September 15 2021 3:23:22.558 PM SPHERE_QUAD_TEST 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 0.311161 -0.152656E-14 -0.130451E-14 -0.119349E-14 0.00000 0.100000 0.145479 0.433628E-14 0.427094E-14 0.468434E-14 0.00000 0.100000E-01 0.711183E-02 -0.347458E-12 -0.347318E-12 -0.347532E-12 0.00000 P(X,Y,Z) = Y 1.00000 -0.619719 -0.111022E-15 0.163064E-15 -0.681837E-15 0.00000 0.100000 -0.485973E-01 0.138947E-13 0.134270E-13 0.141040E-13 0.00000 0.100000E-01 0.112379E-01 -0.111674E-12 -0.112036E-12 -0.111636E-12 0.00000 P(X,Y,Z) = Z 1.00000 -3.20909 -0.555112E-15 0.124900E-15 -0.430211E-15 0.00000 0.100000 0.672446E-01 -0.716439E-13 -0.605846E-13 -0.759467E-13 0.00000 0.100000E-01 0.226512E-01 -0.511487E-11 -0.515603E-11 -0.577833E-11 0.00000 P(X,Y,Z) = X^2 1.00000 4.69628 4.20106 4.18085 4.11426 4.18879 0.100000 4.09289 4.18943 4.18879 4.18686 4.18879 0.100000E-01 4.19242 4.18880 4.18879 4.18877 4.18879 P(X,Y,Z) = Y^2 Z^2 1.00000 1.23317 0.863669 0.846232 0.812460 0.837758 0.100000 0.858217 0.838051 0.837759 0.836889 0.837758 0.100000E-01 0.839040 0.837761 0.837758 0.837749 0.837758 P(X,Y,Z) = X^2 Y^2 Z^2 1.00000 0.126669 0.129578 0.124238 0.101557 0.119680 0.100000 0.116243 0.119712 0.119680 0.119584 0.119680 0.100000E-01 0.119885 0.119680 0.119680 0.119679 0.119680 P(X,Y,Z) = Y^2 Z^4 1.00000 0.518178 0.345359 0.349282 0.406230 0.359039 0.100000 0.366843 0.359204 0.359039 0.358553 0.359039 0.100000E-01 0.357762 0.359041 0.359039 0.359034 0.359039 P(X,Y,Z) = Z^6 1.00000 1.56035 1.74619 1.81365 1.90048 1.79520 0.100000 1.77231 1.79299 1.79520 1.80177 1.79520 0.100000E-01 1.79323 1.79517 1.79520 1.79527 1.79520 P(X,Y,Z) = X Y^2 Z^4 1.00000 -0.229178E-01 -0.390313E-17 -0.867362E-17 0.480763E-33 0.00000 0.100000 -0.384251E-02 0.118362E-15 0.118794E-15 0.116380E-15 0.00000 0.100000E-01 0.930555E-04 0.866907E-16 0.899846E-16 0.872371E-16 0.00000 P(X,Y,Z) = X^2 Y^4 Z^2 1.00000 0.427416E-01 0.376728E-01 0.416209E-01 0.380841E-01 0.398932E-01 0.100000 0.426034E-01 0.399019E-01 0.398933E-01 0.398674E-01 0.398932E-01 0.100000E-01 0.398670E-01 0.398933E-01 0.398932E-01 0.398930E-01 0.398932E-01 P(X,Y,Z) = X^6 Y^2 1.00000 0.239782 0.273328 0.239425 0.420696E-01 0.199466 0.100000 0.205425 0.199478 0.199466 0.199429 0.199466 0.100000E-01 0.199064 0.199466 0.199466 0.199466 0.199466 P(X,Y,Z) = Z^8 1.00000 3.41340 1.33672 1.40644 1.49425 1.39626 0.100000 1.38358 1.39385 1.39627 1.40345 1.39626 0.100000E-01 1.39509 1.39624 1.39626 1.39634 1.39626 P(X,Y,Z) = X^6 Z^4 1.00000 0.695369E-01 0.484962E-01 0.490611E-01 0.698208E-01 0.543999E-01 0.100000 0.601256E-01 0.544168E-01 0.544000E-01 0.543492E-01 0.543999E-01 0.100000E-01 0.546740E-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 0.725422E-02 0.440687E-02 0.514531E-02 0.178519E-02 0.418461E-02 0.100000 0.438869E-02 0.418525E-02 0.418461E-02 0.418267E-02 0.418461E-02 0.100000E-01 0.418310E-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 0.211954E-02 0.954775E-03 0.110087E-02 0.476051E-02 0.195282E-02 0.100000 0.203353E-02 0.195367E-02 0.195282E-02 0.195028E-02 0.195282E-02 0.100000E-01 0.194993E-02 0.195282E-02 0.195282E-02 0.195279E-02 0.195282E-02 P(X,Y,Z) = X^16 1.00000 0.175578 0.355946 0.469493 1.66807 0.739198 0.100000 0.687072 0.739219 0.739197 0.739134 0.739198 0.100000E-01 0.742059 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 0.301981E-13 4 320 12.5664 12.5664 0.319744E-13 8 1280 12.5664 12.5664 0.104805E-12 16 5120 12.5664 12.5664 0.428102E-12 32 20480 12.5664 12.5664 0.255795E-11 P(X,Y,Z) = X 1 20 -0.222045E-15 0.00000 0.222045E-15 2 80 0.832667E-15 0.00000 0.832667E-15 4 320 -0.149880E-14 0.00000 0.149880E-14 8 1280 0.338011E-14 0.00000 0.338011E-14 16 5120 0.669018E-14 0.00000 0.669018E-14 32 20480 -0.990164E-14 0.00000 0.990164E-14 P(X,Y,Z) = Y 1 20 0.555112E-16 0.00000 0.555112E-16 2 80 0.319189E-15 0.00000 0.319189E-15 4 320 -0.714706E-15 0.00000 0.714706E-15 8 1280 0.373703E-14 0.00000 0.373703E-14 16 5120 0.736780E-14 0.00000 0.736780E-14 32 20480 -0.127938E-13 0.00000 0.127938E-13 P(X,Y,Z) = Z 1 20 0.00000 0.00000 0.00000 2 80 0.416334E-16 0.00000 0.416334E-16 4 320 0.119696E-15 0.00000 0.119696E-15 8 1280 -0.347628E-14 0.00000 0.347628E-14 16 5120 -0.219341E-14 0.00000 0.219341E-14 32 20480 0.427188E-14 0.00000 0.427188E-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 0.204281E-13 8 1280 4.18879 4.18879 0.586198E-13 16 5120 4.18879 4.18879 0.196287E-12 32 20480 4.18879 4.18879 0.857092E-12 P(X,Y,Z) = Y^2 Z^2 1 20 0.837758 0.837758 0.333067E-15 2 80 0.837758 0.837758 0.777156E-15 4 320 0.837758 0.837758 0.299760E-14 8 1280 0.837758 0.837758 0.843769E-14 16 5120 0.837758 0.837758 0.358602E-13 32 20480 0.837758 0.837758 0.165867E-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 -0.889385E-17 0.00000 0.889385E-17 4 320 0.108560E-16 0.00000 0.108560E-16 8 1280 -0.100625E-16 0.00000 0.100625E-16 16 5120 -0.303687E-15 0.00000 0.303687E-15 32 20480 -0.221950E-15 0.00000 0.221950E-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 0.284217E-13 4 960 12.5664 12.5664 0.00000 8 3840 12.5664 12.5664 0.710543E-13 16 15360 12.5664 12.5664 0.442313E-12 32 61440 12.5664 12.5664 0.262190E-11 P(X,Y,Z) = X 1 60 0.00000 0.00000 0.00000 2 240 0.416334E-15 0.00000 0.416334E-15 4 960 0.105471E-14 0.00000 0.105471E-14 8 3840 -0.628837E-15 0.00000 0.628837E-15 16 15360 0.251145E-14 0.00000 0.251145E-14 32 61440 -0.358302E-14 0.00000 0.358302E-14 P(X,Y,Z) = Y 1 60 -0.555112E-16 0.00000 0.555112E-16 2 240 0.319189E-15 0.00000 0.319189E-15 4 960 0.985323E-15 0.00000 0.985323E-15 8 3840 0.560142E-14 0.00000 0.560142E-14 16 15360 -0.814019E-14 0.00000 0.814019E-14 32 61440 -0.199941E-13 0.00000 0.199941E-13 P(X,Y,Z) = Z 1 60 0.00000 0.00000 0.00000 2 240 0.152656E-15 0.00000 0.152656E-15 4 960 0.549040E-15 0.00000 0.549040E-15 8 3840 -0.242905E-14 0.00000 0.242905E-14 16 15360 -0.492499E-15 0.00000 0.492499E-15 32 61440 0.704743E-14 0.00000 0.704743E-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 0.532907E-14 8 3840 4.18879 4.18879 0.497380E-13 16 15360 4.18879 4.18879 0.166089E-12 32 61440 4.18879 4.18879 0.874856E-12 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.333067E-15 2 240 0.837758 0.837758 0.555112E-15 4 960 0.837758 0.837758 0.199840E-14 8 3840 0.837758 0.837758 0.888178E-14 16 15360 0.837758 0.837758 0.385247E-13 32 61440 0.837758 0.837758 0.159206E-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 0.224955E-16 0.00000 0.224955E-16 4 960 0.598344E-17 0.00000 0.598344E-17 8 3840 -0.198281E-15 0.00000 0.198281E-15 16 15360 -0.684644E-16 0.00000 0.684644E-16 32 61440 0.154639E-15 0.00000 0.154639E-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 0.284217E-13 4 960 12.5664 12.5664 0.00000 8 3840 12.5664 12.5664 0.710543E-13 16 15360 12.5664 12.5664 0.442313E-12 32 61440 12.5664 12.5664 0.262190E-11 P(X,Y,Z) = X 1 60 0.222045E-15 0.00000 0.222045E-15 2 240 0.158207E-14 0.00000 0.158207E-14 4 960 0.250494E-14 0.00000 0.250494E-14 8 3840 0.136870E-14 0.00000 0.136870E-14 16 15360 0.727001E-14 0.00000 0.727001E-14 32 61440 0.471986E-14 0.00000 0.471986E-14 P(X,Y,Z) = Y 1 60 0.166533E-15 0.00000 0.166533E-15 2 240 -0.971445E-16 0.00000 0.971445E-16 4 960 0.228810E-14 0.00000 0.228810E-14 8 3840 0.552596E-14 0.00000 0.552596E-14 16 15360 -0.287173E-14 0.00000 0.287173E-14 32 61440 -0.135778E-13 0.00000 0.135778E-13 P(X,Y,Z) = Z 1 60 0.00000 0.00000 0.00000 2 240 0.152656E-15 0.00000 0.152656E-15 4 960 0.316587E-15 0.00000 0.316587E-15 8 3840 -0.288376E-14 0.00000 0.288376E-14 16 15360 0.138649E-14 0.00000 0.138649E-14 32 61440 0.638383E-14 0.00000 0.638383E-14 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 0.888178E-15 2 240 4.18879 4.18879 0.532907E-14 4 960 4.18879 4.18879 0.355271E-14 8 3840 4.18879 4.18879 0.497380E-13 16 15360 4.18879 4.18879 0.185629E-12 32 61440 4.18879 4.18879 0.877520E-12 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.111022E-15 2 240 0.837758 0.837758 0.777156E-15 4 960 0.837758 0.837758 0.555112E-15 8 3840 0.837758 0.837758 0.732747E-14 16 15360 0.837758 0.837758 0.381917E-13 32 61440 0.837758 0.837758 0.159983E-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 0.346945E-17 0.00000 0.346945E-17 4 960 0.365529E-16 0.00000 0.365529E-16 8 3840 -0.112978E-15 0.00000 0.112978E-15 16 15360 -0.183242E-15 0.00000 0.183242E-15 32 61440 -0.972666E-16 0.00000 0.972666E-16 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 0.195399E-13 4 960 12.5664 12.5664 0.266454E-13 8 3840 12.5664 12.5664 0.692779E-13 16 15360 12.5664 12.5664 0.619949E-12 32 61440 12.5664 12.5664 0.210321E-11 P(X,Y,Z) = X 1 60 0.222045E-15 0.00000 0.222045E-15 2 240 -0.269229E-14 0.00000 0.269229E-14 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 0.133503E-14 0.00000 0.133503E-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 0.492661E-15 0.00000 0.492661E-15 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 0.177636E-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 0.144329E-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 -0.583301E-16 0.00000 0.583301E-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_TEST Normal end of execution. September 15 2021 3:23:33.666 PM