01 0.398933E-01 0.398674E-01 0.398932E-01 0.100000E-01 0.399785E-01 0.398933E-01 0.398932E-01 0.398930E-01 0.398932E-01 P(X,Y,Z) = X^6 Y^2 1.00000 0.202822E-01 0.273328 0.239425 0.420696E-01 0.199466 0.100000 0.208212 0.199478 0.199466 0.199429 0.199466 0.100000E-01 0.199392 0.199466 0.199466 0.199466 0.199466 P(X,Y,Z) = Z^8 1.00000 1.11685 1.33672 1.40644 1.49425 1.39626 0.100000 1.41548 1.39385 1.39627 1.40345 1.39626 0.100000E-01 1.40273 1.39624 1.39626 1.39634 1.39626 P(X,Y,Z) = X^6 Z^4 1.00000 0.551207E-01 0.484962E-01 0.490611E-01 0.698208E-01 0.543999E-01 0.100000 0.577633E-01 0.544168E-01 0.544000E-01 0.543492E-01 0.543999E-01 0.100000E-01 0.546621E-01 0.544000E-01 0.543999E-01 0.543994E-01 0.543999E-01 P(X,Y,Z) = X^4 Y^6 Z^2 1.00000 0.209369E-02 0.440687E-02 0.514531E-02 0.178519E-02 0.418461E-02 0.100000 0.436554E-02 0.418525E-02 0.418461E-02 0.418267E-02 0.418461E-02 0.100000E-01 0.415988E-02 0.418461E-02 0.418461E-02 0.418458E-02 0.418461E-02 P(X,Y,Z) = X^2 Y^4 Z^8 1.00000 0.304468E-02 0.954775E-03 0.110087E-02 0.476051E-02 0.195282E-02 0.100000 0.205301E-02 0.195367E-02 0.195282E-02 0.195028E-02 0.195282E-02 0.100000E-01 0.195389E-02 0.195282E-02 0.195282E-02 0.195279E-02 0.195282E-02 P(X,Y,Z) = X^16 1.00000 0.584951E-01 0.355946 0.469493 1.66807 0.739198 0.100000 0.749398 0.739219 0.739197 0.739134 0.739198 0.100000E-01 0.735602 0.739199 0.739198 0.739197 0.739198 TEST02 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS1C uses centroids of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 20 12.5664 12.5664 0.00000 2 80 12.5664 12.5664 0.355271E-13 4 320 12.5664 12.5664 0.373035E-13 8 1280 12.5664 12.5664 0.213163E-13 16 5120 12.5664 12.5664 0.305533E-12 32 20480 12.5664 12.5664 0.249578E-11 P(X,Y,Z) = X 1 20 -0.222045E-15 0.00000 0.222045E-15 2 80 0.527356E-15 0.00000 0.527356E-15 4 320 -0.160288E-14 0.00000 0.160288E-14 8 1280 0.624934E-14 0.00000 0.624934E-14 16 5120 -0.102624E-13 0.00000 0.102624E-13 32 20480 0.760747E-14 0.00000 0.760747E-14 P(X,Y,Z) = Y 1 20 0.555112E-16 0.00000 0.555112E-16 2 80 -0.971445E-16 0.00000 0.971445E-16 4 320 -0.115359E-14 0.00000 0.115359E-14 8 1280 0.710803E-14 0.00000 0.710803E-14 16 5120 0.104590E-13 0.00000 0.104590E-13 32 20480 0.140228E-13 0.00000 0.140228E-13 P(X,Y,Z) = Z 1 20 0.00000 0.00000 0.00000 2 80 0.138778E-16 0.00000 0.138778E-16 4 320 -0.867362E-16 0.00000 0.867362E-16 8 1280 -0.143722E-14 0.00000 0.143722E-14 16 5120 0.155152E-14 0.00000 0.155152E-14 32 20480 -0.221572E-14 0.00000 0.221572E-14 P(X,Y,Z) = X^2 1 20 4.18879 4.18879 0.888178E-15 2 80 4.18879 4.18879 0.532907E-14 4 320 4.18879 4.18879 0.213163E-13 8 1280 4.18879 4.18879 0.106581E-13 16 5120 4.18879 4.18879 0.151879E-12 32 20480 4.18879 4.18879 0.845546E-12 P(X,Y,Z) = Y^2 Z^2 1 20 0.837758 0.837758 0.333067E-15 2 80 0.837758 0.837758 0.133227E-14 4 320 0.837758 0.837758 0.233147E-14 8 1280 0.837758 0.837758 0.310862E-14 16 5120 0.837758 0.837758 0.232037E-13 32 20480 0.837758 0.837758 0.174194E-12 P(X,Y,Z) = X^2 Y^2 Z^2 1 20 0.186168 0.119680 0.664887E-01 2 80 0.113393 0.119680 0.628634E-02 4 320 0.118875 0.119680 0.805184E-03 8 1280 0.119502 0.119680 0.177788E-03 16 5120 0.119637 0.119680 0.431778E-04 32 20480 0.119669 0.119680 0.107182E-04 P(X,Y,Z) = Y^2 Z^4 1 20 0.429866 0.359039 0.708270E-01 2 80 0.352343 0.359039 0.669651E-02 4 320 0.358181 0.359039 0.857720E-03 8 1280 0.358850 0.359039 0.189388E-03 16 5120 0.358993 0.359039 0.459951E-04 32 20480 0.359028 0.359039 0.114175E-04 P(X,Y,Z) = Z^6 1 20 1.86168 1.79520 0.664887E-01 2 80 1.78891 1.79520 0.628634E-02 4 320 1.79439 1.79520 0.805184E-03 8 1280 1.79502 1.79520 0.177788E-03 16 5120 1.79515 1.79520 0.431778E-04 32 20480 1.79519 1.79520 0.107182E-04 P(X,Y,Z) = X Y^2 Z^4 1 20 0.346945E-17 0.00000 0.346945E-17 2 80 -0.219009E-16 0.00000 0.219009E-16 4 320 0.475054E-16 0.00000 0.475054E-16 8 1280 0.477429E-16 0.00000 0.477429E-16 16 5120 -0.326402E-15 0.00000 0.326402E-15 32 20480 0.425669E-15 0.00000 0.425669E-15 P(X,Y,Z) = X^2 Y^4 Z^2 1 20 0.620562E-01 0.398932E-01 0.221629E-01 2 80 0.377978E-01 0.398932E-01 0.209545E-02 4 320 0.396248E-01 0.398932E-01 0.268395E-03 8 1280 0.398340E-01 0.398932E-01 0.592626E-04 16 5120 0.398788E-01 0.398932E-01 0.143926E-04 32 20480 0.398897E-01 0.398932E-01 0.357273E-05 P(X,Y,Z) = X^6 Y^2 1 20 0.665831E-01 0.199466 0.132883 2 80 0.212030 0.199466 0.125638E-01 4 320 0.201075 0.199466 0.160923E-02 8 1280 0.199822 0.199466 0.355323E-03 16 5120 0.199552 0.199466 0.862944E-04 32 20480 0.199488 0.199466 0.214212E-04 P(X,Y,Z) = Z^8 1 20 1.52038 1.39626 0.124112 2 80 1.38453 1.39626 0.117345E-01 4 320 1.39476 1.39626 0.150301E-02 8 1280 1.39593 1.39626 0.331871E-03 16 5120 1.39618 1.39626 0.805986E-04 32 20480 1.39624 1.39626 0.200073E-04 P(X,Y,Z) = X^6 Z^4 1 20 0.477629E-01 0.543999E-01 0.663697E-02 2 80 0.524750E-01 0.543999E-01 0.192484E-02 4 320 0.543862E-01 0.543999E-01 0.136573E-04 8 1280 0.543951E-01 0.543999E-01 0.480599E-05 16 5120 0.543986E-01 0.543999E-01 0.124051E-05 32 20480 0.543996E-01 0.543999E-01 0.312007E-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 20 0.689513E-02 0.418461E-02 0.271052E-02 2 80 0.367262E-02 0.418461E-02 0.511990E-03 4 320 0.416014E-02 0.418461E-02 0.244658E-04 8 1280 0.417824E-02 0.418461E-02 0.636252E-05 16 5120 0.418304E-02 0.418461E-02 0.156630E-05 32 20480 0.418422E-02 0.418461E-02 0.389982E-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 20 0.229838E-02 0.195282E-02 0.345560E-03 2 80 0.135900E-02 0.195282E-02 0.593812E-03 4 320 0.194819E-02 0.195282E-02 0.462689E-05 8 1280 0.195051E-02 0.195282E-02 0.230393E-05 16 5120 0.195222E-02 0.195282E-02 0.591288E-06 32 20480 0.195267E-02 0.195282E-02 0.148545E-06 P(X,Y,Z) = X^16 1 20 0.846185 0.739198 0.106987 2 80 0.684352 0.739198 0.548459E-01 4 320 0.737044 0.739198 0.215448E-02 8 1280 0.738656 0.739198 0.542109E-03 16 5120 0.739065 0.739198 0.133553E-03 32 20480 0.739165 0.739198 0.332577E-04 TEST03 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS1M uses midsides of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 60 12.5664 12.5664 0.00000 2 240 12.5664 12.5664 0.390799E-13 4 960 12.5664 12.5664 0.195399E-13 8 3840 12.5664 12.5664 0.781597E-13 16 15360 12.5664 12.5664 0.353495E-12 32 61440 12.5664 12.5664 0.259170E-11 P(X,Y,Z) = X 1 60 0.00000 0.00000 0.00000 2 240 -0.277556E-15 0.00000 0.277556E-15 4 960 -0.222045E-15 0.00000 0.222045E-15 8 3840 0.269489E-14 0.00000 0.269489E-14 16 15360 -0.126609E-13 0.00000 0.126609E-13 32 61440 0.228737E-13 0.00000 0.228737E-13 P(X,Y,Z) = Y 1 60 -0.555112E-16 0.00000 0.555112E-16 2 240 0.00000 0.00000 0.00000 4 960 0.780626E-16 0.00000 0.780626E-16 8 3840 0.276775E-14 0.00000 0.276775E-14 16 15360 -0.924044E-14 0.00000 0.924044E-14 32 61440 -0.268942E-13 0.00000 0.268942E-13 P(X,Y,Z) = Z 1 60 0.00000 0.00000 0.00000 2 240 0.263678E-15 0.00000 0.263678E-15 4 960 0.468375E-15 0.00000 0.468375E-15 8 3840 0.331332E-15 0.00000 0.331332E-15 16 15360 -0.312662E-14 0.00000 0.312662E-14 32 61440 0.495626E-14 0.00000 0.495626E-14 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 0.177636E-14 2 240 4.18879 4.18879 0.266454E-14 4 960 4.18879 4.18879 0.177636E-14 8 3840 4.18879 4.18879 0.115463E-13 16 15360 4.18879 4.18879 0.132339E-12 32 61440 4.18879 4.18879 0.828670E-12 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.333067E-15 2 240 0.837758 0.837758 0.111022E-14 4 960 0.837758 0.837758 0.199840E-14 8 3840 0.837758 0.837758 0.255351E-14 16 15360 0.837758 0.837758 0.340838E-13 32 61440 0.837758 0.837758 0.151767E-12 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.157080 0.119680 0.373999E-01 2 240 0.114761 0.119680 0.491913E-02 4 960 0.118749 0.119680 0.931127E-03 8 3840 0.119455 0.119680 0.224643E-03 16 15360 0.119624 0.119680 0.557779E-04 32 61440 0.119666 0.119680 0.139225E-04 P(X,Y,Z) = Y^2 Z^4 1 60 0.398879 0.359039 0.398402E-01 2 240 0.353799 0.359039 0.524010E-02 4 960 0.358047 0.359039 0.991881E-03 8 3840 0.358800 0.359039 0.239300E-03 16 15360 0.358980 0.359039 0.594173E-04 32 61440 0.359024 0.359039 0.148309E-04 P(X,Y,Z) = Z^6 1 60 1.83260 1.79520 0.373999E-01 2 240 1.79028 1.79520 0.491913E-02 4 960 1.79426 1.79520 0.931127E-03 8 3840 1.79497 1.79520 0.224643E-03 16 15360 1.79514 1.79520 0.557779E-04 32 61440 1.79518 1.79520 0.139225E-04 P(X,Y,Z) = X Y^2 Z^4 1 60 -0.433681E-17 0.00000 0.433681E-17 2 240 0.153313E-17 0.00000 0.153313E-17 4 960 0.200103E-16 0.00000 0.200103E-16 8 3840 -0.104816E-15 0.00000 0.104816E-15 16 15360 0.370733E-16 0.00000 0.370733E-16 32 61440 0.472894E-15 0.00000 0.472894E-15 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.523599E-01 0.398932E-01 0.124666E-01 2 240 0.382535E-01 0.398932E-01 0.163971E-02 4 960 0.395829E-01 0.398932E-01 0.310376E-03 8 3840 0.398184E-01 0.398932E-01 0.748808E-04 16 15360 0.398746E-01 0.398932E-01 0.185926E-04 32 61440 0.398886E-01 0.398932E-01 0.464084E-05 P(X,Y,Z) = X^6 Y^2 1 60 0.124719 0.199466 0.747468E-01 2 240 0.209297 0.199466 0.983129E-02 4 960 0.201327 0.199466 0.186093E-02 8 3840 0.199915 0.199466 0.448966E-03 16 15360 0.199578 0.199466 0.111477E-03 32 61440 0.199494 0.199466 0.278253E-04 P(X,Y,Z) = Z^8 1 60 1.46608 1.39626 0.698132E-01 2 240 1.38708 1.39626 0.918238E-02 4 960 1.39453 1.39626 0.173810E-02 8 3840 1.39584 1.39626 0.419333E-03 16 15360 1.39616 1.39626 0.104119E-03 32 61440 1.39624 1.39626 0.259887E-04 P(X,Y,Z) = X^6 Z^4 1 60 0.604499E-01 0.543999E-01 0.605005E-02 2 240 0.534376E-01 0.543999E-01 0.962232E-03 4 960 0.544116E-01 0.543999E-01 0.117535E-04 8 3840 0.544019E-01 0.543999E-01 0.204057E-05 16 15360 0.544004E-01 0.543999E-01 0.484252E-06 32 61440 0.544000E-01 0.543999E-01 0.119837E-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.623249E-02 0.418461E-02 0.204788E-02 2 240 0.379357E-02 0.418461E-02 0.391039E-03 4 960 0.415299E-02 0.418461E-02 0.316111E-04 8 3840 0.417633E-02 0.418461E-02 0.827905E-05 16 15360 0.418254E-02 0.418461E-02 0.206543E-05 32 61440 0.418409E-02 0.418461E-02 0.516050E-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.377812E-02 0.195282E-02 0.182530E-02 2 240 0.155665E-02 0.195282E-02 0.396162E-03 4 960 0.194661E-02 0.195282E-02 0.621070E-05 8 3840 0.195049E-02 0.195282E-02 0.232510E-05 16 15360 0.195223E-02 0.195282E-02 0.590802E-06 32 61440 0.195267E-02 0.195282E-02 0.148155E-06 P(X,Y,Z) = X^16 1 60 0.950659 0.739198 0.211461 2 240 0.703816 0.739198 0.353820E-01 4 960 0.736920 0.739198 0.227822E-02 8 3840 0.738609 0.739198 0.589261E-03 16 15360 0.739051 0.739198 0.147039E-03 32 61440 0.739162 0.739198 0.367378E-04 TEST04 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS1V uses vertices of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 60 12.5664 12.5664 0.00000 2 240 12.5664 12.5664 0.390799E-13 4 960 12.5664 12.5664 0.195399E-13 8 3840 12.5664 12.5664 0.781597E-13 16 15360 12.5664 12.5664 0.353495E-12 32 61440 12.5664 12.5664 0.259170E-11 P(X,Y,Z) = X 1 60 0.222045E-15 0.00000 0.222045E-15 2 240 0.180411E-14 0.00000 0.180411E-14 4 960 0.860423E-15 0.00000 0.860423E-15 8 3840 0.417635E-14 0.00000 0.417635E-14 16 15360 0.303316E-14 0.00000 0.303316E-14 32 61440 0.433648E-14 0.00000 0.433648E-14 P(X,Y,Z) = Y 1 60 0.166533E-15 0.00000 0.166533E-15 2 240 -0.444089E-15 0.00000 0.444089E-15 4 960 0.182146E-15 0.00000 0.182146E-15 8 3840 0.198799E-14 0.00000 0.198799E-14 16 15360 -0.520330E-14 0.00000 0.520330E-14 32 61440 -0.201578E-13 0.00000 0.201578E-13 P(X,Y,Z) = Z 1 60 0.00000 0.00000 0.00000 2 240 0.208167E-16 0.00000 0.208167E-16 4 960 0.908995E-15 0.00000 0.908995E-15 8 3840 -0.130581E-14 0.00000 0.130581E-14 16 15360 -0.107060E-14 0.00000 0.107060E-14 32 61440 0.388314E-14 0.00000 0.388314E-14 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 0.888178E-15 2 240 4.18879 4.18879 0.444089E-14 4 960 4.18879 4.18879 0.266454E-14 8 3840 4.18879 4.18879 0.142109E-13 16 15360 4.18879 4.18879 0.155431E-12 32 61440 4.18879 4.18879 0.847322E-12 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.111022E-15 2 240 0.837758 0.837758 0.133227E-14 4 960 0.837758 0.837758 0.777156E-15 8 3840 0.837758 0.837758 0.122125E-14 16 15360 0.837758 0.837758 0.318634E-13 32 61440 0.837758 0.837758 0.155764E-12 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.00000 0.119680 0.119680 2 240 0.119708 0.119680 0.278266E-04 4 960 0.118428 0.119680 0.125148E-02 8 3840 0.119317 0.119680 0.362246E-03 16 15360 0.119586 0.119680 0.934031E-04 32 61440 0.119656 0.119680 0.235248E-04 P(X,Y,Z) = Y^2 Z^4 1 60 0.231551 0.359039 0.127489 2 240 0.359069 0.359039 0.296423E-04 4 960 0.357706 0.359039 0.133314E-02 8 3840 0.358653 0.359039 0.385881E-03 16 15360 0.358940 0.359039 0.994975E-04 32 61440 0.359014 0.359039 0.250597E-04 P(X,Y,Z) = Z^6 1 60 1.67552 1.79520 0.119680 2 240 1.79522 1.79520 0.278266E-04 4 960 1.79394 1.79520 0.125148E-02 8 3840 1.79483 1.79520 0.362246E-03 16 15360 1.79510 1.79520 0.934031E-04 32 61440 1.79517 1.79520 0.235248E-04 P(X,Y,Z) = X Y^2 Z^4 1 60 0.00000 0.00000 0.00000 2 240 -0.140946E-17 0.00000 0.140946E-17 4 960 0.437848E-16 0.00000 0.437848E-16 8 3840 -0.493361E-16 0.00000 0.493361E-16 16 15360 -0.874520E-16 0.00000 0.874520E-16 32 61440 0.217735E-15 0.00000 0.217735E-15 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.00000 0.398932E-01 0.398932E-01 2 240 0.399025E-01 0.398932E-01 0.927554E-05 4 960 0.394761E-01 0.398932E-01 0.417161E-03 8 3840 0.397725E-01 0.398932E-01 0.120749E-03 16 15360 0.398621E-01 0.398932E-01 0.311344E-04 32 61440 0.398854E-01 0.398932E-01 0.784158E-05 P(X,Y,Z) = X^6 Y^2 1 60 0.438656 0.199466 0.239190 2 240 0.199411 0.199466 0.556138E-04 4 960 0.201967 0.199466 0.250119E-02 8 3840 0.200190 0.199466 0.723977E-03 16 15360 0.199653 0.199466 0.186674E-03 32 61440 0.199513 0.199466 0.470161E-04 P(X,Y,Z) = Z^8 1 60 1.17286 1.39626 0.223402 2 240 1.39632 1.39626 0.519430E-04 4 960 1.39393 1.39626 0.233610E-02 8 3840 1.39559 1.39626 0.676192E-03 16 15360 1.39609 1.39626 0.174353E-03 32 61440 1.39622 1.39626 0.439129E-04 P(X,Y,Z) = X^6 Z^4 1 60 0.463101E-01 0.543999E-01 0.808975E-02 2 240 0.570858E-01 0.543999E-01 0.268594E-02 4 960 0.544643E-01 0.543999E-01 0.644321E-04 8 3840 0.544212E-01 0.543999E-01 0.212858E-04 16 15360 0.544055E-01 0.543999E-01 0.558033E-05 32 61440 0.544013E-01 0.543999E-01 0.141052E-05 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.00000 0.418461E-02 0.418461E-02 2 240 0.474967E-02 0.418461E-02 0.565062E-03 4 960 0.412851E-02 0.418461E-02 0.560976E-04 8 3840 0.417066E-02 0.418461E-02 0.139433E-04 16 15360 0.418105E-02 0.418461E-02 0.355703E-05 32 61440 0.418371E-02 0.418461E-02 0.893888E-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.00000 0.195282E-02 0.195282E-02 2 240 0.287924E-02 0.195282E-02 0.926421E-03 4 960 0.193413E-02 0.195282E-02 0.186865E-04 8 3840 0.195030E-02 0.195282E-02 0.251926E-05 16 15360 0.195222E-02 0.195282E-02 0.596402E-06 32 61440 0.195267E-02 0.195282E-02 0.147409E-06 P(X,Y,Z) = X^16 1 60 0.314997 0.739198 0.424201 2 240 0.799424 0.739198 0.602253E-01 4 960 0.736166 0.739198 0.303251E-02 8 3840 0.738458 0.739198 0.740636E-03 16 15360 0.739010 0.739198 0.188071E-03 32 61440 0.739151 0.739198 0.472136E-04 TEST05 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS2V uses vertices of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 60 12.5664 12.5664 0.00000 2 240 12.5664 12.5664 0.355271E-13 4 960 12.5664 12.5664 0.301981E-13 8 3840 12.5664 12.5664 0.799361E-13 16 15360 12.5664 12.5664 0.328626E-12 32 61440 12.5664 12.5664 0.148859E-11 P(X,Y,Z) = X 1 60 0.222045E-15 0.00000 0.222045E-15 2 240 -0.804912E-15 0.00000 0.804912E-15 4 960 0.534470E-03 0.00000 0.534470E-03 8 3840 0.173177E-03 0.00000 0.173177E-03 16 15360 0.458415E-04 0.00000 0.458415E-04 32 61440 0.116207E-04 0.00000 0.116207E-04 P(X,Y,Z) = Y 1 60 0.166533E-15 0.00000 0.166533E-15 2 240 -0.169642E-14 0.00000 0.169642E-14 4 960 0.715284E-04 0.00000 0.715284E-04 8 3840 0.231763E-04 0.00000 0.231763E-04 16 15360 0.613500E-05 0.00000 0.613500E-05 32 61440 0.155520E-05 0.00000 0.155520E-05 P(X,Y,Z) = Z 1 60 0.00000 0.00000 0.00000 2 240 0.164452E-14 0.00000 0.164452E-14 4 960 0.715284E-04 0.00000 0.715284E-04 8 3840 0.231763E-04 0.00000 0.231763E-04 16 15360 0.613500E-05 0.00000 0.613500E-05 32 61440 0.155520E-05 0.00000 0.155520E-05 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 0.888178E-15 2 240 4.18879 4.18879 0.355271E-14 4 960 4.18888 4.18879 0.860199E-04 8 3840 4.18882 4.18879 0.264438E-04 16 15360 4.18880 4.18879 0.692668E-05 32 61440 4.18879 4.18879 0.175157E-05 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.111022E-15 2 240 0.837758 0.837758 0.155431E-14 4 960 0.837191 0.837758 0.566911E-03 8 3840 0.837585 0.837758 0.172924E-03 16 15360 0.837713 0.837758 0.450927E-04 32 61440 0.837747 0.837758 0.113882E-04 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.00000 0.119680 0.119680 2 240 0.119708 0.119680 0.278266E-04 4 960 0.120580 0.119680 0.899890E-03 8 3840 0.119930 0.119680 0.250651E-03 16 15360 0.119744 0.119680 0.640413E-04 32 61440 0.119696 0.119680 0.160937E-04 P(X,Y,Z) = Y^2 Z^4 1 60 0.231551 0.359039 0.127489 2 240 0.359069 0.359039 0.296423E-04 4 960 0.359100 0.359039 0.610899E-04 8 3840 0.359051 0.359039 0.118030E-04 16 15360 0.359042 0.359039 0.274873E-05 32 61440 0.359040 0.359039 0.674893E-06 P(X,Y,Z) = Z^6 1 60 1.67552 1.79520 0.119680 2 240 1.79522 1.79520 0.278266E-04 4 960 1.79815 1.79520 0.295262E-02 8 3840 1.79604 1.79520 0.842110E-03 16 15360 1.79541 1.79520 0.216259E-03 32 61440 1.79525 1.79520 0.544132E-04 P(X,Y,Z) = X Y^2 Z^4 1 60 0.00000 0.00000 0.00000 2 240 -0.272135E-16 0.00000 0.272135E-16 4 960 -0.193081E-03 0.00000 0.193081E-03 8 3840 -0.522430E-04 0.00000 0.522430E-04 16 15360 -0.132621E-04 0.00000 0.132621E-04 32 61440 -0.332758E-05 0.00000 0.332758E-05 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.00000 0.398932E-01 0.398932E-01 2 240 0.399025E-01 0.398932E-01 0.927554E-05 4 960 0.403418E-01 0.398932E-01 0.448537E-03 8 3840 0.400148E-01 0.398932E-01 0.121580E-03 16 15360 0.399241E-01 0.398932E-01 0.308818E-04 32 61440 0.399010E-01 0.398932E-01 0.774974E-05 P(X,Y,Z) = X^6 Y^2 1 60 0.438656 0.199466 0.239190 2 240 0.199411 0.199466 0.556138E-04 4 960 0.197658 0.199466 0.180838E-02 8 3840 0.198964 0.199466 0.501827E-03 16 15360 0.199338 0.199466 0.128053E-03 32 61440 0.199434 0.199466 0.321693E-04 P(X,Y,Z) = Z^8 1 60 1.17286 1.39626 0.223402 2 240 1.39632 1.39626 0.519430E-04 4 960 1.40096 1.39626 0.469304E-02 8 3840 1.39759 1.39626 0.132918E-02 16 15360 1.39660 1.39626 0.340760E-03 32 61440 1.39635 1.39626 0.857030E-04 P(X,Y,Z) = X^6 Z^4 1 60 0.463101E-01 0.543999E-01 0.808975E-02 2 240 0.570858E-01 0.543999E-01 0.268594E-02 4 960 0.545543E-01 0.543999E-01 0.154377E-03 8 3840 0.544358E-01 0.543999E-01 0.358900E-04 16 15360 0.544087E-01 0.543999E-01 0.887683E-05 32 61440 0.544021E-01 0.543999E-01 0.221384E-05 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.00000 0.418461E-02 0.418461E-02 2 240 0.474967E-02 0.418461E-02 0.565062E-03 4 960 0.424673E-02 0.418461E-02 0.621264E-04 8 3840 0.419993E-02 0.418461E-02 0.153265E-04 16 15360 0.418846E-02 0.418461E-02 0.385008E-05 32 61440 0.418557E-02 0.418461E-02 0.963891E-06 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.00000 0.195282E-02 0.195282E-02 2 240 0.287924E-02 0.195282E-02 0.926421E-03 4 960 0.197036E-02 0.195282E-02 0.175450E-04 8 3840 0.195619E-02 0.195282E-02 0.337323E-05 16 15360 0.195364E-02 0.195282E-02 0.826031E-06 32 61440 0.195302E-02 0.195282E-02 0.205752E-06 P(X,Y,Z) = X^16 1 60 0.314997 0.739198 0.424201 2 240 0.799424 0.739198 0.602253E-01 4 960 0.741485 0.739198 0.228625E-02 8 3840 0.739758 0.739198 0.559902E-03 16 15360 0.739340 0.739198 0.141507E-03 32 61440 0.739234 0.739198 0.354855E-04 SPHERE_QUAD_PRB Normal end of execution. September 27 2010 11:00:55.873 AM