28 September 2010 11:03:04 AM SPHERE_QUAD_PRB C++ 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 12 36 108 108 0.1 1256 3844 11532 11532 0.01 125663 394384 1183152 1183152 P(X,Y,Z) = 1 1 12.5664 12.5664 12.5664 12.5664 12.5664 0.1 12.5664 12.5664 12.5664 12.5664 12.5664 0.01 12.5664 12.5664 12.5664 12.5664 12.5664 P(X,Y,Z) = X 1 -0.198012 -6.38378e-16 -4.16334e-16 -4.44089e-16 0 0.1 0.414551 -3.40666e-15 -3.32411e-15 -3.47445e-15 0 0.01 0.0142957 -1.01395e-13 -1.01604e-13 -1.0124e-13 0 P(X,Y,Z) = Y 1 -0.101428 7.77156e-16 3.85109e-16 6.50431e-16 0 0.1 -0.0839451 7.56622e-15 7.52949e-15 7.5709e-15 0 0.01 0.015666 -3.49532e-13 -3.49962e-13 -3.49845e-13 0 P(X,Y,Z) = Z 1 -1.1158 -5.55112e-16 5.68989e-16 1.79023e-15 0 0.1 -0.155357 -5.73478e-15 -3.81748e-15 -3.28562e-14 0 0.01 0.00213517 -4.59566e-12 -4.89151e-12 -4.23805e-12 0 P(X,Y,Z) = X^2 1 4.25476 4.20106 4.18085 4.11426 4.18879 0.1 4.09119 4.18943 4.18879 4.18686 4.18879 0.01 4.18453 4.1888 4.18879 4.18877 4.18879 P(X,Y,Z) = Y^2 Z^2 1 0.697976 0.863669 0.846232 0.81246 0.837758 0.1 0.770252 0.838051 0.837759 0.836889 0.837758 0.01 0.839144 0.837761 0.837758 0.837749 0.837758 P(X,Y,Z) = X^2 Y^2 Z^2 1 0.102371 0.129578 0.124238 0.101557 0.11968 0.1 0.119828 0.119712 0.11968 0.119584 0.11968 0.01 0.119617 0.11968 0.11968 0.119679 0.11968 P(X,Y,Z) = Y^2 Z^4 1 0.482055 0.345359 0.349282 0.40623 0.359039 0.1 0.379075 0.359204 0.359039 0.358553 0.359039 0.01 0.360982 0.359041 0.359039 0.359034 0.359039 P(X,Y,Z) = Z^6 1 2.46529 1.74619 1.81365 1.90048 1.7952 0.1 1.79472 1.79299 1.7952 1.80177 1.7952 0.01 1.79991 1.79517 1.7952 1.79527 1.7952 P(X,Y,Z) = X Y^2 Z^4 1 -0.0788419 3.03577e-18 4.33681e-18 1.73472e-18 0 0.1 -0.00220976 7.61654e-17 7.6227e-17 7.0445e-17 0 0.01 -0.000587485 5.08682e-15 5.08682e-15 5.09027e-15 0 P(X,Y,Z) = X^2 Y^4 Z^2 1 0.0352219 0.0376728 0.0416209 0.0380841 0.0398932 0.1 0.0412826 0.0399019 0.0398933 0.0398674 0.0398932 0.01 0.0401128 0.0398933 0.0398932 0.039893 0.0398932 P(X,Y,Z) = X^6 Y^2 1 0.365675 0.273328 0.239425 0.0420696 0.199466 0.1 0.203432 0.199478 0.199466 0.199429 0.199466 0.01 0.199655 0.199466 0.199466 0.199466 0.199466 P(X,Y,Z) = Z^8 1 1.87371 1.33672 1.40644 1.49425 1.39626 0.1 1.45368 1.39385 1.39627 1.40345 1.39626 0.01 1.39174 1.39624 1.39626 1.39634 1.39626 P(X,Y,Z) = X^6 Z^4 1 0.0686874 0.0484962 0.0490611 0.0698208 0.0543999 0.1 0.0532922 0.0544168 0.0544 0.0543492 0.0543999 0.01 0.0542201 0.0544 0.0543999 0.0543994 0.0543999 P(X,Y,Z) = X^4 Y^6 Z^2 1 0.00554309 0.00440687 0.00514531 0.00178519 0.00418461 0.1 0.00402901 0.00418525 0.00418461 0.00418267 0.00418461 0.01 0.00421139 0.00418461 0.00418461 0.00418458 0.00418461 P(X,Y,Z) = X^2 Y^4 Z^8 1 0.00123478 0.000954775 0.00110087 0.00476051 0.00195282 0.1 0.00193823 0.00195367 0.00195282 0.00195028 0.00195282 0.01 0.00194922 0.00195282 0.00195282 0.00195279 0.00195282 P(X,Y,Z) = X^16 1 1.12438 0.355946 0.469493 1.66807 0.739198 0.1 0.741514 0.739219 0.739197 0.739134 0.739198 0.01 0.741946 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 2 80 12.5664 12.5664 3.55271e-14 4 320 12.5664 12.5664 3.73035e-14 8 1280 12.5664 12.5664 2.13163e-14 16 5120 12.5664 12.5664 3.05533e-13 32 20480 12.5664 12.5664 2.49578e-12 P(X,Y,Z) = X 1 20 -2.22045e-16 0 2.22045e-16 2 80 5.27356e-16 0 5.27356e-16 4 320 -1.60288e-15 0 1.60288e-15 8 1280 6.24934e-15 0 6.24934e-15 16 5120 -1.02624e-14 0 1.02624e-14 32 20480 7.60747e-15 0 7.60747e-15 P(X,Y,Z) = Y 1 20 5.55112e-17 0 5.55112e-17 2 80 -9.71445e-17 0 9.71445e-17 4 320 -1.15359e-15 0 1.15359e-15 8 1280 7.10803e-15 0 7.10803e-15 16 5120 1.0459e-14 0 1.0459e-14 32 20480 1.40228e-14 0 1.40228e-14 P(X,Y,Z) = Z 1 20 0 0 0 2 80 1.38778e-17 0 1.38778e-17 4 320 -8.67362e-17 0 8.67362e-17 8 1280 -1.43722e-15 0 1.43722e-15 16 5120 1.55152e-15 0 1.55152e-15 32 20480 -2.21572e-15 0 2.21572e-15 P(X,Y,Z) = X^2 1 20 4.18879 4.18879 8.88178e-16 2 80 4.18879 4.18879 5.32907e-15 4 320 4.18879 4.18879 2.13163e-14 8 1280 4.18879 4.18879 1.06581e-14 16 5120 4.18879 4.18879 1.51879e-13 32 20480 4.18879 4.18879 8.45546e-13 P(X,Y,Z) = Y^2 Z^2 1 20 0.837758 0.837758 3.33067e-16 2 80 0.837758 0.837758 1.33227e-15 4 320 0.837758 0.837758 2.33147e-15 8 1280 0.837758 0.837758 3.10862e-15 16 5120 0.837758 0.837758 2.32037e-14 32 20480 0.837758 0.837758 1.74194e-13 P(X,Y,Z) = X^2 Y^2 Z^2 1 20 0.186168 0.11968 0.0664887 2 80 0.113393 0.11968 0.00628634 4 320 0.118875 0.11968 0.000805184 8 1280 0.119502 0.11968 0.000177788 16 5120 0.119637 0.11968 4.31778e-05 32 20480 0.119669 0.11968 1.07182e-05 P(X,Y,Z) = Y^2 Z^4 1 20 0.429866 0.359039 0.070827 2 80 0.352343 0.359039 0.00669651 4 320 0.358181 0.359039 0.00085772 8 1280 0.35885 0.359039 0.000189388 16 5120 0.358993 0.359039 4.59951e-05 32 20480 0.359028 0.359039 1.14175e-05 P(X,Y,Z) = Z^6 1 20 1.86168 1.7952 0.0664887 2 80 1.78891 1.7952 0.00628634 4 320 1.79439 1.7952 0.000805184 8 1280 1.79502 1.7952 0.000177788 16 5120 1.79515 1.7952 4.31778e-05 32 20480 1.79519 1.7952 1.07182e-05 P(X,Y,Z) = X Y^2 Z^4 1 20 3.46945e-18 0 3.46945e-18 2 80 -2.19009e-17 0 2.19009e-17 4 320 4.75054e-17 0 4.75054e-17 8 1280 4.77429e-17 0 4.77429e-17 16 5120 -3.26402e-16 0 3.26402e-16 32 20480 4.25669e-16 0 4.25669e-16 P(X,Y,Z) = X^2 Y^4 Z^2 1 20 0.0620562 0.0398932 0.0221629 2 80 0.0377978 0.0398932 0.00209545 4 320 0.0396248 0.0398932 0.000268395 8 1280 0.039834 0.0398932 5.92626e-05 16 5120 0.0398788 0.0398932 1.43926e-05 32 20480 0.0398897 0.0398932 3.57273e-06 P(X,Y,Z) = X^6 Y^2 1 20 0.0665831 0.199466 0.132883 2 80 0.21203 0.199466 0.0125638 4 320 0.201075 0.199466 0.00160923 8 1280 0.199822 0.199466 0.000355323 16 5120 0.199552 0.199466 8.62944e-05 32 20480 0.199488 0.199466 2.14212e-05 P(X,Y,Z) = Z^8 1 20 1.52038 1.39626 0.124112 2 80 1.38453 1.39626 0.0117345 4 320 1.39476 1.39626 0.00150301 8 1280 1.39593 1.39626 0.000331871 16 5120 1.39618 1.39626 8.05986e-05 32 20480 1.39624 1.39626 2.00073e-05 P(X,Y,Z) = X^6 Z^4 1 20 0.0477629 0.0543999 0.00663697 2 80 0.052475 0.0543999 0.00192484 4 320 0.0543862 0.0543999 1.36573e-05 8 1280 0.0543951 0.0543999 4.80599e-06 16 5120 0.0543986 0.0543999 1.24051e-06 32 20480 0.0543996 0.0543999 3.12007e-07 P(X,Y,Z) = X^4 Y^6 Z^2 1 20 0.00689513 0.00418461 0.00271052 2 80 0.00367262 0.00418461 0.00051199 4 320 0.00416014 0.00418461 2.44658e-05 8 1280 0.00417824 0.00418461 6.36252e-06 16 5120 0.00418304 0.00418461 1.5663e-06 32 20480 0.00418422 0.00418461 3.89982e-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 20 0.00229838 0.00195282 0.00034556 2 80 0.001359 0.00195282 0.000593812 4 320 0.00194819 0.00195282 4.62689e-06 8 1280 0.00195051 0.00195282 2.30393e-06 16 5120 0.00195222 0.00195282 5.91288e-07 32 20480 0.00195267 0.00195282 1.48545e-07 P(X,Y,Z) = X^16 1 20 0.846185 0.739198 0.106987 2 80 0.684352 0.739198 0.0548459 4 320 0.737044 0.739198 0.00215448 8 1280 0.738656 0.739198 0.000542109 16 5120 0.739065 0.739198 0.000133553 32 20480 0.739165 0.739198 3.32577e-05 TEST03 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS1M uses midpoints of sides of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 60 12.5664 12.5664 0 2 240 12.5664 12.5664 3.90799e-14 4 960 12.5664 12.5664 1.95399e-14 8 3840 12.5664 12.5664 7.81597e-14 16 15360 12.5664 12.5664 3.53495e-13 32 61440 12.5664 12.5664 2.5917e-12 P(X,Y,Z) = X 1 60 0 0 0 2 240 -2.77556e-16 0 2.77556e-16 4 960 -2.22045e-16 0 2.22045e-16 8 3840 2.69489e-15 0 2.69489e-15 16 15360 -1.26609e-14 0 1.26609e-14 32 61440 2.28737e-14 0 2.28737e-14 P(X,Y,Z) = Y 1 60 -5.55112e-17 0 5.55112e-17 2 240 0 0 0 4 960 7.80626e-17 0 7.80626e-17 8 3840 2.76775e-15 0 2.76775e-15 16 15360 -9.24044e-15 0 9.24044e-15 32 61440 -2.68942e-14 0 2.68942e-14 P(X,Y,Z) = Z 1 60 0 0 0 2 240 2.63678e-16 0 2.63678e-16 4 960 4.68375e-16 0 4.68375e-16 8 3840 3.31332e-16 0 3.31332e-16 16 15360 -3.12662e-15 0 3.12662e-15 32 61440 4.95626e-15 0 4.95626e-15 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 1.77636e-15 2 240 4.18879 4.18879 2.66454e-15 4 960 4.18879 4.18879 1.77636e-15 8 3840 4.18879 4.18879 1.15463e-14 16 15360 4.18879 4.18879 1.32339e-13 32 61440 4.18879 4.18879 8.2867e-13 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 3.33067e-16 2 240 0.837758 0.837758 1.11022e-15 4 960 0.837758 0.837758 1.9984e-15 8 3840 0.837758 0.837758 2.55351e-15 16 15360 0.837758 0.837758 3.40838e-14 32 61440 0.837758 0.837758 1.51767e-13 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.15708 0.11968 0.0373999 2 240 0.114761 0.11968 0.00491913 4 960 0.118749 0.11968 0.000931127 8 3840 0.119455 0.11968 0.000224643 16 15360 0.119624 0.11968 5.57779e-05 32 61440 0.119666 0.11968 1.39225e-05 P(X,Y,Z) = Y^2 Z^4 1 60 0.398879 0.359039 0.0398402 2 240 0.353799 0.359039 0.0052401 4 960 0.358047 0.359039 0.000991881 8 3840 0.3588 0.359039 0.0002393 16 15360 0.35898 0.359039 5.94173e-05 32 61440 0.359024 0.359039 1.48309e-05 P(X,Y,Z) = Z^6 1 60 1.8326 1.7952 0.0373999 2 240 1.79028 1.7952 0.00491913 4 960 1.79426 1.7952 0.000931127 8 3840 1.79497 1.7952 0.000224643 16 15360 1.79514 1.7952 5.57779e-05 32 61440 1.79518 1.7952 1.39225e-05 P(X,Y,Z) = X Y^2 Z^4 1 60 -4.33681e-18 0 4.33681e-18 2 240 1.53313e-18 0 1.53313e-18 4 960 2.00103e-17 0 2.00103e-17 8 3840 -1.04816e-16 0 1.04816e-16 16 15360 3.70733e-17 0 3.70733e-17 32 61440 4.72894e-16 0 4.72894e-16 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.0523599 0.0398932 0.0124666 2 240 0.0382535 0.0398932 0.00163971 4 960 0.0395829 0.0398932 0.000310376 8 3840 0.0398184 0.0398932 7.48808e-05 16 15360 0.0398746 0.0398932 1.85926e-05 32 61440 0.0398886 0.0398932 4.64084e-06 P(X,Y,Z) = X^6 Y^2 1 60 0.124719 0.199466 0.0747468 2 240 0.209297 0.199466 0.00983129 4 960 0.201327 0.199466 0.00186093 8 3840 0.199915 0.199466 0.000448966 16 15360 0.199578 0.199466 0.000111477 32 61440 0.199494 0.199466 2.78253e-05 P(X,Y,Z) = Z^8 1 60 1.46608 1.39626 0.0698132 2 240 1.38708 1.39626 0.00918238 4 960 1.39453 1.39626 0.0017381 8 3840 1.39584 1.39626 0.000419333 16 15360 1.39616 1.39626 0.000104119 32 61440 1.39624 1.39626 2.59887e-05 P(X,Y,Z) = X^6 Z^4 1 60 0.0604499 0.0543999 0.00605005 2 240 0.0534376 0.0543999 0.000962232 4 960 0.0544116 0.0543999 1.17535e-05 8 3840 0.0544019 0.0543999 2.04057e-06 16 15360 0.0544004 0.0543999 4.84252e-07 32 61440 0.0544 0.0543999 1.19837e-07 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.00623249 0.00418461 0.00204788 2 240 0.00379357 0.00418461 0.000391039 4 960 0.00415299 0.00418461 3.16111e-05 8 3840 0.00417633 0.00418461 8.27905e-06 16 15360 0.00418254 0.00418461 2.06543e-06 32 61440 0.00418409 0.00418461 5.1605e-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.00377812 0.00195282 0.0018253 2 240 0.00155665 0.00195282 0.000396162 4 960 0.00194661 0.00195282 6.2107e-06 8 3840 0.00195049 0.00195282 2.3251e-06 16 15360 0.00195223 0.00195282 5.90802e-07 32 61440 0.00195267 0.00195282 1.48155e-07 P(X,Y,Z) = X^16 1 60 0.950659 0.739198 0.211461 2 240 0.703816 0.739198 0.035382 4 960 0.73692 0.739198 0.00227822 8 3840 0.738609 0.739198 0.000589261 16 15360 0.739051 0.739198 0.000147039 32 61440 0.739162 0.739198 3.67378e-05 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 2 240 12.5664 12.5664 3.90799e-14 4 960 12.5664 12.5664 1.95399e-14 8 3840 12.5664 12.5664 7.81597e-14 16 15360 12.5664 12.5664 3.53495e-13 32 61440 12.5664 12.5664 2.5917e-12 P(X,Y,Z) = X 1 60 2.22045e-16 0 2.22045e-16 2 240 1.80411e-15 0 1.80411e-15 4 960 8.60423e-16 0 8.60423e-16 8 3840 4.17635e-15 0 4.17635e-15 16 15360 3.03316e-15 0 3.03316e-15 32 61440 4.33648e-15 0 4.33648e-15 P(X,Y,Z) = Y 1 60 1.66533e-16 0 1.66533e-16 2 240 -4.44089e-16 0 4.44089e-16 4 960 1.82146e-16 0 1.82146e-16 8 3840 1.98799e-15 0 1.98799e-15 16 15360 -5.2033e-15 0 5.2033e-15 32 61440 -2.01578e-14 0 2.01578e-14 P(X,Y,Z) = Z 1 60 0 0 0 2 240 2.08167e-17 0 2.08167e-17 4 960 9.08995e-16 0 9.08995e-16 8 3840 -1.30581e-15 0 1.30581e-15 16 15360 -1.0706e-15 0 1.0706e-15 32 61440 3.88314e-15 0 3.88314e-15 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 8.88178e-16 2 240 4.18879 4.18879 4.44089e-15 4 960 4.18879 4.18879 2.66454e-15 8 3840 4.18879 4.18879 1.42109e-14 16 15360 4.18879 4.18879 1.55431e-13 32 61440 4.18879 4.18879 8.47322e-13 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 1.11022e-16 2 240 0.837758 0.837758 1.33227e-15 4 960 0.837758 0.837758 7.77156e-16 8 3840 0.837758 0.837758 1.22125e-15 16 15360 0.837758 0.837758 3.18634e-14 32 61440 0.837758 0.837758 1.55764e-13 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0 0.11968 0.11968 2 240 0.119708 0.11968 2.78266e-05 4 960 0.118428 0.11968 0.00125148 8 3840 0.119317 0.11968 0.000362246 16 15360 0.119586 0.11968 9.34031e-05 32 61440 0.119656 0.11968 2.35248e-05 P(X,Y,Z) = Y^2 Z^4 1 60 0.231551 0.359039 0.127489 2 240 0.359069 0.359039 2.96423e-05 4 960 0.357706 0.359039 0.00133314 8 3840 0.358653 0.359039 0.000385881 16 15360 0.35894 0.359039 9.94975e-05 32 61440 0.359014 0.359039 2.50597e-05 P(X,Y,Z) = Z^6 1 60 1.67552 1.7952 0.11968 2 240 1.79522 1.7952 2.78266e-05 4 960 1.79394 1.7952 0.00125148 8 3840 1.79483 1.7952 0.000362246 16 15360 1.7951 1.7952 9.34031e-05 32 61440 1.79517 1.7952 2.35248e-05 P(X,Y,Z) = X Y^2 Z^4 1 60 0 0 0 2 240 -1.40946e-18 0 1.40946e-18 4 960 4.37848e-17 0 4.37848e-17 8 3840 -4.93361e-17 0 4.93361e-17 16 15360 -8.7452e-17 0 8.7452e-17 32 61440 2.17735e-16 0 2.17735e-16 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0 0.0398932 0.0398932 2 240 0.0399025 0.0398932 9.27554e-06 4 960 0.0394761 0.0398932 0.000417161 8 3840 0.0397725 0.0398932 0.000120749 16 15360 0.0398621 0.0398932 3.11344e-05 32 61440 0.0398854 0.0398932 7.84158e-06 P(X,Y,Z) = X^6 Y^2 1 60 0.438656 0.199466 0.23919 2 240 0.199411 0.199466 5.56138e-05 4 960 0.201967 0.199466 0.00250119 8 3840 0.20019 0.199466 0.000723977 16 15360 0.199653 0.199466 0.000186674 32 61440 0.199513 0.199466 4.70161e-05 P(X,Y,Z) = Z^8 1 60 1.17286 1.39626 0.223402 2 240 1.39632 1.39626 5.1943e-05 4 960 1.39393 1.39626 0.0023361 8 3840 1.39559 1.39626 0.000676192 16 15360 1.39609 1.39626 0.000174353 32 61440 1.39622 1.39626 4.39129e-05 P(X,Y,Z) = X^6 Z^4 1 60 0.0463101 0.0543999 0.00808975 2 240 0.0570858 0.0543999 0.00268594 4 960 0.0544643 0.0543999 6.44321e-05 8 3840 0.0544212 0.0543999 2.12858e-05 16 15360 0.0544055 0.0543999 5.58033e-06 32 61440 0.0544013 0.0543999 1.41052e-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0 0.00418461 0.00418461 2 240 0.00474967 0.00418461 0.000565062 4 960 0.00412851 0.00418461 5.60976e-05 8 3840 0.00417066 0.00418461 1.39433e-05 16 15360 0.00418105 0.00418461 3.55703e-06 32 61440 0.00418371 0.00418461 8.93888e-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0 0.00195282 0.00195282 2 240 0.00287924 0.00195282 0.000926421 4 960 0.00193413 0.00195282 1.86865e-05 8 3840 0.0019503 0.00195282 2.51926e-06 16 15360 0.00195222 0.00195282 5.96402e-07 32 61440 0.00195267 0.00195282 1.47409e-07 P(X,Y,Z) = X^16 1 60 0.314997 0.739198 0.424201 2 240 0.799424 0.739198 0.0602253 4 960 0.736166 0.739198 0.00303251 8 3840 0.738458 0.739198 0.000740636 16 15360 0.73901 0.739198 0.000188071 32 61440 0.739151 0.739198 4.72136e-05 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 2 240 12.5664 12.5664 3.55271e-14 4 960 12.5664 12.5664 3.01981e-14 8 3840 12.5664 12.5664 7.99361e-14 16 15360 12.5664 12.5664 3.28626e-13 32 61440 12.5664 12.5664 1.48859e-12 P(X,Y,Z) = X 1 60 2.22045e-16 0 2.22045e-16 2 240 -8.04912e-16 0 8.04912e-16 4 960 0.00053447 0 0.00053447 8 3840 0.000173177 0 0.000173177 16 15360 4.58415e-05 0 4.58415e-05 32 61440 1.16207e-05 0 1.16207e-05 P(X,Y,Z) = Y 1 60 1.66533e-16 0 1.66533e-16 2 240 -1.69642e-15 0 1.69642e-15 4 960 7.15284e-05 0 7.15284e-05 8 3840 2.31763e-05 0 2.31763e-05 16 15360 6.135e-06 0 6.135e-06 32 61440 1.5552e-06 0 1.5552e-06 P(X,Y,Z) = Z 1 60 0 0 0 2 240 1.64452e-15 0 1.64452e-15 4 960 7.15284e-05 0 7.15284e-05 8 3840 2.31763e-05 0 2.31763e-05 16 15360 6.135e-06 0 6.135e-06 32 61440 1.5552e-06 0 1.5552e-06 P(X,Y,Z) = X^2 1 60 4.18879 4.18879 8.88178e-16 2 240 4.18879 4.18879 3.55271e-15 4 960 4.18888 4.18879 8.60199e-05 8 3840 4.18882 4.18879 2.64438e-05 16 15360 4.1888 4.18879 6.92668e-06 32 61440 4.18879 4.18879 1.75157e-06 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 1.11022e-16 2 240 0.837758 0.837758 1.55431e-15 4 960 0.837191 0.837758 0.000566911 8 3840 0.837585 0.837758 0.000172924 16 15360 0.837713 0.837758 4.50927e-05 32 61440 0.837747 0.837758 1.13882e-05 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0 0.11968 0.11968 2 240 0.119708 0.11968 2.78266e-05 4 960 0.12058 0.11968 0.00089989 8 3840 0.11993 0.11968 0.000250651 16 15360 0.119744 0.11968 6.40413e-05 32 61440 0.119696 0.11968 1.60937e-05 P(X,Y,Z) = Y^2 Z^4 1 60 0.231551 0.359039 0.127489 2 240 0.359069 0.359039 2.96423e-05 4 960 0.3591 0.359039 6.10899e-05 8 3840 0.359051 0.359039 1.1803e-05 16 15360 0.359042 0.359039 2.74873e-06 32 61440 0.35904 0.359039 6.74893e-07 P(X,Y,Z) = Z^6 1 60 1.67552 1.7952 0.11968 2 240 1.79522 1.7952 2.78266e-05 4 960 1.79815 1.7952 0.00295262 8 3840 1.79604 1.7952 0.00084211 16 15360 1.79541 1.7952 0.000216259 32 61440 1.79525 1.7952 5.44132e-05 P(X,Y,Z) = X Y^2 Z^4 1 60 0 0 0 2 240 -2.72135e-17 0 2.72135e-17 4 960 -0.000193081 0 0.000193081 8 3840 -5.2243e-05 0 5.2243e-05 16 15360 -1.32621e-05 0 1.32621e-05 32 61440 -3.32758e-06 0 3.32758e-06 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0 0.0398932 0.0398932 2 240 0.0399025 0.0398932 9.27554e-06 4 960 0.0403418 0.0398932 0.000448537 8 3840 0.0400148 0.0398932 0.00012158 16 15360 0.0399241 0.0398932 3.08818e-05 32 61440 0.039901 0.0398932 7.74974e-06 P(X,Y,Z) = X^6 Y^2 1 60 0.438656 0.199466 0.23919 2 240 0.199411 0.199466 5.56138e-05 4 960 0.197658 0.199466 0.00180838 8 3840 0.198964 0.199466 0.000501827 16 15360 0.199338 0.199466 0.000128053 32 61440 0.199434 0.199466 3.21693e-05 P(X,Y,Z) = Z^8 1 60 1.17286 1.39626 0.223402 2 240 1.39632 1.39626 5.1943e-05 4 960 1.40096 1.39626 0.00469304 8 3840 1.39759 1.39626 0.00132918 16 15360 1.3966 1.39626 0.00034076 32 61440 1.39635 1.39626 8.5703e-05 P(X,Y,Z) = X^6 Z^4 1 60 0.0463101 0.0543999 0.00808975 2 240 0.0570858 0.0543999 0.00268594 4 960 0.0545543 0.0543999 0.000154377 8 3840 0.0544358 0.0543999 3.589e-05 16 15360 0.0544087 0.0543999 8.87683e-06 32 61440 0.0544021 0.0543999 2.21384e-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0 0.00418461 0.00418461 2 240 0.00474967 0.00418461 0.000565062 4 960 0.00424673 0.00418461 6.21264e-05 8 3840 0.00419993 0.00418461 1.53265e-05 16 15360 0.00418846 0.00418461 3.85008e-06 32 61440 0.00418557 0.00418461 9.63891e-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0 0.00195282 0.00195282 2 240 0.00287924 0.00195282 0.000926421 4 960 0.00197036 0.00195282 1.7545e-05 8 3840 0.00195619 0.00195282 3.37323e-06 16 15360 0.00195364 0.00195282 8.26031e-07 32 61440 0.00195302 0.00195282 2.05752e-07 P(X,Y,Z) = X^16 1 60 0.314997 0.739198 0.424201 2 240 0.799424 0.739198 0.0602253 4 960 0.741485 0.739198 0.00228625 8 3840 0.739758 0.739198 0.000559902 16 15360 0.73934 0.739198 0.000141507 32 61440 0.739234 0.739198 3.54855e-05 SPHERE_QUAD_PRB Normal end of execution. 28 September 2010 11:04:40 AM