Warning: X does not support locale en_US.UTF-8 10-May-2023 12:24:15 sphere_quad_test MATLAB version Test sphere_quad. SPHERE_QUAD_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_LLV uses vertices of spherical triangles. SPHERE01_QUAD_LLM uses midsides of spherical triangles. H QUAD_MC QUAD_LLC QUAD_LLV QUAD_LLM EXACT Point counts per method: 1.000000 12 36 108 108 0.100000 1256 3844 11532 11532 P(X,Y,Z) = 1 1.000000 12.566371 -143.798474 -138.976527 -135.622631 -122.799427 -134.436096 -144.419243 -98.028851 -90.359161 -85.246033 -143.798474 -138.976527 -135.622631 -122.799427 -134.436096 -144.419243 -98.028851 -90.359161 -85.246033 -143.798474 -138.976527 -135.622631 -122.799427 -134.436096 -144.419243 -98.028851 -90.359161 -85.246033 12.566371 0.100000 12.566371 -13606.916824 -13025.416684 -13170.552026 -13183.442933 -13668.411521 -12948.323500 -13634.041489 -13693.033159 -13105.443680 -13606.916824 -13025.416684 -13170.552026 -13183.442933 -13668.411521 -12948.323500 -13634.041489 -13693.033159 -13105.443680 -13606.916824 -13025.416684 -13170.552026 -13183.442933 -13668.411521 -12948.323500 -13634.041489 -13693.033159 -13105.443680 12.566371 P(X,Y,Z) = X 1.000000 -0.693451 23.183063 31.997184 31.319010 18.007408 13.909442 11.141821 -16.695096 -23.056411 -11.615408 19.830082 27.158368 26.737000 15.515078 12.052857 9.614382 -14.734901 -20.246789 -10.239676 22.354940 30.761155 30.138617 17.404578 13.457841 10.834334 -16.231130 -22.371413 -11.372564 0.000000 0.100000 0.083578 615.305060 448.652577 645.274777 83.435123 162.852500 257.696543 -389.709524 -320.813336 -442.901975 613.972331 447.629229 643.889126 83.290395 162.611645 257.243571 -388.898704 -320.179323 -442.046005 614.967332 448.396035 644.939343 83.405096 162.797168 257.575601 -389.513819 -320.661528 -442.685645 0.000000 P(X,Y,Z) = Y 1.000000 -2.260513 0.958204 -2.992902 0.885180 -20.280026 -23.645025 -21.420519 24.766864 25.103945 22.509283 1.315537 -1.937512 1.398798 -17.330404 -19.980099 -18.320697 20.562496 20.641434 18.551461 1.271613 -2.485857 1.223898 -19.483544 -22.555845 -20.505657 23.523992 23.752983 21.285598 0.000000 0.100000 -0.142523 -192.077840 -95.333199 -246.075069 -417.599286 -521.279807 -603.975992 438.035715 471.399164 549.185788 -191.784181 -95.176243 -245.656862 -416.640576 -520.150636 -602.678605 437.192946 470.456792 548.164599 -192.006996 -95.297366 -245.961288 -417.360864 -520.994368 -603.663259 437.832397 471.170474 548.929004 0.000000 P(X,Y,Z) = Z 1.000000 -0.683498 31.221504 29.924044 21.952344 0.276843 -8.756470 1.152250 0.500570 7.199222 -4.522294 27.788494 26.844328 19.732258 -0.096595 -7.955303 0.761679 0.582336 6.469088 -4.001982 30.204998 29.006313 21.304002 0.057751 -8.612488 0.938954 0.566802 7.032217 -4.343853 0.000000 0.100000 0.311003 -326.702962 -487.144978 -236.151934 442.501149 322.029175 225.837597 -43.337630 223.505973 71.791653 -326.328372 -486.466699 -235.793434 441.883593 321.660482 225.490863 -43.173714 223.206881 71.737237 -326.605451 -486.974233 -236.046518 442.345606 321.932811 225.735258 -43.301538 223.434905 71.777635 0.000000 P(X,Y,Z) = X^2 1.000000 2.761299 -33.524441 -28.073495 -29.139348 -40.780934 -49.404534 -50.796125 -31.270109 -31.768042 -28.450416 -39.596579 -35.725707 -36.195400 -40.187821 -46.549110 -48.779985 -29.423798 -28.966886 -26.016062 -35.339952 -30.574368 -31.432261 -40.945510 -48.933452 -50.557330 -30.489461 -30.620649 -27.323644 4.188790 0.100000 4.039864 -3791.230042 -3666.779912 -3668.200217 -3246.300645 -3531.130130 -3465.354126 -3136.493694 -3299.574628 -3356.287084 -3791.589574 -3666.649247 -3667.926149 -3248.615097 -3532.538585 -3466.646049 -3139.722685 -3301.815172 -3357.907219 -3791.325269 -3666.759280 -3668.137829 -3246.869542 -3531.479591 -3465.673145 -3137.300967 -3300.128235 -3356.685754 4.188790 P(X,Y,Z) = Y^2 Z^2 1.000000 0.490548 -11.908085 -12.329617 -12.050158 -7.624889 -7.867686 -8.141542 -7.857246 -6.739535 -6.771458 -10.431674 -10.731349 -10.493881 -8.371364 -8.929052 -9.424249 -6.661849 -5.760202 -5.584222 -11.222153 -11.494615 -11.204332 -7.732086 -8.045209 -8.480843 -7.535655 -6.549850 -6.554317 0.837758 0.100000 0.872355 -782.487289 -772.514600 -788.769346 -902.357181 -934.742253 -810.979892 -878.384157 -850.946288 -877.142080 -782.709311 -772.445212 -788.783493 -901.788860 -934.285115 -811.351797 -878.404098 -850.915754 -876.160707 -782.544196 -772.485410 -788.782710 -902.219314 -934.628306 -811.065839 -878.384733 -850.942884 -876.886851 0.837758 P(X,Y,Z) = X^2 Y^2 Z^2 1.000000 0.152610 -1.431665 -1.447207 -1.403418 -1.318524 -1.494046 -1.548020 -0.747851 -0.658972 -0.498392 -1.303959 -1.341419 -1.311735 -1.046420 -1.116132 -1.178031 -0.832731 -0.720025 -0.698028 -1.413167 -1.379817 -1.357013 -1.271084 -1.413647 -1.495995 -0.754445 -0.697274 -0.572284 0.119680 0.100000 0.118621 -110.301498 -105.254134 -107.256778 -108.074708 -112.728676 -107.089872 -98.812449 -99.299608 -102.911369 -110.339761 -105.283332 -107.262705 -108.005867 -112.653097 -107.018480 -98.970505 -99.455741 -103.048119 -110.312552 -105.260394 -107.258288 -108.056698 -112.710780 -107.071828 -98.851287 -99.338111 -102.943819 0.119680 P(X,Y,Z) = Y^2 Z^4 1.000000 0.339160 -4.108930 -4.196702 -4.030556 -3.659602 -3.802920 -3.995335 -4.384819 -3.926796 -4.241880 -5.215837 -5.365675 -5.246940 -4.185682 -4.464526 -4.712125 -3.330924 -2.880101 -2.792111 -4.476656 -4.518020 -4.357557 -3.625540 -3.806487 -4.048925 -3.928426 -3.474215 -3.685688 0.359039 0.100000 0.361874 -381.238548 -385.013698 -385.697876 -450.051710 -467.499447 -376.851661 -455.220229 -447.589018 -435.734767 -381.085534 -384.580446 -385.215824 -449.380727 -466.691261 -377.575676 -454.863059 -447.096463 -435.026782 -381.190142 -384.894449 -385.583705 -449.879702 -467.294506 -377.017612 -455.139855 -447.469192 -435.560405 0.359039 P(X,Y,Z) = Z^6 1.000000 0.988299 -22.791396 -22.129420 -19.573866 -21.392953 -22.574437 -26.167307 -22.314652 -19.406994 -21.304090 -24.288637 -23.560794 -21.628537 -22.013814 -23.493228 -26.553982 -20.828330 -18.343925 -19.377718 -24.161283 -23.465071 -21.240961 -22.164823 -23.509897 -26.867287 -21.514316 -18.756840 -20.239426 1.795196 0.100000 1.863719 -3777.895398 -3710.661962 -3681.248181 -3711.255125 -3742.095237 -3498.416007 -4578.145924 -4582.479845 -3760.491420 -3777.361284 -3709.917198 -3679.183186 -3710.634135 -3741.528202 -3496.876363 -4573.715332 -4578.146405 -3760.471959 -3777.774077 -3710.498690 -3680.734873 -3711.118091 -3741.961728 -3498.038628 -4577.029286 -4581.388433 -3760.512271 1.795196 P(X,Y,Z) = X Y^2 Z^4 1.000000 -0.038140 0.522182 0.508259 0.572706 0.331792 0.312977 0.260349 -0.463248 -0.514749 -0.289147 0.327008 0.405317 0.424644 0.110926 0.162808 0.045655 -0.264141 -0.496398 -0.195002 0.326589 0.359410 0.408916 0.257621 0.239776 0.172897 -0.385713 -0.492165 -0.269713 0.000000 0.100000 -0.001434 1.852545 -1.986543 8.972610 -3.043272 0.147952 -6.413058 5.293203 7.598284 -1.618188 1.995354 -1.770802 8.943812 -3.039625 0.104212 -6.154580 5.079304 7.272671 -1.676453 1.889367 -1.932354 8.972000 -3.038681 0.140148 -6.350437 5.233372 7.509295 -1.640653 0.000000 P(X,Y,Z) = X^2 Y^4 Z^2 1.000000 0.006947 -0.435398 -0.475184 -0.450295 -0.321043 -0.357667 -0.360607 -0.227365 -0.178059 -0.135184 -0.488985 -0.503032 -0.491901 -0.392408 -0.418549 -0.441762 -0.312274 -0.270009 -0.261760 -0.481785 -0.497213 -0.479981 -0.350786 -0.378981 -0.398138 -0.257122 -0.222867 -0.185227 0.039893 0.100000 0.040162 -34.912257 -32.590221 -34.445720 -34.258567 -35.615273 -34.364584 -30.498579 -30.346144 -31.707048 -34.878162 -32.597598 -34.437832 -34.285758 -35.646632 -34.379581 -30.562755 -30.353749 -31.755506 -34.906182 -32.592343 -34.444863 -34.265906 -35.623163 -34.368431 -30.513086 -30.348484 -31.718167 0.039893 P(X,Y,Z) = X^6 Y^2 1.000000 0.137858 -1.288602 -1.124329 -1.005987 -1.921144 -2.512258 -2.520793 -2.747554 -2.593755 -2.545008 -0.478473 -0.481770 -0.465461 -0.310758 -0.317420 -0.346519 -0.275066 -0.251944 -0.224107 -1.328574 -1.192349 -1.106289 -1.786045 -2.275834 -2.297203 -2.258382 -2.134490 -2.059262 0.199466 0.100000 0.210578 -161.549342 -160.271287 -165.354255 -145.087233 -173.870431 -166.487557 -123.132495 -125.582035 -125.940812 -161.614571 -160.171227 -165.313861 -145.408190 -173.671173 -166.346525 -123.400626 -125.906611 -126.405374 -161.563099 -160.249236 -165.344759 -145.166606 -173.830214 -166.459900 -123.203361 -125.655037 -126.052900 0.199466 P(X,Y,Z) = Z^8 1.000000 1.790689 -17.259393 -16.755735 -14.652984 -16.378616 -17.242335 -20.118566 -17.645472 -15.332549 -16.949912 -19.116044 -18.547976 -16.687720 -17.670587 -18.751054 -21.484707 -17.742620 -15.536662 -16.754885 -18.570789 -18.034213 -16.133295 -17.237854 -18.233543 -20.992998 -17.368808 -15.119148 -16.470226 1.396263 0.100000 1.465755 -3242.757232 -3188.394593 -3208.600053 -3191.104379 -3218.057679 -3043.999076 -3997.043917 -3999.424410 -3219.436842 -3243.560356 -3188.936536 -3206.440007 -3191.541035 -3218.508135 -3042.264444 -3993.864520 -3996.330918 -3220.747399 -3242.980498 -3188.566270 -3208.067073 -3191.246725 -3218.188978 -3043.579572 -3996.230159 -3998.633406 -3219.786594 1.396263 P(X,Y,Z) = X^6 Z^4 1.000000 0.030963 -0.611400 -0.491828 -0.613605 -0.855589 -0.980219 -1.003241 -0.001119 -0.100241 0.030241 -0.874850 -0.745797 -0.748756 -0.798187 -0.906164 -0.988471 -0.449895 -0.458598 -0.395255 -0.531328 -0.453819 -0.484444 -0.612294 -0.710922 -0.746418 -0.254706 -0.276515 -0.212466 0.054400 0.100000 0.056145 -55.222959 -52.514142 -51.060644 -43.592120 -42.651919 -44.286806 -48.059305 -51.904486 -53.533172 -55.322893 -52.621370 -50.984226 -43.676362 -42.772822 -44.389973 -48.071512 -51.940596 -53.437462 -55.247103 -52.541355 -51.041542 -43.615045 -42.682316 -44.311243 -48.061398 -51.912538 -53.509376 0.054400 P(X,Y,Z) = X^4 Y^6 Z^2 1.000000 0.003646 -0.034514 -0.041485 -0.036728 -0.039128 -0.045443 -0.045915 -0.030268 -0.023655 -0.018836 -0.022921 -0.023580 -0.023058 -0.018394 -0.019619 -0.020708 -0.014638 -0.012657 -0.012270 -0.057579 -0.059701 -0.057374 -0.040533 -0.043840 -0.045739 -0.032657 -0.028365 -0.023815 0.004185 0.100000 0.004073 -3.537492 -3.257826 -3.506645 -3.407732 -3.562323 -3.523040 -2.897075 -2.908704 -2.978308 -3.536201 -3.262696 -3.511235 -3.407660 -3.562678 -3.525203 -2.901754 -2.905675 -2.978078 -3.537502 -3.259125 -3.507883 -3.408106 -3.562752 -3.523863 -2.897802 -2.907739 -2.977946 0.004185 P(X,Y,Z) = X^2 Y^4 Z^8 1.000000 0.001985 -0.016157 -0.016363 -0.015413 -0.009666 -0.010310 -0.011294 -0.005577 -0.004123 -0.003172 -0.061123 -0.062879 -0.061488 -0.049051 -0.052319 -0.055220 -0.039034 -0.033751 -0.032720 -0.014705 -0.013987 -0.013507 -0.014479 -0.015615 -0.017260 -0.008383 -0.007702 -0.007179 0.001953 0.100000 0.001819 -2.074557 -2.016742 -2.008594 -2.132705 -2.194263 -1.885087 -2.036683 -2.031653 -2.076569 -2.070660 -2.010905 -2.002646 -2.126994 -2.192121 -1.881194 -2.040829 -2.037156 -2.077726 -2.073784 -2.015492 -2.007215 -2.130980 -2.193457 -1.883893 -2.037603 -2.032907 -2.076875 0.001953 P(X,Y,Z) = X^16 1.000000 0.064789 -1.861225 -0.573467 -0.778950 -2.013026 -2.776296 -2.817839 -4.016089 -4.415644 -4.464605 -9.847598 -7.792701 -8.692015 -16.350247 -20.553022 -20.588140 -12.803290 -13.190149 -11.934094 -3.159007 -1.992517 -2.508880 -4.661729 -5.822869 -5.859139 -3.463977 -3.962975 -3.566091 0.739198 0.100000 0.743587 -602.511756 -601.003734 -601.896749 -488.485865 -557.290815 -545.021721 -505.947657 -531.364367 -547.467455 -602.337875 -601.914363 -603.076269 -487.867737 -558.329033 -545.824574 -505.418102 -531.358264 -547.892477 -602.481928 -601.202101 -602.169510 -488.349413 -557.459676 -545.130854 -505.788437 -531.461634 -547.660569 0.739198 SPHERE_QUAD_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 -72.854669 -69.364770 -67.358608 -6.746447e+01 -7.291763e+01 -66.926379 -90.123685 -90.519707 -9.655356e+01 1.256637e+01 87.075921 83.828746 82.653282 8.265459e+01 8.705694e+01 81.628436 104.759885 105.720473 1.109029e+02 2 80 -256.660526 -250.555817 -231.396621 -2.848055e+02 -3.373096e+02 -308.772059 -300.245383 -255.658411 -3.031381e+02 1.256637e+01 277.320913 273.787008 251.714399 3.054663e+02 3.576975e+02 330.383972 322.923304 274.699458 3.247827e+02 4 320 -1026.874041 -1009.308283 -948.727962 -1.204047e+03 -1.311810e+03 -1242.939261 -1250.777971 -1162.110392 -1.282610e+03 1.256637e+01 1070.230489 1054.165953 992.703438 1.248299e+03 1.353106e+03 1286.694346 1294.394276 1202.762619 1.321734e+03 8 1280 -4366.532275 -4283.440647 -4242.451216 -4.548457e+03 -4.707287e+03 -4518.195609 -4642.561676 -4605.029792 -4.764338e+03 1.256637e+01 4514.496761 4437.800243 4379.312879 4.683697e+03 4.861983e+03 4668.051734 4792.102071 4732.507118 4.897504e+03 16 5120 -17845.817460 -16936.395383 -17045.515764 -1.755240e+04 -1.824954e+04 -17235.593843 -17497.440628 -17458.593200 -1.846645e+04 1.256637e+01 18696.397449 17777.334945 17808.394073 1.829862e+04 1.913972e+04 18049.316122 18325.089573 18210.517235 1.931123e+04 32 20480 -68396.767428 -63994.466067 -64271.037292 -6.500253e+04 -6.881825e+04 -64879.150451 -65401.062315 -64894.489869 -6.929068e+04 1.256637e+01 73793.678963 68343.440069 68703.261319 6.944174e+04 7.420633e+04 69211.712768 69835.159984 69430.589641 7.458312e+04 P(X,Y,Z) = X 1 20 -9.940986 -10.551992 -10.484870 -4.960486e+00 -2.751590e+00 -4.803522 -3.150275 -6.641215 -5.165714e+00 0 10.384257 10.959221 10.694326 7.331599e+00 3.678732e+00 5.536093 3.708567 7.600969 5.386466e+00 2 80 14.052130 11.680798 24.378208 1.821735e+01 2.367636e+01 28.157118 -21.647695 -23.338400 -3.198669e+01 0 14.471526 11.764520 24.499345 1.854198e+01 2.378254e+01 28.404939 21.699752 23.338413 3.209349e+01 4 320 -0.822343 -14.876591 27.466724 -5.375840e+01 -7.814214e+00 -39.801741 65.234933 78.817861 6.632403e+01 0 10.710196 15.638094 27.473266 5.393828e+01 8.147863e+00 39.923522 65.266788 79.291129 6.769662e+01 8 1280 138.271267 74.851309 183.191174 6.199360e+01 7.394157e+01 57.575137 -52.551072 -4.112572 -1.338357e+01 0 139.281447 79.330451 183.199945 7.295919e+01 7.510087e+01 61.186921 59.503734 4.662256 1.387747e+01 16 5120 133.297112 0.208586 406.440097 5.074540e+02 5.141615e+02 336.231881 -313.260502 -239.386132 -4.225068e+02 0 156.190886 75.539533 416.045749 5.124731e+02 5.256969e+02 336.756660 337.382644 239.798511 4.429080e+02 32 20480 234.176424 -347.699744 826.274375 1.194319e+03 1.741969e+03 1013.205760 -220.244155 -734.083642 -1.190804e+03 0 234.362958 560.615213 836.158836 1.194502e+03 1.746355e+03 1027.416767 261.557413 757.031872 1.302180e+03 P(X,Y,Z) = Y 1 20 0.029905 -0.876387 -1.421410 -8.762558e+00 -7.985186e+00 -7.701058 -5.104699 -4.937162 -3.074441e+00 0 0.361626 1.182237 2.396149 9.000984e+00 8.411993e+00 8.306738 5.512624 6.721051 3.434075e+00 2 80 -6.934266 -4.384533 5.871714 1.623652e+01 1.281061e+01 2.593647 -11.518208 -7.969695 -1.184794e+01 0 7.494240 5.657010 5.898625 1.666108e+01 1.327072e+01 5.697245 11.595390 8.015991 1.234404e+01 4 320 42.033747 18.963096 53.408657 1.725866e+01 2.832797e+00 -20.826170 9.259880 37.706790 3.088121e+01 0 45.336379 18.978074 53.488863 1.771371e+01 1.489631e+01 21.154420 11.665800 38.537800 3.148636e+01 8 1280 -95.416399 -122.442348 -110.960743 1.777870e+02 1.255601e+02 87.664425 223.061065 214.417404 2.052854e+02 0 95.490917 133.101422 113.216706 1.778056e+02 1.256209e+02 90.149255 223.109664 215.449206 2.074270e+02 16 5120 -402.897583 -316.810489 -385.143649 4.569996e+02 2.684395e+02 172.879459 853.973438 760.749042 8.270264e+02 0 441.833810 402.253816 455.841533 4.707277e+02 2.690840e+02 174.149629 854.969838 764.235209 8.287274e+02 32 20480 -656.698527 190.050721 -494.640631 1.133436e+03 8.370496e+02 383.645051 1773.619376 1726.068108 2.427933e+03 0 905.734371 440.615180 945.723503 1.159193e+03 8.494723e+02 430.575554 1841.963911 1744.056156 2.427943e+03 P(X,Y,Z) = Z 1 20 5.675892 3.770861 3.549041 -4.593659e+00 -3.360077e+00 -0.637843 -19.779543 -21.227403 -2.009528e+01 0 6.380026 4.921532 7.432618 5.744429e+00 3.512819e+00 1.452440 20.312813 21.455118 2.049423e+01 2 80 -10.017170 5.427282 -4.462884 2.054035e+01 4.016814e+00 14.836121 -4.637211 2.623608 -8.939326e+00 0 11.067628 5.543238 5.096987 2.083385e+01 4.369175e+00 15.166312 9.418344 2.840307 1.041910e+01 4 320 -11.883280 -3.670267 -29.162443 7.704522e+01 2.514762e+01 61.587278 -8.514897 32.314934 3.081109e+00 0 14.003995 9.340095 29.220011 7.743782e+01 2.838723e+01 61.587359 10.615573 32.414225 6.433511e+00 8 1280 311.401798 251.142067 254.668505 -7.507707e+01 -5.825874e+01 -16.188882 -99.050340 -32.932935 -1.160762e+02 0 318.663466 260.129976 268.796684 7.781504e+01 6.686418e+01 19.811687 99.391920 50.317738 1.217907e+02 16 5120 943.292769 790.656495 819.759048 -6.871693e+02 -6.517018e+02 -493.295285 -349.121406 -28.264144 -3.977086e+02 0 1001.122549 837.465463 918.517290 6.896431e+02 6.517018e+02 495.980135 377.407129 217.484316 4.035942e+02 32 20480 1533.272195 551.119695 992.195469 -1.841569e+03 -1.813316e+03 -885.669700 -1310.920217 -520.413431 -1.363216e+03 0 1653.851785 808.667235 1301.320227 1.938434e+03 1.833359e+03 888.007269 1310.975653 828.998688 1.415236e+03 P(X,Y,Z) = X^2 1 20 -26.679039 -26.064640 -25.893825 -2.556078e+01 -2.936610e+01 -25.690583 -22.705690 -23.616637 -2.462547e+01 4.188790e+00 31.573574 30.982343 30.678437 3.144188e+01 3.414739e+01 30.723077 27.432569 28.330371 2.920790e+01 2 80 -99.160748 -98.957242 -91.052681 -8.606473e+01 -1.130945e+02 -92.106381 -108.106707 -79.773085 -9.681080e+01 4.188790e+00 106.570202 106.798566 97.342623 9.322403e+01 1.198924e+02 99.278439 115.960084 86.135844 1.033587e+02 4 320 -386.883112 -365.270114 -368.518191 -3.728460e+02 -4.330498e+02 -381.853325 -404.449803 -331.820448 -3.792299e+02 4.188790e+00 402.151559 378.385206 381.454516 3.897284e+02 4.457042e+02 394.765685 422.620043 344.175678 3.919829e+02 8 1280 -1571.726787 -1554.439919 -1535.240933 -1.386302e+03 -1.531817e+03 -1463.610589 -1458.590505 -1501.754896 -1.524299e+03 4.188790e+00 1625.681789 1593.920367 1572.471477 1.436562e+03 1.576218e+03 1512.636204 1516.979447 1541.748200 1.565729e+03 16 5120 -6258.123319 -6131.973439 -6080.599771 -5.443868e+03 -6.052177e+03 -5741.474275 -5321.242092 -5785.441615 -5.900203e+03 4.188790e+00 6586.248900 6354.326074 6284.534851 5.708512e+03 6.321660e+03 6018.614957 5610.710271 6035.622489 6.127447e+03 32 20480 -24318.449913 -23930.851887 -23742.795197 -1.992804e+04 -2.280760e+04 -21412.172391 -19770.448622 -21042.148345 -2.212519e+04 4.188790e+00 26394.973866 25153.322050 24963.352579 2.139481e+04 2.446304e+04 22880.189091 21306.138580 22688.973648 2.355724e+04 P(X,Y,Z) = Y^2 Z^2 1 20 -4.334163 -3.879890 -3.868947 -3.690398e+00 -3.769522e+00 -3.611341 -6.223393 -6.201883 -6.311543e+00 8.377580e-01 5.256628 4.826738 4.929380 4.573835e+00 4.648772e+00 4.509682 7.144788 7.112799 7.236774e+00 2 80 -12.907088 -12.622925 -11.262855 -1.849268e+01 -2.017045e+01 -21.860809 -21.248194 -22.132318 -2.392452e+01 8.377580e-01 14.173402 14.358203 12.602403 1.996039e+01 2.145124e+01 23.249249 22.651301 23.324633 2.528319e+01 4 320 -50.778129 -51.598526 -46.940985 -8.863506e+01 -9.394893e+01 -90.932534 -92.004926 -94.060647 -1.021715e+02 8.377580e-01 53.407393 54.700161 49.952804 9.153168e+01 9.693717e+01 93.877410 94.504475 96.815719 1.047020e+02 8 1280 -240.732819 -242.995549 -245.817337 -3.366414e+02 -3.336003e+02 -308.144377 -336.398763 -315.931445 -3.469051e+02 8.377580e-01 251.784627 254.874676 256.536256 3.468431e+02 3.448023e+02 317.665111 347.283039 324.435111 3.551478e+02 16 5120 -1006.362407 -996.429747 -1035.994886 -1.259498e+03 -1.265968e+03 -1162.977082 -1225.593694 -1122.582996 -1.315276e+03 8.377580e-01 1057.898769 1053.927730 1093.038568 1.316811e+03 1.323136e+03 1211.007804 1293.293808 1166.825227 1.377306e+03 32 20480 -3680.561103 -3625.921666 -3709.571080 -4.577944e+03 -4.838120e+03 -4369.142315 -4546.328497 -4314.277329 -5.000286e+03 8.377580e-01 3955.732041 3898.652910 4011.498853 4.916958e+03 5.189358e+03 4620.201390 4869.459546 4546.508310 5.399907e+03 P(X,Y,Z) = X^2 Y^2 Z^2 1 20 -0.594296 -0.589709 -0.593519 -8.250377e-01 -8.400039e-01 -0.830875 -1.257446 -1.259885 -1.255708e+00 1.196797e-01 0.719461 0.715892 0.719292 9.488638e-01 9.630446e-01 0.954858 1.383318 1.385518 1.381490e+00 2 80 -1.791964 -1.761097 -1.878414 -2.651894e+00 -2.792274e+00 -2.685994 -2.670668 -2.620782 -2.690337e+00 1.196797e-01 1.945242 1.928691 2.037312 2.820838e+00 2.946975e+00 2.850014 2.835705 2.775407 2.851465e+00 4 320 -8.417765 -8.198031 -8.075020 -1.087346e+01 -1.184626e+01 -11.221833 -10.726198 -10.334675 -1.057387e+01 1.196797e-01 8.760784 8.522428 8.387591 1.120324e+01 1.216412e+01 11.539828 11.037820 10.644342 1.087228e+01 8 1280 -35.930425 -34.256834 -34.824760 -4.165696e+01 -4.401397e+01 -39.296378 -42.000873 -41.927647 -4.463254e+01 1.196797e-01 36.983521 35.252776 35.834771 4.261148e+01 4.508365e+01 40.281232 42.929287 42.755295 4.543635e+01 16 5120 -149.924942 -142.256821 -145.902106 -1.618436e+02 -1.670662e+02 -153.012220 -154.966309 -155.694282 -1.670712e+02 1.196797e-01 154.629461 146.998557 150.002386 1.659645e+02 1.719322e+02 157.855473 159.555399 159.796063 1.716265e+02 32 20480 -609.490579 -568.876393 -570.135991 -5.913389e+02 -6.297555e+02 -582.165315 -596.614690 -591.641399 -6.386410e+02 1.196797e-01 638.315571 590.178768 591.992957 6.139418e+02 6.585716e+02 604.465893 618.498217 614.308235 6.665863e+02 P(X,Y,Z) = Y^2 Z^4 1 20 -2.820737 -2.431725 -2.416011 -1.885590e+00 -1.930424e+00 -1.807154 -3.396428 -3.373711 -3.476166e+00 3.590392e-01 3.250993 2.885851 2.995226 2.283463e+00 2.326017e+00 2.222342 3.827621 3.794251 3.911561e+00 2 80 -4.495017 -4.353621 -3.589815 -8.586878e+00 -9.244835e+00 -10.288035 -9.443201 -9.444523 -1.043075e+01 3.590392e-01 5.056945 5.158500 4.201995 9.174793e+00 9.752270e+00 10.908979 10.055182 9.931125 1.100815e+01 4 320 -21.525639 -20.223773 -20.688386 -3.693308e+01 -4.028818e+01 -38.325336 -39.006482 -41.507883 -4.358042e+01 3.590392e-01 22.587598 21.398482 21.971757 3.817076e+01 4.159690e+01 39.769570 40.086472 42.628424 4.466473e+01 8 1280 -98.447011 -100.109350 -102.158027 -1.456841e+02 -1.444770e+02 -128.521838 -139.852370 -135.444128 -1.426642e+02 3.590392e-01 102.904644 104.749135 107.007331 1.500963e+02 1.487146e+02 133.107244 144.136757 138.765667 1.464610e+02 16 5120 -418.084722 -428.964387 -431.276847 -5.282186e+02 -5.421651e+02 -459.708475 -514.829917 -488.591259 -5.382777e+02 3.590392e-01 440.393779 452.187407 459.498032 5.536510e+02 5.633995e+02 480.160244 541.958071 506.859440 5.661583e+02 32 20480 -1514.572203 -1564.237215 -1505.152536 -1.882451e+03 -2.085839e+03 -1691.738535 -1964.148294 -1915.241022 -2.075020e+03 3.590392e-01 1631.378787 1682.479662 1636.793755 2.036697e+03 2.225702e+03 1791.132714 2096.947609 2016.567112 2.248497e+03 P(X,Y,Z) = Z^6 1 20 -15.901683 -13.260408 -13.130509 -8.132316e+00 -8.360491e+00 -7.560689 -15.937751 -15.770029 -1.649784e+01 1.795196e+00 18.172993 15.709478 16.567318 1.020792e+01 1.042548e+01 9.790770 18.249791 17.997122 1.884288e+01 2 80 -25.809532 -16.465675 -21.746625 -4.860441e+01 -5.555718e+01 -54.298927 -46.001934 -39.723384 -4.488197e+01 1.795196e+00 29.450797 20.014783 26.658073 5.134573e+01 5.824420e+01 57.741552 49.249454 42.468602 4.875763e+01 4 320 -153.950343 -139.201437 -144.032207 -1.435083e+02 -1.562656e+02 -180.755903 -189.915160 -198.456730 -1.915515e+02 1.795196e+00 159.305961 144.432553 151.944779 1.492849e+02 1.622595e+02 190.630003 194.696579 203.442928 1.977773e+02 8 1280 -639.683188 -621.433065 -586.824570 -6.224206e+02 -6.254232e+02 -597.977453 -722.924323 -728.618795 -7.008925e+02 1.795196e+00 655.483659 639.876130 611.582379 6.400704e+02 6.442230e+02 629.317830 736.564536 742.065132 7.275048e+02 16 5120 -2687.827875 -2557.853911 -2341.267187 -2.437408e+03 -2.479972e+03 -2126.682644 -2816.040589 -2811.582162 -2.667879e+03 1.795196e+00 2800.536903 2681.390800 2493.614703 2.540075e+03 2.576102e+03 2283.614134 2898.581517 2894.562122 2.844146e+03 32 20480 -10079.531969 -9195.408347 -8574.703715 -9.067207e+03 -9.524500e+03 -7976.913097 -11067.251376 -11009.172946 -1.002998e+04 1.795196e+00 10845.030768 9891.356609 9380.008981 9.756950e+03 1.015000e+04 8793.171270 11601.858310 11562.731280 1.109254e+04 P(X,Y,Z) = X Y^2 Z^4 1 20 0.243503 0.249656 0.253418 -3.848373e-01 -3.791088e-01 -0.378737 0.132277 0.135413 1.361587e-01 0 0.244324 0.250965 0.254500 3.854677e-01 3.795382e-01 0.379154 0.132336 0.135533 1.361705e-01 2 80 -0.096131 -0.273642 -0.104161 -2.792304e-01 -3.285576e-01 -0.486116 0.423985 0.575853 5.939763e-01 0 0.100235 0.281617 0.107434 2.810052e-01 3.285734e-01 0.486350 0.425168 0.582555 5.990455e-01 4 320 -0.480743 -1.569038 0.400423 -1.616671e+00 -2.356702e-01 -1.761741 3.317067 3.548730 2.527676e+00 0 0.486444 1.574014 0.401761 1.616743e+00 3.836134e-01 1.762155 3.328691 3.587347 2.532537e+00 8 1280 -2.191171 -3.312959 1.056416 -4.847375e-01 -1.871965e-01 -5.259241 2.533051 6.975169 2.558118e+00 0 2.193368 3.316239 1.065540 1.373929e+00 1.154813e+00 5.275467 2.554077 7.055298 2.602684e+00 16 5120 -5.890368 -8.914772 2.820618 2.292648e+00 6.522019e+00 -2.470364 -2.048816 3.407302 -7.974468e+00 0 6.104131 8.965879 3.538648 2.343281e+00 7.215931e+00 3.835158 2.281552 5.303279 8.749208e+00 32 20480 -23.128355 -35.194193 4.794752 1.720757e+01 2.890456e+01 12.851843 1.446902 4.239311 -8.343868e+00 0 24.238134 35.995205 4.989387 2.160690e+01 2.899279e+01 16.711024 8.318749 11.050478 1.900972e+01 P(X,Y,Z) = X^2 Y^4 Z^2 1 20 -0.198099 -0.196570 -0.197840 -2.750126e-01 -2.800013e-01 -0.276958 -0.419149 -0.419962 -4.185694e-01 3.989324e-02 0.239820 0.238631 0.239764 3.162879e-01 3.210149e-01 0.318286 0.461106 0.461839 4.604965e-01 2 80 -0.584232 -0.569650 -0.604982 -8.331459e-01 -8.917151e-01 -0.858740 -0.906704 -0.948067 -9.324806e-01 3.989324e-02 0.635113 0.628404 0.659195 8.942890e-01 9.454301e-01 0.911447 0.962719 1.001207 9.859766e-01 4 320 -2.549936 -2.646464 -2.389766 -3.877952e+00 -4.111741e+00 -3.879707 -3.735983 -3.642546 -3.861253e+00 3.989324e-02 2.668045 2.773545 2.497888 3.994270e+00 4.221468e+00 3.983549 3.827874 3.744960 3.960710e+00 8 1280 -11.555181 -10.835498 -11.436581 -1.395311e+01 -1.485606e+01 -13.067777 -14.496787 -14.155484 -1.514845e+01 3.989324e-02 11.919542 11.215979 11.807263 1.425571e+01 1.523751e+01 13.366108 14.834446 14.446614 1.541239e+01 16 5120 -49.114115 -45.418494 -48.465135 -5.559940e+01 -5.720276e+01 -53.785909 -52.499116 -50.162638 -5.569358e+01 3.989324e-02 50.540048 46.924267 49.857143 5.698541e+01 5.904500e+01 55.448920 54.183996 51.501719 5.720617e+01 32 20480 -197.659873 -178.776636 -186.336920 -2.087200e+02 -2.180201e+02 -208.012939 -199.145918 -187.533111 -2.111759e+02 3.989324e-02 206.367800 184.942619 194.405002 2.165896e+02 2.288846e+02 215.930498 207.060427 193.980309 2.205351e+02 P(X,Y,Z) = X^6 Y^2 1 20 -0.217932 -0.219051 -0.216793 -3.034184e-01 -3.095351e-01 -0.305543 -0.463568 -0.463476 -4.701985e-01 1.994662e-01 0.418720 0.420069 0.417749 5.043336e-01 5.102883e-01 0.506592 0.665426 0.665890 6.719181e-01 2 80 -4.350037 -5.037444 -3.961257 -5.058686e+00 -6.157249e+00 -4.828896 -6.052865 -4.818821 -5.922910e+00 1.994662e-01 4.730042 5.408618 4.266566 5.428958e+00 6.508089e+00 5.156181 6.462378 5.135904 6.266306e+00 4 320 -17.348297 -18.897528 -17.497520 -2.204790e+01 -2.538345e+01 -22.386493 -17.474050 -13.052895 -1.542911e+01 1.994662e-01 18.196190 19.600257 18.192390 2.293351e+01 2.606246e+01 23.023966 18.436421 13.673893 1.599008e+01 8 1280 -71.785268 -76.459053 -76.234192 -7.135484e+01 -9.033949e+01 -85.011915 -68.724613 -67.269147 -6.877840e+01 1.994662e-01 75.282646 78.624944 78.978714 7.390352e+01 9.271846e+01 88.071771 72.359322 69.525845 7.168760e+01 16 5120 -301.819669 -314.268012 -309.842060 -2.600560e+02 -3.481990e+02 -310.717607 -252.524560 -274.167748 -2.685700e+02 1.994662e-01 320.520794 327.065205 325.516542 2.727947e+02 3.663385e+02 331.350576 271.406753 287.913023 2.827738e+02 32 20480 -1197.019275 -1240.894762 -1204.975423 -9.682465e+02 -1.309546e+03 -1121.225554 -863.726505 -958.531168 -9.200620e+02 1.994662e-01 1307.163808 1315.393697 1291.362162 1.032900e+03 1.429741e+03 1224.125322 953.063346 1050.676478 9.930991e+02 P(X,Y,Z) = Z^8 1 20 -13.521387 -11.220219 -11.104727 -6.623483e+00 -6.808204e+00 -6.121374 -13.215786 -13.066424 -1.370298e+01 1.396263e+00 15.333946 13.191537 13.961027 8.267890e+00 8.445741e+00 7.909712 15.070042 14.844662 1.558695e+01 2 80 -18.743378 -10.731276 -15.423882 -3.848287e+01 -4.417149e+01 -42.613982 -35.790805 -30.917832 -3.479795e+01 1.396263e+00 21.744753 13.541125 19.715036 4.061129e+01 4.627791e+01 45.261909 38.359839 33.102127 3.796622e+01 4 320 -122.061371 -111.110359 -114.861490 -1.081727e+02 -1.167338e+02 -141.558843 -145.849524 -153.016127 -1.463895e+02 1.396263e+00 126.204762 115.139903 121.255404 1.125595e+02 1.213247e+02 149.563251 149.418882 156.723539 1.513589e+02 8 1280 -504.392620 -488.282539 -464.491823 -4.705896e+02 -4.757961e+02 -459.044432 -563.024450 -567.776177 -5.418903e+02 1.396263e+00 515.850185 501.447078 483.899687 4.833010e+02 4.893897e+02 483.967062 572.683056 577.281810 5.631937e+02 16 5120 -2111.977732 -2009.067340 -1844.605929 -1.874923e+03 -1.919549e+03 -1642.491212 -2209.327344 -2213.660502 -2.066431e+03 1.396263e+00 2194.327835 2098.371182 1965.221190 1.948650e+03 1.989997e+03 1768.694008 2266.175656 2271.148250 2.206310e+03 32 20480 -7930.700430 -7229.471605 -6769.040291 -7.087118e+03 -7.464975e+03 -6273.104434 -8725.434560 -8703.843593 -7.732768e+03 1.396263e+00 8501.083686 7746.688512 7423.752422 7.593113e+03 7.936926e+03 6945.676563 9107.114859 9101.766443 8.577642e+03 P(X,Y,Z) = X^6 Z^4 1 20 -0.312062 -0.302167 -0.303137 -2.907760e-01 -3.367709e-01 -0.292222 -0.241553 -0.253589 -2.589625e-01 5.439987e-02 0.374827 0.365215 0.364460 3.648103e-01 3.973792e-01 0.355668 0.301129 0.311977 3.171315e-01 2 80 -1.604734 -1.304154 -1.425417 -9.452241e-01 -1.277988e+00 -1.246857 -1.340980 -0.836408 -9.374998e-01 5.439987e-02 1.688750 1.399204 1.495662 1.018855e+00 1.354884e+00 1.373217 1.431834 0.909155 1.010714e+00 4 320 -5.333754 -4.366097 -5.086300 -3.654024e+00 -4.452201e+00 -3.831147 -5.893877 -5.149894 -5.852342e+00 5.439987e-02 5.509924 4.548589 5.292114 3.858515e+00 4.615998e+00 4.046495 6.113083 5.341901 6.039381e+00 8 1280 -20.212181 -20.622847 -19.035048 -1.703469e+01 -1.603470e+01 -16.462589 -21.012365 -22.650923 -2.239488e+01 5.439987e-02 20.857645 21.402862 19.498990 1.779422e+01 1.685444e+01 17.265612 21.665311 23.304820 2.290045e+01 16 5120 -82.940434 -77.073924 -74.337406 -6.692222e+01 -6.057359e+01 -65.757751 -73.356888 -80.983105 -8.494345e+01 5.439987e-02 87.532188 81.944343 77.171065 7.159778e+01 6.454315e+01 69.498367 76.660425 85.826706 8.818838e+01 32 20480 -322.081335 -291.136468 -288.346740 -2.277288e+02 -2.120515e+02 -242.600600 -266.236167 -285.275300 -3.318350e+02 5.439987e-02 353.147315 314.286847 305.146140 2.519077e+02 2.299002e+02 263.341052 283.986073 315.455032 3.560628e+02 P(X,Y,Z) = X^4 Y^6 Z^2 1 20 -0.022011 -0.021841 -0.021982 -3.055695e-02 -3.111126e-02 -0.030773 -0.046572 -0.046662 -4.650771e-02 4.184606e-03 0.026401 0.026269 0.026395 3.489622e-02 3.542121e-02 0.035118 0.050987 0.051069 5.091940e-02 2 80 -0.052887 -0.052038 -0.053507 -8.356912e-02 -8.560477e-02 -0.084097 -0.091281 -0.092925 -9.218852e-02 4.184606e-03 0.058068 0.057444 0.058758 8.885556e-02 9.060789e-02 0.089059 0.097051 0.098245 9.769053e-02 4 320 -0.274441 -0.295489 -0.254391 -4.211186e-01 -4.439752e-01 -0.413397 -0.361869 -0.339801 -3.693711e-01 4.184606e-03 0.287274 0.309240 0.264876 4.328595e-01 4.545937e-01 0.422567 0.372050 0.349869 3.793825e-01 8 1280 -1.255296 -1.180091 -1.250239 -1.406441e+00 -1.523844e+00 -1.323018 -1.460344 -1.421073 -1.496659e+00 4.184606e-03 1.293223 1.219453 1.290411 1.433548e+00 1.560443e+00 1.352117 1.495726 1.449905 1.525236e+00 16 5120 -5.357672 -4.892192 -5.217758 -5.532873e+00 -5.920779e+00 -5.534530 -5.322934 -5.260256 -5.532948e+00 4.184606e-03 5.502925 5.038056 5.367610 5.666815e+00 6.114910e+00 5.721757 5.472325 5.392721 5.665725e+00 32 20480 -21.883510 -19.384902 -20.303601 -2.103448e+01 -2.282292e+01 -21.678936 -19.948794 -19.073273 -2.055430e+01 4.184606e-03 22.780957 19.943954 21.208295 2.172308e+01 2.397662e+01 22.577362 20.644928 19.719816 2.132808e+01 P(X,Y,Z) = X^2 Y^4 Z^8 1 20 -0.007337 -0.007280 -0.007327 -1.018565e-02 -1.037042e-02 -0.010258 -0.015524 -0.015554 -1.550257e-02 1.952816e-03 0.009354 0.009309 0.009352 1.218766e-02 1.236313e-02 0.012262 0.017551 0.017578 1.752867e-02 2 80 -0.021414 -0.020714 -0.023764 -3.168988e-02 -3.420327e-02 -0.032618 -0.030470 -0.030508 -3.046482e-02 1.952816e-03 0.023693 0.023340 0.026237 3.444537e-02 3.661240e-02 0.035230 0.032862 0.032834 3.279319e-02 4 320 -0.126309 -0.112649 -0.123868 -1.796240e-01 -1.968186e-01 -0.183162 -0.189300 -0.203549 -1.982619e-01 1.952816e-03 0.131625 0.117459 0.129211 1.848762e-01 2.026523e-01 0.189819 0.193926 0.209119 2.034055e-01 8 1280 -0.532036 -0.520641 -0.526986 -7.528609e-01 -7.593290e-01 -0.664115 -0.695024 -0.729486 -7.688001e-01 1.952816e-03 0.547966 0.538347 0.545827 7.707050e-01 7.762777e-01 0.682782 0.709179 0.742842 7.840395e-01 16 5120 -2.217494 -2.171818 -2.232965 -2.841970e+00 -2.904661e+00 -2.425474 -2.668343 -2.586301 -2.777240e+00 1.952816e-03 2.292963 2.255435 2.312324 2.913663e+00 2.970009e+00 2.497287 2.759730 2.659454 2.878214e+00 32 20480 -8.839948 -8.445734 -8.276064 -1.018288e+01 -1.093210e+01 -8.941374 -10.666723 -10.351752 -1.090320e+01 1.952816e-03 9.275954 8.829049 8.614660 1.065808e+01 1.137288e+01 9.217293 11.116429 10.727319 1.147493e+01 P(X,Y,Z) = X^16 1 20 -7.684024 -7.390962 -7.408033 -6.219894e+00 -7.604096e+00 -6.244825 -3.184752 -3.552092 -3.734327e+00 7.391983e-01 8.693616 8.405333 8.362156 7.736198e+00 8.558242e+00 7.314783 4.128254 4.431980 4.600318e+00 2 80 -17.721741 -17.945812 -15.561905 -1.275618e+01 -2.039954e+01 -13.953816 -17.249283 -10.659776 -1.487572e+01 7.391983e-01 19.442160 19.659456 16.812720 1.449455e+01 2.178926e+01 15.135752 18.737643 11.971905 1.604118e+01 4 320 -75.174055 -69.009606 -71.808752 -6.097538e+01 -7.341650e+01 -63.482313 -77.615191 -55.712784 -6.665802e+01 7.391983e-01 77.863258 70.658721 73.385880 6.514270e+01 7.550445e+01 65.409373 81.742402 57.409005 6.888676e+01 8 1280 -327.515301 -300.808331 -300.044794 -2.270332e+02 -2.525285e+02 -242.697592 -244.005242 -246.942993 -2.525910e+02 7.391983e-01 336.550872 303.674195 302.933517 2.370139e+02 2.569479e+02 247.593263 256.716974 251.302511 2.572347e+02 16 5120 -1175.741047 -1172.129035 -1171.077451 -9.914734e+02 -1.077933e+03 -1038.217786 -886.980183 -974.854233 -1.003569e+03 7.391983e-01 1235.037586 1185.563911 1184.615375 1.037759e+03 1.103325e+03 1063.970415 945.067017 998.034597 1.026413e+03 32 20480 -4283.501725 -4667.116228 -4658.345741 -3.728796e+03 -4.223533e+03 -3980.724106 -3640.440802 -3853.686919 -4.036484e+03 7.391983e-01 4656.972859 4765.244081 4759.620804 4.019815e+03 4.404014e+03 4142.568290 3993.970342 4030.687106 4.208216e+03 SPHERE_QUAD_TEST03 Approximate the integral of a function on the unit sphere. SPHERE01_QUAD_ICOS1M uses midpoints of spherical triangles. FACTOR N QUAD EXACT ERROR P(X,Y,Z) = 1 1 60 -72.854669 -69.364770 -67.358608 -6.746447e+01 -7.291763e+01 -66.926379 -90.123685 -90.519707 -9.655356e+01 1.256637e+01 87.075921 83.828746 82.653282 8.265459e+01 8.705694e+01 81.628436 104.759885 105.720473 1.109029e+02 2 240 -256.660526 -250.555817 -231.396621 -2.848055e+02 -3.373096e+02 -308.772059 -300.245383 -255.658411 -3.031381e+02 1.256637e+01 277.320913 273.787008 251.714399 3.054663e+02 3.576975e+02 330.383972 322.923304 274.699458 3.247827e+02 4 960 -1026.874041 -1009.308283 -948.727962 -1.204047e+03 -1.311810e+03 -1242.939261 -1250.777971 -1162.110392 -1.282610e+03 1.256637e+01 1070.230489 1054.165953 992.703438 1.248299e+03 1.353106e+03 1286.694346 1294.394276 1202.762619 1.321734e+03 8 3840 -4366.532275 -4283.440647 -4242.451216 -4.548457e+03 -4.707287e+03 -4518.195609 -4642.561676 -4605.029792 -4.764338e+03 1.256637e+01 4514.496761 4437.800243 4379.312879 4.683697e+03 4.861983e+03 4668.051734 4792.102071 4732.507118 4.897504e+03 16 15360 -17845.817460 -16936.395383 -17045.515764 -1.755240e+04 -1.824954e+04 -17235.593843 -17497.440628 -17458.593200 -1.846645e+04 1.256637e+01 18696.397449 17777.334945 17808.394073 1.829862e+04 1.913972e+04 18049.316122 18325.089573 18210.517235 1.931123e+04 32 61440 -68396.767428 -63994.466067 -64271.037292 -6.500253e+04 -6.881825e+04 -64879.150451 -65401.062315 -64894.489869 -6.929068e+04 1.256637e+01 73793.678963 68343.440069 68703.261319 6.944174e+04 7.420633e+04 69211.712768 69835.159984 69430.589641 7.458312e+04 P(X,Y,Z) = X 1 60 -9.286594 -9.857379 -9.794676 -4.633949e+00 -2.570460e+00 -4.487318 -2.942900 -6.204040 -4.825667e+00 0 9.700686 10.237801 9.990343 6.848977e+00 3.436570e+00 5.171665 3.464441 7.100615 5.031887e+00 2 240 13.990915 11.658725 24.167873 1.786244e+01 2.326227e+01 27.656965 -21.317284 -22.896455 -3.147203e+01 0 14.399873 11.741531 24.286817 1.818488e+01 2.336418e+01 27.900408 21.371160 22.896499 3.157947e+01 4 960 -0.846001 -14.850197 27.363857 -5.347833e+01 -7.689659e+00 -39.640153 64.974436 78.510496 6.607934e+01 0 10.674103 15.611581 27.370282 5.365659e+01 8.021110e+00 39.761411 65.006199 78.983123 6.744819e+01 8 3840 138.075196 74.640307 182.915846 6.198576e+01 7.394113e+01 57.529539 -52.512319 -4.085942 -1.331122e+01 0 139.085277 79.134143 182.924470 7.293820e+01 7.510237e+01 61.138928 59.463494 4.634758 1.381128e+01 16 15360 133.288095 0.158091 406.322087 5.073297e+02 5.140797e+02 336.139634 -313.211907 -239.357830 -4.224121e+02 0 156.171520 75.539676 415.923922 5.123465e+02 5.256163e+02 336.664739 337.332972 239.769856 4.428033e+02 32 61440 234.180128 -347.696127 826.219893 1.194245e+03 1.741873e+03 1013.131522 -220.237090 -734.054304 -1.190736e+03 0 234.367006 560.601508 836.101224 1.194429e+03 1.746257e+03 1027.343907 261.548604 757.001625 1.302102e+03 P(X,Y,Z) = Y 1 60 0.027937 -0.818696 -1.327842 -8.185739e+00 -7.459540e+00 -7.194115 -4.768668 -4.612161 -2.872058e+00 0 0.337821 1.104414 2.238416 8.408471e+00 7.858251e+00 7.759925 5.149741 6.278620 3.208018e+00 2 240 -6.783120 -4.222781 5.907504 1.599470e+01 1.264484e+01 2.575935 -11.403907 -8.034466 -1.176403e+01 0 7.341673 5.511448 5.933643 1.640915e+01 1.309772e+01 5.651960 11.478583 8.078632 1.224235e+01 4 960 41.912352 18.909780 53.233839 1.720201e+01 2.844188e+00 -20.755967 9.221223 37.570130 3.078843e+01 0 45.201531 18.924355 53.313549 1.765442e+01 1.483592e+01 21.084684 11.627261 38.400347 3.138695e+01 8 3840 -95.289747 -122.335323 -110.832907 1.775550e+02 1.254144e+02 87.473910 222.840492 214.235885 2.051309e+02 0 95.363710 132.988636 113.088362 1.775736e+02 1.254748e+02 89.966420 222.889094 215.267253 2.072687e+02 16 15360 -402.832818 -316.784611 -385.089008 4.568813e+02 2.684011e+02 172.790112 853.769132 760.570665 8.268738e+02 0 441.753041 402.212266 455.767001 4.706064e+02 2.690447e+02 174.057529 854.764899 764.055552 8.285752e+02 32 61440 -656.675769 190.017420 -494.626768 1.133376e+03 8.370145e+02 383.610420 1773.501297 1725.964307 2.427806e+03 0 905.693281 440.588733 945.685211 1.159129e+03 8.494389e+02 430.545479 1841.841259 1743.951076 2.427816e+03 P(X,Y,Z) = Z 1 60 5.302261 3.522634 3.315416 -4.291269e+00 -3.138891e+00 -0.595856 -18.477503 -19.830053 -1.877246e+01 0 5.960044 4.597559 6.943346 5.366287e+00 3.281579e+00 1.356830 18.975668 20.042778 1.914514e+01 2 240 -9.819456 5.403248 -4.371768 2.035986e+01 4.066505e+00 14.717027 -4.544474 2.578195 -8.793903e+00 0 10.841431 5.520576 4.990165 2.064736e+01 4.409365e+00 15.036809 9.288500 2.787852 1.026543e+01 4 960 -11.819153 -3.649124 -29.032336 7.675179e+01 2.507642e+01 61.335563 -8.453126 32.201172 3.126464e+00 0 13.926630 9.306493 29.091039 7.714273e+01 2.830295e+01 61.335662 10.555995 32.300633 6.432095e+00 8 3840 311.198392 250.941941 254.507721 -7.498712e+01 -5.817272e+01 -16.193451 -99.081003 -32.980879 -1.160215e+02 0 318.457444 259.923078 268.625068 7.772360e+01 6.677962e+01 19.804611 99.418556 50.316191 1.217278e+02 16 15360 943.116961 790.470384 819.577191 -6.870383e+02 -6.515647e+02 -493.216359 -349.102843 -28.291671 -3.976198e+02 0 1000.937601 837.269016 918.313918 6.895116e+02 6.515647e+02 495.902078 377.366638 217.433278 4.035035e+02 32 61440 1533.196738 551.070741 992.138772 -1.841476e+03 -1.813221e+03 -885.637263 -1310.875231 -520.403569 -1.363143e+03 0 1653.771717 808.603122 1301.243372 1.938337e+03 1.833263e+03 887.975293 1310.930821 828.952449 1.415160e+03 P(X,Y,Z) = X^2 1 60 -26.221797 -25.502568 -25.236661 -2.497396e+01 -2.839968e+01 -25.044719 -24.106654 -24.868836 -2.606912e+01 4.188790e+00 31.086274 30.401826 30.073290 3.068599e+01 3.316792e+01 30.051971 28.862533 29.647539 3.068925e+01 2 240 -98.547253 -98.240366 -90.385162 -8.660994e+01 -1.131935e+02 -92.745790 -107.705635 -79.961936 -9.694125e+01 4.188790e+00 105.934885 106.081995 96.689367 9.376406e+01 1.199941e+02 99.924806 115.539980 86.323948 1.035129e+02 4 960 -386.330367 -364.938647 -367.971902 -3.731443e+02 -4.331232e+02 -382.175515 -404.637079 -332.436635 -3.798315e+02 4.188790e+00 401.590171 378.075172 380.924979 3.900051e+02 4.457925e+02 395.110782 422.758107 344.805547 3.925861e+02 8 3840 -1571.325132 -1554.041897 -1534.875825 -1.386653e+03 -1.531949e+03 -1463.720675 -1458.875563 -1501.892879 -1.524523e+03 4.188790e+00 1625.267975 1593.553823 1572.126718 1.436898e+03 1.576372e+03 1512.748936 1517.237360 1541.894398 1.565958e+03 16 15360 -6257.863749 -6131.597626 -6080.322371 -5.444153e+03 -6.052225e+03 -5741.513555 -5321.597214 -5785.456976 -5.900398e+03 4.188790e+00 6585.955189 6353.985923 6284.287554 5.708781e+03 6.321728e+03 6018.647166 5611.056355 6035.641314 6.127676e+03 32 61440 -24318.153736 -23930.389230 -23742.392246 -1.992835e+04 -2.280762e+04 -21412.241252 -19770.790833 -21042.237579 -2.212539e+04 4.188790e+00 26394.623963 25152.892588 24962.989452 2.139511e+04 2.446308e+04 22880.254457 21306.466227 22689.040282 2.355750e+04 P(X,Y,Z) = Y^2 Z^2 1 60 -4.664156 -4.268730 -4.174546 -4.000678e+00 -4.159535e+00 -3.924323 -6.413579 -6.387213 -6.694112e+00 8.377580e-01 5.600826 5.229569 5.248627 4.927344e+00 5.070865e+00 4.864004 7.373336 7.363321 7.649034e+00 2 240 -13.339716 -13.002144 -11.696984 -1.877191e+01 -2.057726e+01 -21.899554 -20.901859 -21.393023 -2.338369e+01 8.377580e-01 14.615994 14.708613 13.050093 2.022151e+01 2.186715e+01 23.295330 22.314325 22.594118 2.476162e+01 4 960 -51.293249 -52.102972 -47.367310 -8.844027e+01 -9.374337e+01 -90.750246 -91.709460 -93.628265 -1.017449e+02 8.377580e-01 53.930389 55.209773 50.383608 9.133394e+01 9.672644e+01 93.699278 94.214148 96.387300 1.042799e+02 8 3840 -241.102717 -243.282766 -246.066347 -3.364523e+02 -3.334322e+02 -308.118341 -336.225937 -315.869514 -3.466983e+02 8.377580e-01 252.139744 255.160134 256.780268 3.466393e+02 3.446335e+02 317.643912 347.095441 324.375676 3.549486e+02 16 15360 -1006.702417 -996.607635 -1036.135790 -1.259372e+03 -1.265847e+03 -1162.942184 -1225.584537 -1122.699982 -1.315161e+03 8.377580e-01 1058.241271 1054.117281 1093.179848 1.316667e+03 1.323027e+03 1210.986583 1293.250996 1166.955643 1.377191e+03 32 61440 -3680.964190 -3626.126272 -3709.771588 -4.577889e+03 -4.837976e+03 -4369.129837 -4546.337340 -4314.320414 -5.000131e+03 8.377580e-01 3956.165216 3898.880429 4011.716993 4.916879e+03 5.189228e+03 4620.213180 4869.448984 4546.583264 5.399748e+03 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 -0.842476 -0.805478 -0.785116 -8.187758e-01 -8.776842e-01 -0.813992 -1.115617 -1.120085 -1.182350e+00 1.196797e-01 0.980440 0.946167 0.934196 9.656775e-01 1.013997e+00 0.956119 1.257308 1.267219 1.321252e+00 2 240 -1.970354 -1.940583 -1.989663 -2.633679e+00 -2.854479e+00 -2.730074 -2.772778 -2.635385 -2.785796e+00 1.196797e-01 2.131766 2.121115 2.154489 2.809636e+00 3.017193e+00 2.906234 2.949171 2.794538 2.955260e+00 4 960 -8.488507 -8.256533 -8.117726 -1.092087e+01 -1.190590e+01 -11.253724 -10.783222 -10.376365 -1.067505e+01 1.196797e-01 8.835888 8.587556 8.437420 1.125667e+01 1.222831e+01 11.577643 11.101244 10.691291 1.097765e+01 8 3840 -35.987340 -34.335049 -34.890549 -4.168234e+01 -4.402309e+01 -39.348115 -42.024411 -41.948057 -4.463011e+01 1.196797e-01 37.047505 35.340256 35.907087 4.264338e+01 4.510019e+01 40.341304 42.961299 42.782667 4.544125e+01 16 15360 -149.978156 -142.307604 -145.938527 -1.618431e+02 -1.670765e+02 -153.036982 -154.996929 -155.714461 -1.670919e+02 1.196797e-01 154.696915 147.063690 150.052906 1.659773e+02 1.719572e+02 157.893319 159.600248 159.829818 1.716612e+02 32 61440 -609.505566 -568.883897 -570.144340 -5.913378e+02 -6.297600e+02 -582.171362 -596.612245 -591.636824 -6.386410e+02 1.196797e-01 638.352757 590.205302 592.021189 6.139605e+02 6.585980e+02 604.490509 618.515336 614.324022 6.666080e+02 P(X,Y,Z) = Y^2 Z^4 1 60 -2.410711 -2.125117 -2.107233 -1.801037e+00 -1.857926e+00 -1.745929 -3.057794 -3.044229 -3.138351e+00 3.590392e-01 2.826106 2.557300 2.622824 2.196357e+00 2.248079e+00 2.151133 3.474766 3.455899 3.556985e+00 2 240 -4.861528 -4.553855 -4.014267 -8.502098e+00 -9.255653e+00 -10.118044 -9.309973 -9.254429 -1.020431e+01 3.590392e-01 5.431533 5.335942 4.641521 9.093958e+00 9.773111e+00 10.740886 9.922324 9.750238 1.079582e+01 4 960 -21.757189 -20.492378 -20.848844 -3.675933e+01 -4.005932e+01 -38.248465 -38.977179 -41.367314 -4.344891e+01 3.590392e-01 22.822450 21.671111 22.138064 3.799655e+01 4.136244e+01 39.690295 40.055194 42.488139 4.453554e+01 8 3840 -98.660028 -100.288072 -102.271894 -1.455077e+02 -1.443097e+02 -128.483626 -139.911254 -135.473955 -1.427126e+02 3.590392e-01 103.112885 104.927215 107.117192 1.499148e+02 1.485519e+02 133.068918 144.191107 138.795845 1.465115e+02 16 15360 -418.268059 -429.049275 -431.346946 -5.281643e+02 -5.420644e+02 -459.765968 -514.899907 -488.644218 -5.383388e+02 3.590392e-01 440.576023 452.278034 459.554576 5.535874e+02 5.633054e+02 480.229699 542.015745 506.912172 5.662212e+02 32 61440 -1514.774336 -1564.306125 -1505.279764 -1.882450e+03 -2.085721e+03 -1691.826556 -1964.184920 -1915.251733 -2.075034e+03 3.590392e-01 1631.590821 1682.551317 1636.923399 2.036679e+03 2.225584e+03 1791.244283 2096.975658 2016.579280 2.248518e+03 P(X,Y,Z) = Z^6 1 60 -13.777921 -11.694844 -11.599665 -8.096356e+00 -8.339822e+00 -7.660621 -14.949028 -14.831660 -1.540088e+01 1.795196e+00 15.952845 14.001543 14.618843 1.011591e+01 1.034014e+01 9.778158 17.139661 16.960112 1.761400e+01 2 240 -26.530988 -17.590711 -22.583039 -4.795695e+01 -5.478892e+01 -53.817787 -45.755814 -39.613866 -4.479845e+01 1.795196e+00 30.087913 21.118683 27.272838 5.069843e+01 5.746499e+01 57.251367 48.977647 42.335884 4.859453e+01 4 960 -153.604419 -138.893204 -143.653519 -1.438058e+02 -1.566753e+02 -180.539532 -190.093033 -198.516413 -1.917511e+02 1.795196e+00 158.960780 144.130670 151.535498 1.495904e+02 1.626697e+02 190.350220 194.889187 203.515173 1.979604e+02 8 3840 -639.448042 -621.272780 -586.605135 -6.227018e+02 -6.256394e+02 -598.112244 -722.838354 -728.497979 -7.009698e+02 1.795196e+00 655.271963 639.742206 611.345616 6.403748e+02 6.444589e+02 629.418082 736.506513 741.967741 7.275492e+02 16 15360 -2687.565891 -2557.654668 -2341.095483 -2.437518e+03 -2.479998e+03 -2126.841332 -2815.782520 -2811.294420 -2.667929e+03 1.795196e+00 2800.299925 2681.222178 2493.400025 2.540216e+03 2.576148e+03 2283.722695 2898.370631 2894.312468 2.844146e+03 32 61440 -10079.278771 -9195.251697 -8574.552639 -9.067137e+03 -9.524407e+03 -7976.927083 -11066.910157 -11008.823439 -1.003011e+04 1.795196e+00 10844.793501 9891.218807 9379.777277 9.756904e+03 1.014992e+04 8793.096947 11601.556228 11562.421404 1.109260e+04 P(X,Y,Z) = X Y^2 Z^4 1 60 0.094167 0.095071 0.097305 -2.182710e-01 -2.078219e-01 -0.214391 0.050847 0.040147 4.898417e-02 0 0.094168 0.095136 0.097443 2.184454e-01 2.078251e-01 0.214403 0.051509 0.042748 4.918243e-02 2 240 -0.069109 -0.260957 -0.096932 -2.183186e-01 -2.267283e-01 -0.389508 0.315889 0.466806 4.937255e-01 0 0.076577 0.268733 0.099734 2.200425e-01 2.268729e-01 0.389793 0.317426 0.473916 4.989826e-01 4 960 -0.504491 -1.536484 0.355399 -1.571808e+00 -2.448517e-01 -1.689611 3.215989 3.430455 2.435137e+00 0 0.507848 1.541934 0.356337 1.571839e+00 3.731048e-01 1.689871 3.227403 3.467259 2.440023e+00 8 3840 -2.166222 -3.287998 1.016824 -4.934048e-01 -1.706548e-01 -5.178710 2.522458 6.897932 2.554157e+00 0 2.168631 3.291689 1.024751 1.361799e+00 1.142644e+00 5.194272 2.543109 6.976778 2.596438e+00 16 15360 -5.869173 -8.896984 2.816864 2.293745e+00 6.525195e+00 -2.450842 -2.054816 3.384981 -7.967859e+00 0 6.082127 8.948233 3.532189 2.344485e+00 7.218772e+00 3.811996 2.283312 5.277386 8.739114e+00 32 61440 -23.109751 -35.172476 4.799106 1.720636e+01 2.890062e+01 12.851771 1.438889 4.227863 -8.353189e+00 0 24.217145 35.973420 4.992711 2.159939e+01 2.898914e+01 16.705626 8.313750 11.038888 1.900549e+01 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 -0.241156 -0.239340 -0.226050 -2.704061e-01 -2.816755e-01 -0.269715 -0.411810 -0.409138 -4.426686e-01 3.989324e-02 0.285211 0.284047 0.273076 3.168594e-01 3.273928e-01 0.316830 0.459993 0.462588 4.896570e-01 2 240 -0.638489 -0.647917 -0.640276 -8.462800e-01 -9.181345e-01 -0.881796 -0.918412 -0.929561 -9.633140e-01 3.989324e-02 0.691333 0.710444 0.695548 9.087111e-01 9.746225e-01 0.938185 0.978099 0.983891 1.020012e+00 4 960 -2.582718 -2.673163 -2.413304 -3.909217e+00 -4.144448e+00 -3.902956 -3.722141 -3.627887 -3.860054e+00 3.989324e-02 2.702431 2.802083 2.523589 4.026773e+00 4.255505e+00 4.008254 3.816786 3.732691 3.960791e+00 8 3840 -11.581873 -10.866173 -11.463947 -1.397785e+01 -1.486850e+01 -13.104275 -14.481523 -14.139703 -1.513188e+01 3.989324e-02 11.948571 11.249564 11.836451 1.428257e+01 1.525240e+01 13.405395 14.821825 14.433279 1.539816e+01 16 15360 -49.127927 -45.433422 -48.477673 -5.560213e+01 -5.720748e+01 -53.790704 -52.505546 -50.168859 -5.570152e+01 3.989324e-02 50.558429 46.944463 49.874940 5.699193e+01 5.905473e+01 55.457332 54.195189 51.512522 5.721901e+01 32 61440 -197.664164 -178.780465 -186.340480 -2.087188e+02 -2.180220e+02 -208.010446 -199.144593 -187.535965 -2.111761e+02 3.989324e-02 206.378999 184.953504 194.415843 2.165940e+02 2.288943e+02 215.933483 207.065451 193.990322 2.205426e+02 P(X,Y,Z) = X^6 Y^2 1 60 -0.685076 -0.677435 -0.666235 -7.153270e-01 -7.981004e-01 -0.719155 -0.761249 -0.778095 -8.172409e-01 1.994662e-01 0.898656 0.891640 0.878314 9.463326e-01 1.010991e+00 0.936772 0.974136 0.993560 1.027103e+00 2 240 -4.374040 -4.982943 -4.020106 -4.779270e+00 -5.907419e+00 -4.635219 -5.809977 -4.588929 -5.622663e+00 1.994662e-01 4.736886 5.348968 4.320267 5.134285e+00 6.247790e+00 4.956240 6.212936 4.899769 5.955311e+00 4 960 -17.417945 -18.825523 -17.492527 -2.194082e+01 -2.523008e+01 -22.228416 -17.497359 -13.154250 -1.552937e+01 1.994662e-01 18.260007 19.525473 18.182366 2.282155e+01 2.590352e+01 22.861432 18.456645 13.772789 1.609297e+01 8 3840 -71.850863 -76.427687 -76.238693 -7.134128e+01 -9.014754e+01 -84.837014 -68.713394 -67.303310 -6.880870e+01 1.994662e-01 75.331912 78.589792 78.970072 7.388473e+01 9.252092e+01 87.883779 72.336389 69.554650 7.170402e+01 16 15360 -301.818774 -314.183957 -309.801442 -2.601128e+02 -3.480379e+02 -310.626470 -252.524317 -274.166960 -2.685929e+02 1.994662e-01 320.501792 326.968837 325.455411 2.728475e+02 3.661570e+02 331.229857 271.385142 287.903266 2.827808e+02 32 61440 -1197.009338 -1240.800064 -1204.922643 -9.682973e+02 -1.309414e+03 -1121.190308 -863.798711 -958.556742 -9.201482e+02 1.994662e-01 1307.134061 1315.276739 1291.286295 1.032952e+03 1.429572e+03 1224.055562 953.115511 1050.682909 9.931706e+02 P(X,Y,Z) = Z^8 1 60 -11.525892 -9.709396 -9.624102 -6.425212e+00 -6.601578e+00 -6.039228 -12.199853 -12.088570 -1.258429e+01 1.396263e+00 13.250166 11.551774 12.114116 8.010554e+00 8.177184e+00 7.720177 13.943424 13.776569 1.434934e+01 2 240 -19.479420 -11.881097 -16.271086 -3.800264e+01 -4.353072e+01 -42.326692 -35.602781 -30.796702 -3.480496e+01 1.396263e+00 22.391335 14.666017 20.310951 4.013026e+01 4.562639e+01 44.981617 38.147990 32.955770 3.789968e+01 4 960 -121.680400 -110.715533 -114.401491 -1.085841e+02 -1.173080e+02 -141.401786 -146.123468 -153.227524 -1.466817e+02 1.396263e+00 125.824223 114.748089 120.761172 1.129820e+02 1.219070e+02 149.351941 149.709643 156.952433 1.516331e+02 8 3840 -504.149902 -488.093851 -464.167412 -4.710274e+02 -4.761526e+02 -459.241356 -562.914086 -567.657039 -5.419180e+02 1.396263e+00 515.633234 501.292849 483.566756 4.837685e+02 4.897721e+02 484.139569 572.601726 577.190977 5.632026e+02 16 15360 -2111.779433 -2008.905406 -1844.337995 -1.875069e+03 -1.919621e+03 -1642.570870 -2209.111306 -2213.402837 -2.066444e+03 1.396263e+00 2194.174678 2098.264254 1964.930887 1.948841e+03 1.990099e+03 1768.733971 2266.016558 2270.942894 2.206296e+03 32 61440 -7930.484477 -7229.308018 -6768.771404 -7.087027e+03 -7.464875e+03 -6272.945353 -8725.160052 -8703.548580 -7.732870e+03 1.396263e+00 8500.922729 7746.581088 7423.413447 7.593079e+03 7.936858e+03 6945.429961 9106.905219 9101.536595 8.577695e+03 P(X,Y,Z) = X^6 Z^4 1 60 -0.370021 -0.358253 -0.359228 -3.540628e-01 -4.046996e-01 -0.355669 -0.322404 -0.335445 -3.417979e-01 5.439987e-02 0.434025 0.422686 0.421960 4.295833e-01 4.661174e-01 0.420213 0.382888 0.394705 4.007978e-01 2 240 -1.534671 -1.276320 -1.393050 -9.829725e-01 -1.309503e+00 -1.244082 -1.362422 -0.899042 -1.013885e+00 5.439987e-02 1.620042 1.371841 1.466390 1.059451e+00 1.387408e+00 1.363549 1.453958 0.973294 1.089959e+00 4 960 -5.338545 -4.381028 -5.073364 -3.680748e+00 -4.480214e+00 -3.875138 -5.877518 -5.144429 -5.820883e+00 5.439987e-02 5.515279 4.562515 5.276998 3.884058e+00 4.643954e+00 4.088548 6.095855 5.335039 6.006675e+00 8 3840 -20.220674 -20.614471 -19.027001 -1.704755e+01 -1.606810e+01 -16.478955 -21.003953 -22.632269 -2.238195e+01 5.439987e-02 20.865587 21.390983 19.491030 1.780591e+01 1.688496e+01 17.280141 21.655780 23.284424 2.288831e+01 16 15360 -82.941491 -77.083254 -74.336947 -6.693983e+01 -6.061683e+01 -65.765561 -73.355984 -80.977799 -8.492987e+01 5.439987e-02 87.532186 81.948006 77.168678 7.161097e+01 6.458265e+01 69.505007 76.659079 85.816154 8.817556e+01 32 61440 -322.084646 -291.150667 -288.351766 -2.277519e+02 -2.121000e+02 -242.603647 -266.248747 -285.283497 -3.318131e+02 5.439987e-02 353.147881 314.295539 305.147346 2.519276e+02 2.299474e+02 263.340014 283.999590 315.455014 3.560389e+02 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 -0.025079 -0.026341 -0.024211 -3.323215e-02 -3.445626e-02 -0.033391 -0.050518 -0.050050 -5.510838e-02 4.184606e-03 0.029613 0.030914 0.028853 3.819839e-02 3.940951e-02 0.038474 0.055747 0.056266 6.013970e-02 2 240 -0.062035 -0.065296 -0.062487 -8.419499e-02 -9.078258e-02 -0.084558 -0.096044 -0.093948 -9.741801e-02 4.184606e-03 0.067389 0.071214 0.067953 9.003530e-02 9.632076e-02 0.090082 0.102334 0.099457 1.031880e-01 4 960 -0.277824 -0.297004 -0.257651 -4.242010e-01 -4.476567e-01 -0.415394 -0.359819 -0.338798 -3.681111e-01 4.184606e-03 0.290810 0.310894 0.268494 4.361479e-01 4.584662e-01 0.424891 0.370206 0.349151 3.782407e-01 8 3840 -1.257640 -1.181616 -1.252263 -1.410009e+00 -1.527176e+00 -1.329269 -1.457504 -1.419022 -1.494175e+00 4.184606e-03 1.295785 1.221221 1.292608 1.437389e+00 1.564040e+00 1.358746 1.493109 1.448136 1.522982e+00 16 15360 -5.358476 -4.893193 -5.218530 -5.534795e+00 -5.922265e+00 -5.536054 -5.323295 -5.259629 -5.533535e+00 4.184606e-03 5.504183 5.039570 5.368936 5.669058e+00 6.116928e+00 5.723668 5.473233 5.392633 5.666875e+00 32 61440 -21.883727 -19.384960 -20.303316 -2.103586e+01 -2.282353e+01 -21.679205 -19.948715 -19.072738 -2.055412e+01 4.184606e-03 22.781976 19.944773 21.208704 2.172508e+01 2.397812e+01 22.578141 20.645602 19.720047 2.132866e+01 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 -0.023216 -0.020270 -0.020151 -1.673866e-02 -1.718310e-02 -0.016165 -0.029160 -0.029009 -2.980456e-02 1.952816e-03 0.025750 0.022992 0.023803 1.903014e-02 1.943956e-02 0.018578 0.031688 0.031460 3.236059e-02 2 240 -0.024959 -0.023805 -0.025830 -3.638437e-02 -3.929876e-02 -0.039367 -0.036015 -0.035428 -3.729801e-02 1.952816e-03 0.027442 0.026767 0.028513 3.922419e-02 4.181222e-02 0.042225 0.038634 0.037858 3.988867e-02 4 960 -0.127246 -0.113954 -0.124290 -1.791011e-01 -1.966455e-01 -0.183474 -0.190692 -0.203417 -1.998117e-01 1.952816e-03 0.132595 0.118826 0.129757 1.845133e-01 2.025139e-01 0.190191 0.195446 0.208985 2.049969e-01 8 3840 -0.532785 -0.521523 -0.527673 -7.521373e-01 -7.589416e-01 -0.663794 -0.696746 -0.729329 -7.686466e-01 1.952816e-03 0.548843 0.539310 0.546608 7.700596e-01 7.760227e-01 0.682562 0.711029 0.742777 7.839601e-01 16 15360 -2.219060 -2.173531 -2.233519 -2.841061e+00 -2.903647e+00 -2.425456 -2.668691 -2.586759 -2.777718e+00 1.952816e-03 2.294752 2.257345 2.313125 2.913011e+00 2.969236e+00 2.497470 2.760205 2.660014 2.878849e+00 32 61440 -8.840503 -8.446768 -8.276329 -1.018192e+01 -1.093113e+01 -8.941265 -10.666431 -10.351744 -1.090321e+01 1.952816e-03 9.276800 8.830393 8.615229 1.065740e+01 1.137223e+01 9.217508 11.116342 10.727550 1.147528e+01 P(X,Y,Z) = X^16 1 60 -8.304968 -7.993646 -8.012820 -6.825396e+00 -8.293919e+00 -6.853511 -3.744511 -4.133763 -4.325307e+00 7.391983e-01 9.332521 9.026821 8.982170 8.377865e+00 9.260615e+00 7.941380 4.695928 5.020984 5.198641e+00 2 240 -18.164336 -18.268981 -15.922714 -1.325207e+01 -2.080012e+01 -14.512632 -18.016660 -11.391087 -1.554695e+01 7.391983e-01 19.881376 19.980333 17.172012 1.496542e+01 2.218733e+01 15.713767 19.517567 12.699021 1.672567e+01 4 960 -75.004242 -69.144967 -71.789585 -6.071748e+01 -7.328539e+01 -63.310336 -77.743975 -55.811287 -6.698913e+01 7.391983e-01 77.709794 70.827372 73.394356 6.483619e+01 7.538716e+01 65.249548 81.858011 57.530228 6.923477e+01 8 3840 -326.927940 -300.814555 -300.031227 -2.267658e+02 -2.526319e+02 -242.708794 -244.147594 -247.293443 -2.530008e+02 7.391983e-01 335.996892 303.708751 302.948514 2.367523e+02 2.570895e+02 247.651962 256.863954 251.686745 2.576764e+02 16 15360 -1175.453417 -1172.152539 -1171.078303 -9.910287e+02 -1.078073e+03 -1038.269474 -886.929261 -975.086559 -1.003844e+03 7.391983e-01 1234.799673 1185.637807 1184.664415 1.037343e+03 1.103544e+03 1064.099788 945.035420 998.334850 1.026745e+03 32 61440 -4283.448193 -4667.184024 -4658.397981 -3.728345e+03 -4.223632e+03 -3980.731217 -3640.047241 -3853.639426 -4.036553e+03 7.391983e-01 4656.982990 4765.398967 4759.758418 4.019379e+03 4.404246e+03 4142.689428 3993.563617 4030.776126 4.208386e+03 SPHERE_QUAD_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 -72.854669 -69.364770 -67.358608 -6.746447e+01 -7.291763e+01 -66.926379 -90.123685 -90.519707 -9.655356e+01 1.256637e+01 87.075921 83.828746 82.653282 8.265459e+01 8.705694e+01 81.628436 104.759885 105.720473 1.109029e+02 2 240 -256.660526 -250.555817 -231.396621 -2.848055e+02 -3.373096e+02 -308.772059 -300.245383 -255.658411 -3.031381e+02 1.256637e+01 277.320913 273.787008 251.714399 3.054663e+02 3.576975e+02 330.383972 322.923304 274.699458 3.247827e+02 4 960 -1026.874041 -1009.308283 -948.727962 -1.204047e+03 -1.311810e+03 -1242.939261 -1250.777971 -1162.110392 -1.282610e+03 1.256637e+01 1070.230489 1054.165953 992.703438 1.248299e+03 1.353106e+03 1286.694346 1294.394276 1202.762619 1.321734e+03 8 3840 -4366.532275 -4283.440647 -4242.451216 -4.548457e+03 -4.707287e+03 -4518.195609 -4642.561676 -4605.029792 -4.764338e+03 1.256637e+01 4514.496761 4437.800243 4379.312879 4.683697e+03 4.861983e+03 4668.051734 4792.102071 4732.507118 4.897504e+03 16 15360 -17845.817460 -16936.395383 -17045.515764 -1.755240e+04 -1.824954e+04 -17235.593843 -17497.440628 -17458.593200 -1.846645e+04 1.256637e+01 18696.397449 17777.334945 17808.394073 1.829862e+04 1.913972e+04 18049.316122 18325.089573 18210.517235 1.931123e+04 32 61440 -68396.767428 -63994.466067 -64271.037292 -6.500253e+04 -6.881825e+04 -64879.150451 -65401.062315 -64894.489869 -6.929068e+04 1.256637e+01 73793.678963 68343.440069 68703.261319 6.944174e+04 7.420633e+04 69211.712768 69835.159984 69430.589641 7.458312e+04 P(X,Y,Z) = X 1 60 -7.899649 -8.385188 -8.331849 -3.941872e+00 -2.186564e+00 -3.817140 -2.503380 -5.277472 -4.104958e+00 0 8.251896 8.708794 8.498294 5.826088e+00 2.923321e+00 4.399281 2.947029 6.040144 4.280379e+00 2 240 13.711503 11.486460 23.463221 1.691879e+01 2.213541e+01 26.300260 -20.388015 -21.714022 -3.004389e+01 0 14.094228 11.566481 23.576277 1.723322e+01 2.222727e+01 26.531808 20.445390 21.714198 3.015162e+01 4 960 -0.919027 -14.769883 27.070561 -5.265400e+01 -7.321761e+00 -39.158360 64.188620 77.588297 6.534358e+01 0 10.570527 15.531071 27.076731 5.282716e+01 7.648157e+00 39.278335 64.220248 78.058520 6.670161e+01 8 3840 137.496676 74.020595 182.101048 6.196165e+01 7.394394e+01 57.396695 -52.403032 -4.014987 -1.310373e+01 0 138.506356 78.557608 182.109240 7.287499e+01 7.511115e+01 60.998669 59.348786 4.560229 1.362197e+01 16 15360 133.261575 0.007068 405.970717 5.069569e+02 5.138364e+02 335.863560 -313.067348 -239.275046 -4.221310e+02 0 156.113744 75.540801 415.561088 5.119669e+02 5.253769e+02 336.389634 337.184808 239.686016 4.424926e+02 32 61440 234.190773 -347.685761 826.056782 1.194025e+03 1.741583e+03 1012.909260 -220.216092 -733.966581 -1.190533e+03 0 234.378687 560.560734 835.928771 1.194209e+03 1.745964e+03 1027.125773 261.522320 756.911232 1.301871e+03 P(X,Y,Z) = Y 1 60 0.023764 -0.696425 -1.129530 -6.963206e+00 -6.345464e+00 -6.119680 -4.056472 -3.923338 -2.443118e+00 0 0.287367 0.939470 1.904110 7.152672e+00 6.684628e+00 6.600987 4.380631 5.340913 2.728903e+00 2 240 -6.390042 -3.834204 5.920173 1.531141e+01 1.215873e+01 2.511237 -11.039822 -8.085887 -1.146008e+01 0 6.939933 5.147454 5.944449 1.570007e+01 1.259140e+01 5.495630 11.108437 8.125287 1.189622e+01 4 960 41.543926 18.732644 52.692004 1.702656e+01 2.868477e+00 -20.542245 9.132403 37.181146 3.052429e+01 0 44.795568 18.745991 52.770024 1.747123e+01 1.466227e+01 20.872226 11.536551 38.008925 3.110413e+01 8 3840 -94.916427 -122.017678 -110.459704 1.768664e+02 1.249854e+02 86.918163 222.188120 213.695076 2.046699e+02 0 94.988777 132.653186 112.713453 1.768846e+02 1.250447e+02 89.432958 222.236721 214.725179 2.067963e+02 16 15360 -402.637621 -316.704442 -384.924845 4.565280e+02 2.682878e+02 172.524905 853.156810 760.033907 8.264152e+02 0 441.509926 402.085118 455.543101 4.702440e+02 2.689287e+02 173.784089 854.150708 763.514871 8.281177e+02 32 61440 -656.606437 189.919271 -494.584171 1.133194e+03 8.369095e+02 383.506727 1773.146613 1725.651743 2.427424e+03 0 905.568922 440.509725 945.569667 1.158937e+03 8.493388e+02 430.455435 1841.472910 1743.634649 2.427433e+03 P(X,Y,Z) = Z 1 60 4.510373 2.996532 2.820262 -3.650372e+00 -2.670100e+00 -0.506865 -15.717902 -16.868451 -1.596881e+01 0 5.069917 3.910917 5.906363 4.564836e+00 2.791478e+00 1.154188 16.141668 17.049406 1.628583e+01 2 240 -9.295962 5.293528 -4.132292 1.975963e+01 4.128569e+00 14.307212 -4.298815 2.454986 -8.390651e+00 0 10.246586 5.412555 4.710735 2.003139e+01 4.448382e+00 14.601808 8.914111 2.647456 9.829278e+00 4 960 -11.613073 -3.576640 -28.628136 7.586940e+01 2.485945e+01 60.580821 -8.279739 31.869452 3.240290e+00 0 13.684884 9.208699 28.690539 7.625514e+01 2.804932e+01 60.580984 10.388120 31.969168 6.424325e+00 8 3840 310.592985 250.350024 254.027917 -7.472490e+01 -5.792040e+01 -16.209666 -99.163490 -33.119817 -1.158522e+02 0 317.844150 259.310713 268.113040 7.745653e+01 6.653049e+01 19.786361 99.489312 50.309051 1.215346e+02 16 15360 942.590974 789.913191 819.031973 -6.866479e+02 -6.511556e+02 -492.980720 -349.045069 -28.371889 -3.973521e+02 0 1000.384231 836.680811 917.703926 6.891198e+02 6.511556e+02 495.669011 377.243330 217.279810 4.032305e+02 32 61440 1532.970386 550.923735 991.968321 -1.841197e+03 -1.812937e+03 -885.540043 -1310.739502 -520.373207 -1.362924e+03 0 1653.531599 808.410644 1301.012371 1.938046e+03 1.832975e+03 887.879458 1310.795557 828.813282 1.414934e+03 P(X,Y,Z) = X^2 1 60 -25.355586 -24.437762 -23.991712 -2.386227e+01 -2.656888e+01 -23.821176 -26.760676 -27.241036 -2.880401e+01 4.188790e+00 30.163897 29.302125 28.936587 2.926971e+01 3.131242e+01 28.780693 31.571496 32.146342 3.349645e+01 2 240 -96.784030 -96.292718 -88.463791 -8.803372e+01 -1.132841e+02 -94.441918 -106.610898 -80.533493 -9.746964e+01 4.188790e+00 104.110098 104.129268 94.803763 9.515278e+01 1.200849e+02 101.630181 114.397384 86.891177 1.041164e+02 4 960 -384.770022 -364.011530 -366.338671 -3.740543e+02 -4.332734e+02 -383.147061 -405.102453 -334.211056 -3.815634e+02 4.188790e+00 400.004881 377.212535 379.341595 3.908498e+02 4.459838e+02 396.146145 423.081102 346.621868 3.943252e+02 8 3840 -1570.165399 -1552.908205 -1533.820849 -1.387734e+03 -1.532336e+03 -1464.077335 -1459.649356 -1502.245460 -1.525158e+03 4.188790e+00 1624.071225 1592.514629 1571.132946 1.437932e+03 1.576826e+03 1513.112833 1517.930513 1542.271996 1.566610e+03 16 15360 -6257.107618 -6130.496316 -6079.508050 -5.445009e+03 -6.052355e+03 -5741.633359 -5322.635573 -5785.482716 -5.900968e+03 4.188790e+00 6585.096293 6352.992133 6283.563929 5.709591e+03 6.321922e+03 6018.745520 5612.067456 6035.676981 6.128350e+03 32 61440 -24317.276336 -23929.011193 -23741.190804 -1.992925e+04 -2.280768e+04 -21412.446473 -19771.809830 -21042.500589 -2.212599e+04 4.188790e+00 26393.584806 25151.614423 24961.907687 2.139600e+04 2.446321e+04 22880.448895 21307.441258 22689.235267 2.355827e+04 P(X,Y,Z) = Y^2 Z^2 1 60 -4.068670 -3.992069 -3.724387 -4.316958e+00 -4.447933e+00 -4.282774 -7.022150 -6.942259 -7.608736e+00 8.377580e-01 4.977180 4.914280 4.712964 5.256318e+00 5.392774e+00 5.252377 8.021245 8.052683 8.586241e+00 2 240 -14.388955 -14.158632 -12.763085 -1.903223e+01 -2.124998e+01 -21.593722 -20.427428 -19.884073 -2.242244e+01 8.377580e-01 15.677910 15.789563 14.131222 2.044087e+01 2.257295e+01 23.025359 21.882986 21.105597 2.384828e+01 4 960 -52.814315 -53.549993 -48.572643 -8.779744e+01 -9.306183e+01 -90.117630 -90.895220 -92.414970 -1.005208e+02 8.377580e-01 55.465152 56.671657 51.602868 9.067644e+01 9.603006e+01 93.076944 93.412573 95.182009 1.030686e+02 8 3840 -242.213273 -244.181620 -246.824100 -3.358398e+02 -3.329299e+02 -307.999570 -335.746279 -315.683410 -3.460857e+02 8.377580e-01 253.202671 256.056712 257.521240 3.459818e+02 3.441298e+02 317.537461 346.571022 324.196651 3.543595e+02 16 15360 -1007.720300 -997.171481 -1036.574815 -1.258986e+03 -1.265495e+03 -1162.825704 -1225.559725 -1123.034306 -1.314808e+03 8.377580e-01 1059.263830 1054.715771 1093.618223 1.316225e+03 1.322712e+03 1210.911248 1293.126031 1167.330614 1.376838e+03 32 61440 -3682.166678 -3626.749364 -3710.380054 -4.577727e+03 -4.837551e+03 -4369.087274 -4546.364913 -4314.443374 -4.999667e+03 8.377580e-01 3957.455825 3899.572629 4012.377635 4.916645e+03 5.188848e+03 4620.242880 4869.418991 4546.802078 5.399270e+03 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 1.196797e-01 0.119680 0.119680 0.119680 1.196797e-01 1.196797e-01 0.119680 0.119680 0.119680 1.196797e-01 2 240 -2.322670 -2.318761 -2.138720 -2.721914e+00 -3.149938e+00 -2.942043 -2.889749 -2.491270 -2.872130e+00 1.196797e-01 2.502339 2.530175 2.316183 2.906156e+00 3.329481e+00 3.140363 3.096503 2.661073 3.059666e+00 4 960 -8.656647 -8.377126 -8.204131 -1.101345e+01 -1.204673e+01 -11.303895 -10.924531 -10.478010 -1.094319e+01 1.196797e-01 9.014325 8.726401 8.543853 1.136508e+01 1.237949e+01 11.643795 11.259896 10.806091 1.125561e+01 8 3840 -36.165547 -34.577422 -35.096331 -4.175597e+01 -4.404460e+01 -39.501729 -42.090629 -42.006113 -4.461450e+01 1.196797e-01 37.246644 35.609578 36.131827 4.273584e+01 4.514299e+01 40.519201 43.052910 42.861133 4.544683e+01 16 15360 -150.143117 -142.466721 -146.063052 -1.618430e+02 -1.670977e+02 -153.105041 -155.084609 -155.779574 -1.671484e+02 1.196797e-01 154.904462 147.265650 150.219800 1.660170e+02 1.720224e+02 158.000765 159.730849 159.935890 1.717593e+02 32 61440 -609.553029 -568.909767 -570.177045 -5.913368e+02 -6.297681e+02 -582.186448 -596.602743 -591.626555 -6.386392e+02 1.196797e-01 638.466790 590.288309 592.113681 6.140188e+02 6.586718e+02 604.561383 618.564630 614.375018 6.666710e+02 P(X,Y,Z) = Y^2 Z^4 1 60 -1.124553 -1.103381 -1.029395 -1.193178e+00 -1.229378e+00 -1.183730 -1.940875 -1.918793 -2.103003e+00 3.590392e-01 1.501488 1.483758 1.426399 1.578032e+00 1.615681e+00 1.576265 2.342080 2.349109 2.498697e+00 2 240 -5.446781 -5.070240 -4.771196 -8.557373e+00 -9.407032e+00 -9.856608 -9.083743 -8.828543 -9.807682e+00 3.590392e-01 6.013033 5.788643 5.392710 9.145304e+00 9.940410e+00 10.482386 9.691190 9.335187 1.041294e+01 4 960 -22.441807 -21.228771 -21.295688 -3.635185e+01 -3.944038e+01 -38.017524 -38.819987 -40.955407 -4.307263e+01 3.590392e-01 23.512694 22.418838 22.599701 3.758351e+01 4.072810e+01 39.449722 39.887794 42.077396 4.416634e+01 8 3840 -99.319861 -100.831528 -102.631266 -1.450126e+02 -1.438271e+02 -128.374551 -140.035605 -135.546572 -1.428304e+02 3.590392e-01 103.757290 105.471022 107.464476 1.494040e+02 1.480840e+02 132.959087 144.302636 138.870960 1.466376e+02 16 15360 -418.833870 -429.324829 -431.580558 -5.280034e+02 -5.417615e+02 -459.933757 -515.087968 -488.790824 -5.385045e+02 3.590392e-01 441.137056 452.570679 459.747121 5.533989e+02 5.630234e+02 480.434089 542.168082 507.059088 5.663926e+02 32 61440 -1515.386882 -1564.521658 -1505.673508 -1.882447e+03 -2.085368e+03 -1692.084879 -1964.288682 -1915.278595 -2.075072e+03 3.590392e-01 1632.231394 1682.774749 1637.323827 2.036625e+03 2.225233e+03 1791.573422 2097.054090 2016.611015 2.248575e+03 P(X,Y,Z) = Z^6 1 60 -11.139981 -10.004807 -9.945083 -8.365825e+00 -9.028170e+00 -8.171943 -11.794992 -11.867258 -1.226958e+01 1.795196e+00 13.220156 12.148243 12.353368 1.047390e+01 1.099995e+01 10.230380 13.852398 13.891239 1.431658e+01 2 240 -28.206987 -20.055621 -24.677925 -4.662859e+01 -5.336435e+01 -52.509194 -45.290031 -39.488633 -4.421834e+01 1.795196e+00 31.565084 23.508740 28.890602 4.940492e+01 5.602966e+01 55.908323 48.430740 42.163236 4.779013e+01 4 960 -152.577785 -137.958583 -142.635751 -1.446488e+02 -1.578987e+02 -179.829194 -190.769705 -198.821063 -1.925302e+02 1.795196e+00 157.944834 143.211339 150.426868 1.504598e+02 1.638988e+02 189.459438 195.615907 203.858537 1.986881e+02 8 3840 -638.700800 -620.696766 -585.971398 -6.235050e+02 -6.262694e+02 -598.394524 -722.687810 -728.252114 -7.012658e+02 1.795196e+00 654.596894 639.243074 610.662215 6.412511e+02 6.451537e+02 629.599858 736.442027 741.790837 7.277416e+02 16 15360 -2686.773418 -2557.016603 -2340.592846 -2.437843e+03 -2.480086e+03 -2127.286417 -2815.042011 -2810.466898 -2.668086e+03 1.795196e+00 2799.583781 2680.673896 2492.769889 2.540636e+03 2.576300e+03 2284.018859 2897.772455 2893.598865 2.844151e+03 32 61440 -10078.523908 -9194.771854 -8574.099605 -9.066926e+03 -9.524139e+03 -7976.971047 -11065.892840 -11007.776989 -1.003051e+04 1.795196e+00 10844.087414 9890.793870 9379.082584 9.756766e+03 1.014970e+04 8792.876253 11600.657667 11561.493904 1.109278e+04 P(X,Y,Z) = X Y^2 Z^4 1 60 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 2 240 -0.073029 -0.252758 -0.079010 -3.781018e-02 -3.150181e-02 -0.165442 0.124231 0.205678 2.462592e-01 0 0.080065 0.258210 0.084670 4.394799e-02 3.156845e-02 0.167611 0.128195 0.212994 2.534680e-01 4 960 -0.570871 -1.450141 0.225864 -1.423404e+00 -2.395731e-01 -1.482034 2.939299 3.092427 2.178932e+00 0 0.571184 1.456324 0.226252 1.423430e+00 3.294600e-01 1.482041 2.950178 3.124559 2.184033e+00 8 3840 -2.100107 -3.226946 0.881892 -5.119409e-01 -1.127857e-01 -4.928678 2.483506 6.666387 2.539106e+00 0 2.103145 3.232045 0.886704 1.322146e+00 1.106466e+00 4.942297 2.503140 6.741192 2.574977e+00 16 15360 -5.815427 -8.854647 2.793414 2.308303e+00 6.542293e+00 -2.382886 -2.075549 3.318514 -7.946656e+00 0 6.025642 8.906327 3.502819 2.359038e+00 7.233847e+00 3.737579 2.291231 5.199913 8.707279e+00 32 61440 -23.056214 -35.109905 4.809152 1.720524e+01 2.889009e+01 12.853869 1.413323 4.192649 -8.381792e+00 0 24.156415 35.910658 4.999950 2.157903e+01 2.897948e+01 16.691433 8.298341 11.003891 1.899260e+01 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 3.989324e-02 0.039893 0.039893 0.039893 3.989324e-02 3.989324e-02 0.039893 0.039893 0.039893 3.989324e-02 2 240 -0.759354 -0.830268 -0.712051 -9.466545e-01 -1.065111e+00 -0.967803 -0.891944 -0.799946 -9.520315e-01 3.989324e-02 0.815161 0.898547 0.770321 1.008595e+00 1.127953e+00 1.031111 0.962179 0.857546 1.016197e+00 4 960 -2.665149 -2.731633 -2.476770 -3.957778e+00 -4.217771e+00 -3.929172 -3.692047 -3.581618 -3.856733e+00 3.989324e-02 2.788563 2.864839 2.593298 4.077849e+00 4.332096e+00 4.038458 3.795246 3.691848 3.960199e+00 8 3840 -11.658200 -10.963177 -11.553399 -1.403541e+01 -1.490136e+01 -13.194749 -14.449878 -14.096199 -1.508602e+01 3.989324e-02 12.031746 11.355184 11.931194 1.434647e+01 1.529256e+01 13.503908 14.798144 14.396568 1.535892e+01 16 15360 -49.169117 -45.478699 -48.520100 -5.560777e+01 -5.721886e+01 -53.800273 -52.527539 -50.189354 -5.572384e+01 3.989324e-02 50.613213 47.005339 49.933116 5.700900e+01 5.908129e+01 55.477805 54.231563 51.546775 5.725587e+01 32 61440 -197.676670 -178.791707 -186.352476 -2.087157e+02 -2.180266e+02 -208.002425 -199.140675 -187.545654 -2.111759e+02 3.989324e-02 206.412198 184.985956 194.449738 2.166079e+02 2.289227e+02 215.941879 207.080673 194.021509 2.205642e+02 P(X,Y,Z) = X^6 Y^2 1 60 -2.538764 -2.524925 -2.463693 -2.618292e+00 -2.941530e+00 -2.632432 -2.705877 -2.766876 -2.958025e+00 1.994662e-01 2.803470 2.791973 2.721086 2.974480e+00 3.208338e+00 2.923742 2.974388 3.056011 3.208964e+00 2 240 -4.493331 -4.872612 -4.105931 -4.354490e+00 -5.477369e+00 -4.399906 -5.429809 -4.190669 -5.113496e+00 1.994662e-01 4.837056 5.233387 4.395965 4.696351e+00 5.811416e+00 4.737649 5.820226 4.494026 5.435360e+00 4 960 -17.548602 -18.596358 -17.433865 -2.162842e+01 -2.479868e+01 -21.797574 -17.713501 -13.497623 -1.589557e+01 1.994662e-01 18.377293 19.287826 18.108015 2.249533e+01 2.545865e+01 22.422150 18.662768 14.109813 1.646621e+01 8 3840 -72.047166 -76.306784 -76.210166 -7.125785e+01 -8.959654e+01 -84.347432 -68.731930 -67.405998 -6.888954e+01 1.994662e-01 75.480859 78.457343 78.901857 7.378544e+01 9.195357e+01 87.354722 72.319992 69.639831 7.174204e+01 16 15360 -301.813749 -313.913303 -309.648401 -2.602725e+02 -3.475827e+02 -310.381232 -252.540498 -274.150962 -2.686498e+02 1.994662e-01 320.442776 326.660906 325.240755 2.729950e+02 3.656408e+02 330.894944 271.337087 287.859300 2.827894e+02 32 61440 -1196.977422 -1240.507582 -1204.750402 -9.684461e+02 -1.309031e+03 -1121.095168 -864.021881 -958.627622 -9.204018e+02 1.994662e-01 1307.043039 1314.917213 1291.044399 1.033102e+03 1.429078e+03 1223.856660 953.278766 1050.695740 9.933801e+02 P(X,Y,Z) = Z^8 1 60 -7.868870 -7.051067 -7.020488 -5.849749e+00 -6.322843e+00 -5.711068 -8.203395 -8.259460 -8.519116e+00 1.396263e+00 9.465256 8.691776 8.846960 7.463846e+00 7.839742e+00 7.288134 9.779239 9.807492 1.008862e+01 2 240 -21.113015 -14.079308 -18.220809 -3.702403e+01 -4.248629e+01 -41.457068 -35.358627 -30.714851 -3.433104e+01 1.396263e+00 23.832820 16.786199 21.781010 3.917673e+01 4.457031e+01 44.102611 37.834290 32.829148 3.722471e+01 4 960 -120.492218 -109.471765 -113.121739 -1.096101e+02 -1.188839e+02 -140.747379 -147.171513 -154.035582 -1.477150e+02 1.396263e+00 124.647992 113.509151 119.385255 1.140455e+02 1.235056e+02 148.545729 150.818018 157.811501 1.526076e+02 8 3840 -503.364132 -487.422849 -463.255524 -4.722677e+02 -4.771795e+02 -459.659403 -562.747528 -567.466311 -5.420741e+02 1.396263e+00 514.927309 500.721837 482.631683 4.851017e+02 4.908813e+02 484.486367 572.525384 577.083797 5.632924e+02 16 15360 -2111.170532 -2008.373600 -1843.569029 -1.875514e+03 -1.919860e+03 -1642.770777 -2208.499477 -2212.668585 -2.066471e+03 1.396263e+00 2193.702321 2097.894474 1964.095469 1.949423e+03 1.990434e+03 1768.814883 2265.576855 2270.365660 2.206240e+03 32 61440 -7929.840061 -7228.808990 -6767.973129 -7.086760e+03 -7.464594e+03 -6272.473189 -8724.337071 -8702.662633 -7.733153e+03 1.396263e+00 8500.444813 7746.248832 7422.405150 7.592987e+03 7.936677e+03 6944.694411 9106.278664 9100.846829 8.577830e+03 P(X,Y,Z) = X^6 Z^4 1 60 -0.312526 -0.279638 -0.278720 -2.308128e-01 -2.497363e-01 -0.225261 -0.322541 -0.324896 -3.345823e-01 5.439987e-02 0.374937 0.343830 0.350346 2.939109e-01 3.088908e-01 0.286819 0.384010 0.385144 3.958194e-01 2 240 -1.403654 -1.224649 -1.294740 -1.142510e+00 -1.459274e+00 -1.317538 -1.452436 -1.071548 -1.222659e+00 5.439987e-02 1.497025 1.322997 1.377192 1.225724e+00 1.540574e+00 1.419996 1.548098 1.151344 1.307761e+00 4 960 -5.314009 -4.416118 -5.043791 -3.765627e+00 -4.564753e+00 -3.991314 -5.842391 -5.122996 -5.722559e+00 5.439987e-02 5.492461 4.593599 5.241596 3.966953e+00 4.729003e+00 4.201223 6.060811 5.309145 5.906333e+00 8 3840 -20.231263 -20.588444 -19.003415 -1.708455e+01 -1.616911e+01 -16.523679 -20.984371 -22.581423 -2.235174e+01 5.439987e-02 20.875022 21.354658 19.467895 1.783989e+01 1.697744e+01 17.319970 21.633149 23.228351 2.286051e+01 16 15360 -82.937218 -77.107683 -74.333593 -6.699538e+01 -6.074867e+01 -65.789501 -73.353895 -80.962964 -8.489165e+01 5.439987e-02 87.525036 81.955654 77.159521 7.165301e+01 6.470299e+01 69.525162 76.655846 85.785758 8.813978e+01 32 61440 -322.091195 -291.192186 -288.365745 -2.278229e+02 -2.122460e+02 -242.613245 -266.285419 -285.308133 -3.317481e+02 5.439987e-02 353.146548 314.320692 305.149866 2.519884e+02 2.300893e+02 263.337237 284.039067 315.455347 3.559683e+02 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 4.184606e-03 0.004185 0.004185 0.004185 4.184606e-03 4.184606e-03 0.004185 0.004185 0.004185 4.184606e-03 2 240 -0.096291 -0.110671 -0.091615 -1.121434e-01 -1.264056e-01 -0.109475 -0.099941 -0.089052 -1.093600e-01 4.184606e-03 0.102120 0.118017 0.097729 1.189700e-01 1.336716e-01 0.116188 0.107959 0.095518 1.164625e-01 4 960 -0.286714 -0.299788 -0.266163 -4.295410e-01 -4.548700e-01 -0.418295 -0.352718 -0.334204 -3.641593e-01 4.184606e-03 0.300036 0.313838 0.277930 4.417783e-01 4.661422e-01 0.428740 0.363948 0.345345 3.746086e-01 8 3840 -1.264445 -1.187479 -1.259864 -1.418857e+00 -1.535594e+00 -1.346893 -1.450733 -1.413578 -1.487759e+00 4.184606e-03 1.303238 1.227734 1.300664 1.447039e+00 1.573232e+00 1.377535 1.487046 1.443501 1.517186e+00 16 15360 -5.361510 -4.896493 -5.222032 -5.539990e+00 -5.925349e+00 -5.540060 -5.324731 -5.258548 -5.535523e+00 4.184606e-03 5.508561 5.044366 5.374084 5.675240e+00 6.121648e+00 5.728910 5.476321 5.393158 5.670523e+00 32 61440 -21.884637 -19.385278 -20.302809 -2.103993e+01 -2.282480e+01 -21.679897 -19.948577 -19.071485 -2.055370e+01 4.184606e-03 22.785287 19.947372 21.210299 2.173106e+01 2.398206e+01 22.580390 20.647740 19.721101 2.133053e+01 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0.000000 0 1.952816e-03 0.001953 0.001953 0.001953 1.952816e-03 1.952816e-03 0.001953 0.001953 0.001953 1.952816e-03 2 240 -0.039080 -0.035243 -0.034417 -7.272780e-02 -7.897179e-02 -0.082924 -0.074099 -0.070519 -7.803588e-02 1.952816e-03 0.042732 0.040088 0.038684 7.632046e-02 8.208299e-02 0.087048 0.077948 0.073521 8.186208e-02 4 960 -0.128411 -0.116823 -0.122541 -1.797012e-01 -1.960992e-01 -0.186072 -0.193036 -0.203387 -2.033051e-01 1.952816e-03 0.133865 0.122047 0.128328 1.854536e-01 2.019964e-01 0.192730 0.198029 0.208895 2.086091e-01 8 3840 -0.536193 -0.525457 -0.529789 -7.503997e-01 -7.575150e-01 -0.663725 -0.700713 -0.727540 -7.672423e-01 1.952816e-03 0.552619 0.543482 0.548987 7.685282e-01 7.750091e-01 0.682754 0.715396 0.741268 7.827955e-01 16 15360 -2.224091 -2.179134 -2.235700 -2.838766e+00 -2.900881e+00 -2.425616 -2.669582 -2.588020 -2.778532e+00 1.952816e-03 2.300432 2.263573 2.316033 2.911492e+00 2.967209e+00 2.498231 2.761505 2.661602 2.880152e+00 32 61440 -8.842370 -8.450059 -8.277369 -1.017904e+01 -1.092822e+01 -8.940954 -10.665514 -10.351669 -1.090297e+01 1.952816e-03 9.279532 8.834620 8.617182 1.065537e+01 1.137027e+01 9.218179 11.116056 10.728204 1.147607e+01 P(X,Y,Z) = X^16 1 60 -1.823213 -1.813179 -1.769226 -1.880045e+00 -2.112114e+00 -1.890177 -1.943193 -1.986984 -2.124215e+00 7.391983e-01 2.598542 2.589772 2.540304 2.707104e+00 2.889709e+00 2.680702 2.721136 2.776779 2.892775e+00 2 240 -20.380820 -20.739876 -18.037943 -1.506889e+01 -2.339028e+01 -16.377731 -20.382373 -13.020974 -1.770530e+01 7.391983e-01 22.169569 22.537055 19.334324 1.686237e+01 2.484797e+01 17.646954 21.977494 14.377928 1.893307e+01 4 960 -74.803911 -70.042142 -72.296197 -5.988633e+01 -7.264666e+01 -62.678371 -77.722295 -55.809654 -6.730738e+01 7.391983e-01 77.524863 71.833179 73.996579 6.389924e+01 7.479703e+01 64.655184 81.770609 57.584230 6.958933e+01 8 3840 -324.992887 -300.821575 -299.995113 -2.262281e+02 -2.527375e+02 -242.566235 -244.464490 -248.549256 -2.543900e+02 7.391983e-01 334.145059 303.803899 303.000715 2.362347e+02 2.573058e+02 247.646223 257.183685 253.044170 2.591634e+02 16 15360 -1174.521301 -1172.306047 -1171.179981 -9.898129e+02 -1.078411e+03 -1038.335979 -886.728461 -975.901721 -1.004787e+03 7.391983e-01 1234.010888 1185.945182 1184.912051 1.036213e+03 1.104119e+03 1064.400863 944.892271 999.355340 1.027857e+03 32 61440 -4283.247793 -4667.423746 -4658.603483 -3.727029e+03 -4.223910e+03 -3980.728383 -3638.862296 -3853.534558 -4.036807e+03 7.391983e-01 4656.968406 4765.902084 4760.221584 4.018109e+03 4.404925e+03 4143.027806 3992.338283 4031.084399 4.208947e+03 SPHERE_QUAD_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 12.566371 12.566371 0.000000 2 240 12.566371 12.566371 0.000000 4 960 12.566371 12.566371 0.000000 8 3840 12.566371 12.566371 0.000000 16 15360 12.566371 12.566371 0.000000 32 61440 12.566371 12.566371 0.000000 P(X,Y,Z) = X 1 60 0.000000 0.000000 0.000000 2 240 0.000000 0.000000 0.000000 4 960 0.000534 0.000000 0.000534 8 3840 0.000173 0.000000 0.000173 16 15360 0.000046 0.000000 0.000046 32 61440 0.000012 0.000000 0.000012 P(X,Y,Z) = Y 1 60 0.000000 0.000000 0.000000 2 240 0.000000 0.000000 0.000000 4 960 0.000072 0.000000 0.000072 8 3840 0.000023 0.000000 0.000023 16 15360 0.000006 0.000000 0.000006 32 61440 0.000002 0.000000 0.000002 P(X,Y,Z) = Z 1 60 0.000000 0.000000 0.000000 2 240 -0.000000 0.000000 0.000000 4 960 0.000072 0.000000 0.000072 8 3840 0.000023 0.000000 0.000023 16 15360 0.000006 0.000000 0.000006 32 61440 0.000002 0.000000 0.000002 P(X,Y,Z) = X^2 1 60 4.188790 4.188790 0.000000 2 240 4.188790 4.188790 0.000000 4 960 4.188876 4.188790 0.000086 8 3840 4.188817 4.188790 0.000026 16 15360 4.188797 4.188790 0.000007 32 61440 4.188792 4.188790 0.000002 P(X,Y,Z) = Y^2 Z^2 1 60 0.837758 0.837758 0.000000 2 240 0.837758 0.837758 0.000000 4 960 0.837191 0.837758 0.000567 8 3840 0.837585 0.837758 0.000173 16 15360 0.837713 0.837758 0.000045 32 61440 0.837747 0.837758 0.000011 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 0.000000 0.119680 0.119680 2 240 0.119708 0.119680 0.000028 4 960 0.120580 0.119680 0.000900 8 3840 0.119930 0.119680 0.000251 16 15360 0.119744 0.119680 0.000064 32 61440 0.119696 0.119680 0.000016 P(X,Y,Z) = Y^2 Z^4 1 60 0.231551 0.359039 0.127489 2 240 0.359069 0.359039 0.000030 4 960 0.359100 0.359039 0.000061 8 3840 0.359051 0.359039 0.000012 16 15360 0.359042 0.359039 0.000003 32 61440 0.359040 0.359039 0.000001 P(X,Y,Z) = Z^6 1 60 1.675516 1.795196 0.119680 2 240 1.795224 1.795196 0.000028 4 960 1.798148 1.795196 0.002953 8 3840 1.796038 1.795196 0.000842 16 15360 1.795412 1.795196 0.000216 32 61440 1.795250 1.795196 0.000054 P(X,Y,Z) = X Y^2 Z^4 1 60 0.000000 0.000000 0.000000 2 240 0.000000 0.000000 0.000000 4 960 -0.000193 0.000000 0.000193 8 3840 -0.000052 0.000000 0.000052 16 15360 -0.000013 0.000000 0.000013 32 61440 -0.000003 0.000000 0.000003 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.000000 0.039893 0.039893 2 240 0.039903 0.039893 0.000009 4 960 0.040342 0.039893 0.000449 8 3840 0.040015 0.039893 0.000122 16 15360 0.039924 0.039893 0.000031 32 61440 0.039901 0.039893 0.000008 P(X,Y,Z) = X^6 Y^2 1 60 0.438656 0.199466 0.239190 2 240 0.199411 0.199466 0.000056 4 960 0.197658 0.199466 0.001808 8 3840 0.198964 0.199466 0.000502 16 15360 0.199338 0.199466 0.000128 32 61440 0.199434 0.199466 0.000032 P(X,Y,Z) = Z^8 1 60 1.172861 1.396263 0.223402 2 240 1.396315 1.396263 0.000052 4 960 1.400956 1.396263 0.004693 8 3840 1.397593 1.396263 0.001329 16 15360 1.396604 1.396263 0.000341 32 61440 1.396349 1.396263 0.000086 P(X,Y,Z) = X^6 Z^4 1 60 0.046310 0.054400 0.008090 2 240 0.057086 0.054400 0.002686 4 960 0.054554 0.054400 0.000154 8 3840 0.054436 0.054400 0.000036 16 15360 0.054409 0.054400 0.000009 32 61440 0.054402 0.054400 0.000002 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.000000 0.004185 0.004185 2 240 0.004750 0.004185 0.000565 4 960 0.004247 0.004185 0.000062 8 3840 0.004200 0.004185 0.000015 16 15360 0.004188 0.004185 0.000004 32 61440 0.004186 0.004185 0.000001 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.000000 0.001953 0.001953 2 240 0.002879 0.001953 0.000926 4 960 0.001970 0.001953 0.000018 8 3840 0.001956 0.001953 0.000003 16 15360 0.001954 0.001953 0.000001 32 61440 0.001953 0.001953 0.000000 P(X,Y,Z) = X^16 1 60 0.314997 0.739198 0.424201 2 240 0.799424 0.739198 0.060225 4 960 0.741485 0.739198 0.002286 8 3840 0.739758 0.739198 0.000560 16 15360 0.739340 0.739198 0.000142 32 61440 0.739234 0.739198 0.000035 sphere_quad_test Normal end of execution. 10-May-2023 12:26:49