08-Oct-2025 16:44:49 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 189.210347 187.749109 184.819819 178.793468 186.006354 188.589579 184.714487 192.384177 178.647750 189.210347 187.749109 184.819819 178.793468 186.006354 188.589579 184.714487 192.384177 178.647750 189.210347 187.749109 184.819819 178.793468 186.006354 188.589579 184.714487 192.384177 178.647750 12.566371 0.100000 12.566371 20077.239608 19873.341584 19169.002750 19903.810895 20034.594467 19158.753420 20144.362723 20148.202906 19095.881019 20077.239608 19873.341584 19169.002750 19903.810895 20034.594467 19158.753420 20144.362723 20148.202906 19095.881019 20077.239608 19873.341584 19169.002750 19903.810895 20034.594467 19158.753420 20144.362723 20148.202906 19095.881019 12.566371 P(X,Y,Z) = X 1.000000 1.140662 -2.103507 -8.633340 -2.034414 -5.605660 -7.133723 -6.541689 -0.447239 -0.535968 -3.758898 -1.749101 -7.241278 -1.686178 -4.583144 -5.950970 -5.427523 -0.359055 -0.380863 -3.141588 -2.019792 -8.248544 -1.911096 -5.327242 -6.818262 -6.271056 -0.443524 -0.502698 -3.601034 0.000000 0.100000 -0.036500 -93.248288 -26.823751 -87.416204 -23.032263 -51.018679 -89.024897 27.098219 -8.397194 -43.652906 -93.029787 -26.749299 -87.239461 -22.963818 -50.909993 -88.846325 27.044513 -8.375377 -43.579438 -93.190949 -26.803758 -87.373426 -23.014371 -50.989814 -88.979887 27.087449 -8.389642 -43.634783 0.000000 P(X,Y,Z) = Y 1.000000 -3.265493 2.599305 6.097269 3.304284 9.000510 10.227854 7.919887 10.618106 4.078858 9.700567 2.157986 5.097634 2.772496 7.660441 8.638344 6.670147 8.928399 3.565940 8.199914 2.445287 5.804909 3.167499 8.662588 9.750442 7.528262 10.181671 3.949941 9.304000 0.000000 0.100000 0.141070 63.488339 32.644775 84.499282 43.197982 57.148111 66.800710 -13.848734 -2.870412 4.892695 63.360296 32.568390 84.335828 43.098393 57.014447 66.671569 -13.823894 -2.869322 4.891686 63.454814 32.624404 84.458013 43.171197 57.112045 66.769635 -13.844706 -2.873019 4.892687 0.000000 P(X,Y,Z) = Z 1.000000 2.183474 -3.701815 -4.861011 -5.571859 -3.986693 -2.167682 0.341921 -3.445340 -4.145804 -2.864823 -3.416935 -4.361101 -4.935893 -3.312609 -1.672118 0.507586 -2.993020 -3.643546 -2.521021 -3.630369 -4.710676 -5.376622 -3.758378 -1.989071 0.407629 -3.303136 -3.992463 -2.760639 0.000000 0.100000 -0.056626 -36.424600 11.944100 -0.184543 -29.350089 46.642691 -21.667406 -37.358681 -25.042992 3.717700 -36.377675 11.931427 -0.177013 -29.313146 46.567579 -21.647469 -37.336814 -25.008365 3.703369 -36.412741 11.940940 -0.184442 -29.341057 46.623970 -21.660939 -37.351687 -25.035696 3.714085 0.000000 P(X,Y,Z) = X^2 1.000000 3.967028 54.089974 54.037826 52.510392 54.082527 58.851276 58.552534 56.936935 60.868626 57.717198 55.960198 55.642279 54.387188 54.321758 57.908846 58.295964 56.446401 60.044906 56.450745 54.863644 54.700280 53.228953 54.342217 58.746613 58.642842 57.051034 60.792200 57.499948 4.188790 0.100000 4.187184 5064.844851 5235.180022 5206.912557 4908.680872 5222.217456 5146.904243 4945.844413 5149.134305 5115.713487 5067.788414 5236.380856 5207.716523 4912.404287 5224.049228 5148.340540 4949.443955 5151.241119 5117.050171 5065.585125 5235.483935 5207.115369 4909.615458 5222.678379 5147.264953 4946.749215 5149.663971 5116.047715 4.188790 P(X,Y,Z) = Y^2 Z^2 1.000000 0.702287 14.605827 14.197177 14.145167 13.379390 13.285096 13.727765 13.950571 14.007566 12.780861 13.522970 13.223295 13.068064 12.441687 12.669397 12.959598 12.973105 13.089354 12.087237 13.971639 13.660127 13.557710 12.787504 12.829209 13.226824 13.273706 13.461071 12.334370 0.837758 0.100000 0.839629 1276.636644 1270.385516 1231.151888 1266.257019 1284.599028 1214.078135 1277.341662 1284.388214 1229.497801 1276.415208 1269.723978 1230.468298 1266.041957 1283.864176 1213.645507 1277.206374 1283.794006 1228.764634 1276.583170 1270.220520 1230.979086 1266.206432 1284.416870 1213.969280 1277.311461 1284.242171 1229.313007 0.837758 P(X,Y,Z) = X^2 Y^2 Z^2 1.000000 0.127802 1.940228 1.908565 1.879181 1.920965 1.997110 1.991800 2.039356 2.067205 1.918994 1.690371 1.652912 1.633508 1.555211 1.583675 1.619950 1.621638 1.636169 1.510905 1.836665 1.813012 1.786729 1.784804 1.859605 1.870035 1.854341 1.920110 1.782446 0.119680 0.100000 0.123502 174.056784 171.127377 169.522995 171.441845 173.692174 169.804526 170.865445 170.971151 169.651636 173.704150 170.787063 169.152199 171.100359 173.332470 169.420855 170.569935 170.675428 169.290568 173.967911 171.041675 169.429547 171.356014 173.601571 169.707817 170.790948 170.896387 169.561167 0.119680 P(X,Y,Z) = Y^2 Z^4 1.000000 0.303074 6.528117 6.417711 6.397988 6.106608 6.181588 6.230181 6.310944 6.247415 5.672996 6.761485 6.611647 6.534032 6.220844 6.334699 6.479799 6.486553 6.544677 6.043619 6.359291 6.253613 6.217727 5.878814 5.993913 6.078782 6.097977 6.082540 5.579634 0.359039 0.100000 0.353429 627.844738 637.936085 585.876358 620.439502 637.768758 568.671933 642.116985 654.507723 589.271645 627.628549 637.310103 585.741892 620.205214 637.137186 568.860955 641.641192 653.698302 588.983578 627.789961 637.776512 585.839519 620.381286 637.609298 568.719430 642.000259 654.303969 589.197044 0.359039 P(X,Y,Z) = Z^6 1.000000 2.128645 34.460673 34.949493 34.513945 32.175392 34.331321 33.902709 33.382442 33.132691 30.885860 34.878025 35.082269 34.658331 32.702258 34.626237 34.445276 33.887742 34.015953 31.673163 35.292101 35.577747 35.197019 33.041462 35.122356 34.780369 34.263754 34.045376 31.721884 1.795196 0.100000 1.736753 5938.983502 5933.253470 5217.886848 5940.638001 5914.007197 5202.637793 6210.514103 6212.391583 5229.472486 5936.254602 5930.170542 5216.686363 5937.595188 5911.221727 5201.446071 6206.754107 6208.630204 5228.797769 5938.294171 5932.474746 5217.590087 5939.868158 5913.303527 5202.342967 6209.558716 6211.437510 5229.311110 1.795196 P(X,Y,Z) = X Y^2 Z^4 1.000000 0.042117 -0.056291 -0.112009 -0.090030 -0.010477 -0.094983 -0.062552 -0.000537 -0.007885 -0.087792 -0.020093 -0.080623 0.008123 0.041506 -0.045452 -0.023765 0.013539 0.058962 0.013258 -0.013393 -0.066204 -0.019199 0.009818 -0.047004 -0.032124 0.013953 0.027429 -0.024519 0.000000 0.100000 -0.002529 0.641912 0.758464 -1.052825 1.097222 0.801036 -0.003465 -0.519250 -0.391587 -0.371915 0.636157 0.792131 -1.044931 1.123046 0.865566 -0.008098 -0.453617 -0.295465 -0.365807 0.640850 0.767364 -1.050678 1.103368 0.817674 -0.004375 -0.502300 -0.366217 -0.368905 0.000000 P(X,Y,Z) = X^2 Y^4 Z^2 1.000000 0.036984 0.559426 0.546328 0.536389 0.539229 0.542923 0.550441 0.586299 0.584126 0.538577 0.633889 0.619842 0.612566 0.583204 0.593878 0.607481 0.608114 0.613563 0.566589 0.584587 0.575584 0.565204 0.552114 0.557572 0.572441 0.579096 0.601722 0.553882 0.039893 0.100000 0.043605 54.713522 53.236129 53.958003 53.854852 54.246628 53.910554 53.374327 52.936267 53.504057 54.609076 53.123168 53.839073 53.776686 54.142798 53.803200 53.287052 52.834563 53.399266 54.687478 53.207757 53.928039 53.835189 54.220285 53.883254 53.352000 52.910677 53.477602 0.039893 P(X,Y,Z) = X^6 Y^2 1.000000 0.164023 3.049766 3.128863 2.943245 2.996893 3.285379 3.278055 3.358390 3.596026 3.447631 0.547760 0.544463 0.534695 0.506853 0.503260 0.526316 0.513400 0.557998 0.507601 2.768015 2.819331 2.671459 2.715624 2.952887 2.952011 3.005883 3.207220 3.061071 0.199466 0.100000 0.193580 215.518105 227.507766 223.783021 204.329253 226.689596 217.838187 206.451488 221.340792 216.803146 215.901809 227.686869 224.139503 204.919595 226.958245 218.328351 206.910844 221.559482 217.247398 215.612469 227.552345 223.873000 204.477306 226.758790 217.962450 206.569440 221.394863 216.914489 0.199466 P(X,Y,Z) = Z^8 1.000000 1.095078 26.526865 26.978221 26.619127 24.736588 26.439318 26.077234 25.670344 25.469680 23.747433 28.269646 28.575913 28.210875 26.442610 28.111037 27.864478 27.417774 27.398437 25.525716 27.611331 27.921197 27.598747 25.814058 27.495157 27.185780 26.776324 26.582708 24.774809 1.396263 0.100000 1.315709 5150.290420 5150.681180 4524.355566 5156.811676 5131.169150 4511.757220 5391.079326 5392.861971 4514.494585 5148.427714 5148.472945 4522.830480 5154.622767 5129.158804 4510.198591 5388.755144 5390.525919 4514.150063 5149.822612 5150.127855 4523.981303 5156.263457 5130.664954 4511.374842 5390.487531 5392.268641 4514.422096 1.396263 P(X,Y,Z) = X^6 Z^4 1.000000 0.090739 0.768326 0.722982 0.730616 0.790663 0.860150 0.851506 0.759123 0.810508 0.761255 1.085577 1.083731 1.079749 1.088610 1.179027 1.164215 1.106584 1.161286 1.090661 0.723884 0.712112 0.704115 0.725593 0.788556 0.781074 0.739960 0.779855 0.736387 0.054400 0.100000 0.058699 72.952154 70.875792 72.272980 71.025001 71.244531 72.806074 71.188882 70.611052 71.727370 73.033335 71.032036 72.238265 71.101413 71.375794 72.778623 71.293481 70.781148 71.718396 72.973052 70.915442 72.263590 71.045291 71.277420 72.799052 71.215605 70.653736 71.724938 0.054400 P(X,Y,Z) = X^4 Y^6 Z^2 1.000000 0.002646 0.061259 0.060908 0.058432 0.060039 0.061684 0.061382 0.067179 0.066532 0.061818 0.029714 0.029055 0.028714 0.027338 0.027838 0.028476 0.028505 0.028761 0.026559 0.070300 0.069307 0.067966 0.066537 0.066850 0.068782 0.070024 0.073033 0.067084 0.004185 0.100000 0.004231 5.433378 5.253028 5.364322 5.326744 5.367675 5.382559 5.292437 5.243307 5.321256 5.424062 5.244707 5.353919 5.321082 5.360181 5.373796 5.283754 5.232780 5.310186 5.431076 5.250964 5.361656 5.325321 5.365841 5.380308 5.290181 5.240615 5.318405 0.004185 P(X,Y,Z) = X^2 Y^4 Z^8 1.000000 0.000092 0.017218 0.016921 0.016949 0.016601 0.017093 0.017125 0.017609 0.017287 0.016030 0.079236 0.077480 0.076571 0.072901 0.074235 0.075935 0.076014 0.076695 0.070824 0.019921 0.019798 0.019703 0.019315 0.020469 0.020236 0.019679 0.019885 0.018447 0.001953 0.100000 0.002025 3.349177 3.341821 3.187780 3.323009 3.370175 3.107928 3.341729 3.364454 3.221756 3.340740 3.333717 3.177902 3.313751 3.361531 3.100220 3.336816 3.359940 3.213160 3.347033 3.339755 3.185289 3.320630 3.367951 3.105989 3.340457 3.363296 3.219652 0.001953 P(X,Y,Z) = X^16 1.000000 0.350761 3.520094 3.679320 3.591736 3.789706 4.278715 4.237174 3.859429 4.588403 4.357562 19.712411 19.656550 18.757205 19.484510 21.589464 21.562591 20.896133 22.611882 21.757083 5.494636 5.466000 5.330022 5.657968 6.295908 6.259886 5.778018 6.473907 6.173293 0.739198 0.100000 0.698617 742.779324 872.750334 873.249379 718.244199 839.489362 837.163987 738.798087 835.444063 840.979995 743.161632 872.282194 873.057418 717.566062 839.096920 836.711924 738.100364 834.472769 840.172258 742.880628 872.635401 873.198668 718.070926 839.377776 837.029516 738.598695 835.206812 840.778112 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 20 109.357705 106.564418 108.570581 108.465 109.295 102.719624 104.655060 110.542222 110.792 12.5664 98.254896 95.656572 98.287187 98.0986 98.1212 92.041912 94.391274 100.743965 100.202 2 80 434.489858 421.745011 422.054651 418.911 441.805 426.360622 422.320927 422.925602 431.995 12.5664 427.133699 416.116811 414.153171 412.305 435.638 420.857298 417.524926 414.620257 426.303 4 320 1718.877938 1723.877326 1727.908979 1717.63 1722.97 1729.007389 1727.451865 1734.438035 1739.6 12.5664 1725.240881 1730.786883 1733.139806 1727.82 1732.74 1739.384294 1737.886611 1741.153195 1747.04 8 1280 6779.838460 6762.399123 6778.255813 6792.69 6828.64 6766.405202 6786.552398 6817.801097 6859.56 12.5664 6855.665364 6840.952922 6844.542370 6863.25 6915.25 6846.695687 6868.836279 6883.723482 6931.67 16 5120 25376.214268 24827.937354 25158.639944 25217.2 25267.8 24968.561866 24983.175234 25197.951851 25446.7 12.5664 25960.509224 25388.362890 25660.977174 25721.3 25896.9 25516.278978 25548.774330 25703.796666 26045.1 32 20480 89505.962526 88925.697939 90213.639856 90299 88933.7 89743.756773 89190.428983 89929.479285 89265.5 12.5664 93673.571831 92084.040768 93402.302294 93524.5 93144.3 92903.244310 92469.983952 93234.822123 93411.9 P(X,Y,Z) = X 1 20 2.654530 2.043524 2.110646 1.43835 -2.22233 1.595315 -0.051936 2.326702 1.56022 0 4.007010 3.596661 2.981764 5.58702 3.3016 3.181121 1.957532 4.368356 2.18259 2 80 -4.201395 -3.755516 -5.547273 -7.1522 0.801195 -5.998421 2.102641 5.086732 6.21675 0 5.441914 4.008340 6.057484 7.94276 2.38353 7.070948 2.584114 5.086792 6.74477 4 320 1.195019 4.444865 0.923754 7.32454 -0.15845 -3.415093 -0.187699 -7.398829 0.343579 0 10.745238 6.556969 1.101237 8.54523 2.31319 4.622978 2.047518 11.382906 13.5674 8 1280 -26.255942 -7.077222 -35.713848 20.4466 12.7812 -2.951534 10.998077 -3.044114 -19.775 0 31.140850 27.215605 35.758812 43.5649 18.3343 20.920194 30.000615 3.753666 20.1126 16 5120 -89.240211 -57.044029 -48.898053 -100.806 12.4709 5.390170 -79.019663 25.114581 56.2235 0 120.794404 94.658327 101.447194 123.616 110.23 19.550561 148.118243 28.781036 144.279 32 20480 -524.824454 21.735706 164.682131 -296.408 168.473 -29.807657 -227.004375 19.559030 44.0463 0 524.907713 440.303017 208.692261 297.146 209 172.880877 267.274725 186.013487 528.771 P(X,Y,Z) = Y 1 20 0.886265 2.221953 1.676929 1.59098 2.36835 0.410499 2.150499 2.318035 -1.68882 0 0.956736 2.359387 2.556015 2.60125 3.55071 3.140720 2.992611 5.115686 2.27877 2 80 5.285269 2.954263 -1.858663 -4.13263 0.171845 -1.186736 -2.468984 -0.201265 0.109277 0 6.001138 4.637381 1.942006 5.57186 3.46838 5.209601 2.807104 0.883502 3.46606 4 320 -8.814977 -5.284153 -15.723643 1.48048 -5.01548 -1.699093 -3.452350 1.129274 -0.369564 0 19.137794 5.337657 15.993961 4.25514 15.4606 4.082532 7.890768 8.039608 6.15449 8 1280 5.934239 -0.879317 19.559609 -54.9302 -72.0507 -35.405002 -61.163300 -41.088250 -43.5963 0 7.031449 52.198017 29.804603 54.9904 72.1565 41.174640 61.340302 46.171216 52.7684 16 5120 -62.963785 -200.083082 -76.063885 -247.499 -416.926 -183.770302 -373.235043 -353.242923 -349.495 0 191.976799 318.547464 255.424329 272.014 417.341 184.965698 375.509238 360.689495 353.501 32 20480 -572.191789 -1040.638338 -848.074415 -553.326 -1646.45 -472.488953 -1074.406392 -1220.697915 -1612.12 0 846.466325 1113.979628 1170.022993 604.334 1652.8 511.329241 1183.830415 1246.003275 1612.13 P(X,Y,Z) = Z 1 20 -2.435665 1.528882 1.307062 2.13228 1.12388 0.218517 1.456790 2.250909 3.38303 0 3.797559 3.512772 6.660069 4.05504 1.52082 1.323060 4.847914 3.845261 5.25717 2 80 -0.123213 -7.559123 -3.885666 -6.61481 1.73678 -2.099478 -7.670764 -5.699091 2.38752 0 4.707854 7.642803 4.600037 7.47657 2.44362 3.783431 11.226848 5.802040 5.86058 4 320 3.494051 4.078985 16.003800 -10.1787 3.35154 4.314880 11.988017 4.626845 9.60999 0 8.191943 9.508136 16.108462 12.8163 13.5891 4.316036 13.560954 5.275858 11.1467 8 1280 9.959231 37.898753 22.400455 61.8975 78.5394 72.455171 55.034210 42.509277 67.6928 0 68.370398 77.663261 88.867261 65.1913 85.1185 73.349675 55.646636 57.046781 77.0819 16 5120 232.214684 240.799694 208.803736 461.545 571.501 266.081173 398.847627 287.779002 394.958 0 407.883280 366.326632 463.969952 465.22 571.501 271.026286 423.827576 359.607174 400.884 32 20480 1558.041937 1846.050846 1265.165131 1600.15 2191.5 1028.407082 1961.553217 1914.027972 2105.26 0 1676.841311 1938.585439 1519.745141 1710.74 2208.11 1030.420894 1961.590266 2019.879146 2139.31 P(X,Y,Z) = X^2 1 20 36.647234 37.261633 37.432447 35.1767 36.8546 35.046875 32.054150 36.626401 36.4176 4.18879 33.130322 33.740902 33.783775 32.616 33.2741 31.675730 28.385050 32.888703 32.5812 2 80 143.871487 141.529676 141.101573 138.472 150.124 141.235833 139.544369 138.730992 144.433 4.18879 142.082148 140.104778 138.382653 136.298 148.04 139.159406 138.410964 135.909496 141.953 4 320 570.147008 584.522463 588.601172 562.118 574.205 574.409997 566.861908 572.991602 581.21 4.18879 573.670069 586.056869 590.029564 566.585 576.535 576.162872 572.907705 573.664822 582.747 8 1280 2227.396290 2342.185579 2321.298396 2179.44 2320.3 2280.404442 2182.204700 2321.496767 2302.5 4.18879 2258.756950 2361.670524 2339.192082 2204.98 2342.98 2305.383040 2214.781407 2340.734369 2323.24 16 5120 8237.929671 8694.452173 8690.588785 8059.71 8687.14 8412.286184 7983.607678 8616.797225 8645.06 4.18879 8482.724238 8845.657161 8827.472533 8233.91 8870.03 8596.928738 8172.574959 8779.860058 8794.79 32 20480 28600.825416 31604.158327 31596.111130 29001.1 30854.3 29945.287484 28744.326028 30321.295197 30993 4.18879 30378.800474 32532.468592 32516.138772 30021.1 32090.4 31005.030521 29814.606234 31479.646747 32024.1 P(X,Y,Z) = Y^2 Z^2 1 20 7.534075 7.290217 7.301160 7.47971 7.40059 6.860634 7.739241 7.760751 7.65109 0.837758 6.761955 6.532642 6.627313 6.67318 6.59202 6.067766 6.987031 6.997371 6.90506 2 80 29.076982 28.392725 28.767091 27.9387 29.1099 29.445902 28.325095 28.756437 29.6673 0.837758 28.450278 28.004361 28.150371 27.5538 28.6029 29.047006 27.943619 28.211111 29.2782 4 320 114.415968 113.076988 114.303444 115.139 115.745 117.622429 116.337486 117.838693 118.082 0.837758 114.403494 113.314555 114.398147 115.92 116.688 118.447630 116.839715 118.561355 118.735 8 1280 447.563916 442.344177 449.592784 459.022 453.73 453.212850 457.183130 447.770737 463.703 0.837758 452.331090 447.698936 454.261146 465.125 460.599 458.349634 463.819077 452.398609 468.454 16 5120 1671.162085 1617.569155 1664.132567 1662.31 1646.05 1674.276279 1635.558023 1639.192854 1716.01 0.837758 1701.376205 1652.283751 1698.899939 1704.71 1688.97 1706.596438 1685.462877 1668.416717 1762.57 32 20480 5992.341626 5832.189443 5944.198742 5775.99 5792.28 6078.190817 5636.900167 5972.495037 5931.53 0.837758 6163.865427 6004.229598 6135.839721 6046.79 6087.26 6259.692904 5899.162211 6140.945387 6270.64 P(X,Y,Z) = X^2 Y^2 Z^2 1 20 1.732809 1.737396 1.733587 1.73478 1.71981 1.728941 1.767791 1.765353 1.76953 0.11968 1.615565 1.620579 1.616609 1.61753 1.60215 1.611807 1.653289 1.650667 1.65494 2 80 3.842017 3.829049 3.878414 3.83229 3.94626 3.903449 3.862755 3.883418 3.87231 0.11968 3.739703 3.733891 3.779728 3.74953 3.8533 3.816764 3.777009 3.789258 3.78377 4 320 15.746410 15.738082 15.757988 15.6087 15.9685 15.881070 15.800703 15.941400 15.9428 0.11968 15.749860 15.728381 15.740244 15.6388 15.999 15.904689 15.814389 15.947894 15.9445 8 1280 62.934322 62.725029 62.692721 63.4598 64.2846 62.845519 63.542692 63.890214 64.159 0.11968 63.354952 63.090754 63.074579 63.8939 64.822 63.273082 63.962967 64.239541 64.5192 16 5120 242.537963 236.741320 238.475705 240.438 243.888 238.177357 240.222594 240.252998 245.339 0.11968 245.282502 239.431219 240.815176 243.033 247.047 241.123266 243.013726 242.736074 248.265 32 20480 898.080317 886.492811 889.899412 896.149 898.092 889.661563 891.982151 892.367920 901.304 0.11968 917.690257 900.117646 903.865092 911.027 918.329 904.216768 906.568698 907.359001 921.117 P(X,Y,Z) = Y^2 Z^4 1 20 3.771078 3.550846 3.566559 3.72045 3.67561 3.189639 3.893519 3.916236 3.81378 0.359039 3.478503 3.275271 3.399802 3.38746 3.34191 2.873796 3.611053 3.621680 3.53931 2 80 12.102222 11.791382 11.878980 11.776 12.2225 12.266240 11.655013 11.825909 12.358 0.359039 11.828490 11.623227 11.609150 11.5971 11.984 12.141954 11.516153 11.576119 12.1957 4 320 47.935278 47.606416 47.835551 48.0026 48.8738 48.998108 48.756154 49.982022 49.4658 0.359039 47.903642 47.608376 47.893456 48.3344 49.3131 49.506533 48.985322 50.267124 49.7568 8 1280 188.465228 189.145293 186.409277 191.836 192.839 184.579191 193.134921 192.460854 191.981 0.359039 190.291010 191.098754 188.561690 194.587 195.415 187.201288 195.649447 194.207408 194.202 16 5120 701.763880 700.852621 677.214862 687.286 702.994 676.453547 691.832236 709.408435 704.95 0.359039 714.716902 714.734990 694.955184 706.402 718.876 689.924290 711.641814 721.515865 725.847 32 20480 2506.594040 2515.868869 2398.192377 2352.95 2510.82 2453.543870 2397.856879 2581.986743 2412.24 0.359039 2578.292838 2590.476033 2482.364479 2477.47 2627.53 2522.514224 2507.168942 2657.408686 2562.37 P(X,Y,Z) = Z^6 1 20 15.746954 14.212407 14.342306 15.3844 15.1692 11.780225 16.370113 16.550803 15.823 1.7952 14.550934 13.202410 14.461305 13.7954 13.58 10.393624 15.199529 15.267195 14.7377 2 80 62.331845 57.851368 57.335185 60.6999 63.2655 57.966086 59.926482 59.789526 57.8618 1.7952 61.400443 56.651801 56.930887 59.7162 62.3032 57.816131 59.331185 58.678207 57.8101 4 320 244.211257 245.219848 237.584648 244.659 248.406 241.556352 253.102602 256.675121 244.402 1.7952 244.718743 245.430791 239.621055 245.266 249.323 245.968100 253.592803 257.394576 246.152 8 1280 988.748662 978.616175 900.298283 988.327 985.43 886.672273 1019.133109 1015.619161 932.716 1.7952 996.113174 987.525809 913.710882 996.639 994.565 905.163600 1025.809614 1022.250016 949.793 16 5120 3758.872594 3652.292687 3262.769632 3708.97 3701.47 3217.185843 3868.893231 3852.585952 3336.02 1.7952 3837.260124 3736.868342 3370.775464 3774.31 3763.6 3320.122379 3926.324427 3910.497048 3475.49 32 20480 13242.792068 12673.357672 11637.872851 13203.2 13377.4 11530.454351 14184.693539 14088.565172 11099.2 1.7952 13831.324345 13184.038765 12240.365114 13683.1 13826.7 12106.612114 14602.531618 14522.135642 12064.9 P(X,Y,Z) = X Y^2 Z^4 1 20 -0.025208 -0.019055 -0.015293 0.0182293 0.0239577 0.024330 -0.002079 0.001057 0.00180317 0 0.032193 0.031913 0.027983 0.0285991 0.0299948 0.030129 0.004463 0.005807 0.00254238 2 80 -0.015355 0.057994 0.013743 -0.0684526 0.0910432 0.053123 0.025619 -0.010666 -0.046878 0 0.032276 0.088269 0.029689 0.0753663 0.0910998 0.055224 0.040757 0.088757 0.0908033 4 320 0.031064 0.333240 0.019651 0.0860789 0.281025 0.033092 -0.171029 -0.186577 -0.126907 0 0.080491 0.355936 0.038200 0.0874051 0.41303 0.050536 0.326348 0.557122 0.201755 8 1280 0.368883 0.251122 -0.827593 0.97673 0.753383 1.056393 -0.202478 -0.378957 -0.779579 0 0.381716 0.291219 0.839208 1.61453 1.36607 1.134418 0.384659 1.125993 0.91528 16 5120 1.839565 2.345677 0.274675 2.99665 4.54192 0.668009 0.631468 2.273818 0.874476 0 2.438848 2.532988 2.154434 3.03557 5.49199 3.008650 1.185994 4.656748 3.70422 32 20480 2.292635 10.357552 0.260908 4.06395 14.7708 -9.082475 6.992988 14.577613 -5.85529 0 7.604112 12.818051 1.404425 13.6848 14.9427 14.020693 10.770791 17.794608 18.0564 P(X,Y,Z) = X^2 Y^4 Z^2 1 20 0.577603 0.579132 0.577862 0.57826 0.573271 0.576314 0.589264 0.588451 0.589843 0.0398932 0.538522 0.540193 0.538870 0.539176 0.53405 0.537269 0.551096 0.550222 0.551647 2 80 1.278078 1.280028 1.290197 1.26179 1.31561 1.302702 1.294868 1.310226 1.2957 0.0398932 1.243760 1.249513 1.257749 1.23717 1.28585 1.271959 1.267179 1.280662 1.26637 4 320 5.245951 5.219086 5.242690 5.1987 5.31129 5.324917 5.275236 5.317903 5.35194 0.0398932 5.245406 5.224947 5.235007 5.21709 5.32656 5.332624 5.272968 5.321818 5.35594 8 1280 20.873638 20.576196 20.947417 21.2332 21.3161 21.226685 21.174048 21.097347 21.5261 0.0398932 21.016057 20.718682 21.090911 21.3676 21.5167 21.347646 21.340061 21.227629 21.6452 16 5120 80.488002 77.786417 79.955948 80.7046 80.8242 80.264721 79.994734 78.770483 82.5137 0.0398932 81.302387 78.612619 80.743872 81.5991 82.0712 81.322744 81.045262 79.565311 83.4761 32 20480 300.581097 294.166082 296.630492 300.778 295.051 299.330642 295.531787 294.704382 302.781 0.0398932 306.312727 297.890308 301.700135 306.225 303.1 304.819538 300.856264 298.784018 309.316 P(X,Y,Z) = X^6 Y^2 1 20 0.614356 0.613238 0.615495 0.617758 0.611641 0.615633 0.624066 0.624158 0.628753 0.199466 0.416219 0.415341 0.417520 0.420033 0.413763 0.418086 0.428325 0.429279 0.432793 2 80 7.360417 7.700990 7.363064 7.1641 7.89462 7.384123 7.067647 7.159487 7.61334 0.199466 7.276986 7.622386 7.225586 7.09447 7.82066 7.274686 7.059928 7.045296 7.53317 4 320 28.570174 30.032551 29.707711 28.7086 29.2317 29.505035 27.892273 28.927317 29.0988 0.199466 28.776282 30.157716 29.807989 29.0477 29.4557 29.644457 28.185812 28.924725 29.0964 8 1280 107.614966 119.749763 116.307105 105.726 118.743 114.435303 106.386704 116.995598 113.478 0.199466 109.652927 120.820639 117.798629 107.133 120.216 116.385067 108.448477 117.996465 114.949 16 5120 389.047121 442.879260 421.003361 383.29 438.851 399.026793 380.386152 435.944172 419.814 0.199466 403.386316 451.715898 432.332267 391.717 453.032 414.954232 392.853800 444.398458 428.719 32 20480 1324.887689 1601.557099 1464.911278 1381.39 1499.13 1337.123530 1335.364476 1530.326888 1480.18 0.199466 1424.831006 1659.605966 1536.408283 1427.13 1604.84 1424.168066 1394.498929 1589.354132 1526.33 P(X,Y,Z) = Z^8 1 20 12.774907 11.431928 11.547420 12.4604 12.2774 9.318396 13.308265 13.459279 12.8227 1.39626 11.919190 10.749678 11.903004 11.2453 11.0642 8.295110 12.469562 12.518427 12.0636 2 80 48.075786 44.458454 43.801734 46.8201 48.9626 44.212381 46.134548 46.108975 44.1212 1.39626 47.394165 43.481457 43.634726 46.0679 48.2471 44.101685 45.717757 45.285502 44.2361 4 320 188.876940 189.982334 182.735950 189.656 192.503 186.874365 196.578222 199.513897 188.625 1.39626 189.300974 190.168775 184.583558 190.015 193.097 190.617758 196.826516 199.924181 190.062 8 1280 768.248307 761.520292 694.277285 767.419 766.667 683.028941 793.589890 792.308411 719.339 1.39626 773.525097 767.758023 705.117939 773.046 772.935 697.740346 798.101424 796.767875 733.123 16 5120 2937.502745 2866.618052 2521.439773 2905.06 2903.54 2481.653732 3042.583695 3036.045586 2570.93 1.39626 2994.903383 2927.574699 2608.637484 2950.92 2948.3 2564.681183 3081.732343 3075.830687 2682.24 32 20480 10402.525493 10003.481186 9010.088746 10418.3 10532.3 8915.793090 11271.053709 11213.710802 8534.75 1.39626 10841.298590 10381.109554 9509.459980 10766.6 10869.6 9398.911357 11566.639260 11522.888039 9304.67 P(X,Y,Z) = X^6 Z^4 1 20 0.420361 0.430257 0.429287 0.399811 0.42151 0.398364 0.365359 0.421017 0.415644 0.0543999 0.374338 0.384070 0.381496 0.365033 0.373718 0.353078 0.315889 0.369974 0.364518 2 80 1.895091 1.693002 1.724388 1.81594 1.85013 1.795085 1.862856 1.780833 1.77208 0.0543999 1.867430 1.672459 1.684044 1.77252 1.81248 1.795115 1.836730 1.735971 1.72861 4 320 7.421112 7.321933 7.553239 7.23566 7.29508 7.174687 7.461995 7.373076 7.46275 0.0543999 7.456240 7.346149 7.603438 7.25991 7.30927 7.209379 7.540574 7.417159 7.51453 8 1280 29.270190 29.202344 29.223037 29.0445 28.7065 28.779160 28.948453 29.329330 29.5008 0.0543999 29.628862 29.667097 29.438291 29.4113 29.0888 29.161657 29.333316 29.742302 29.7918 16 5120 109.196343 101.646286 109.236228 105.938 104.478 108.325131 105.080932 102.896491 109.229 0.0543999 112.630837 105.294863 111.094123 108.866 106.744 110.550147 107.322766 106.656655 111.676 32 20480 370.912586 345.141748 395.740581 367.23 371.085 388.680963 373.738767 337.124263 388.307 0.0543999 398.092186 364.786758 408.052084 382.61 381.482 401.867723 386.493764 362.925519 409.109 P(X,Y,Z) = X^4 Y^6 Z^2 1 20 0.064178 0.064348 0.064207 0.0642511 0.0636968 0.064035 0.065474 0.065383 0.0655381 0.00418461 0.060083 0.060269 0.060122 0.060156 0.0595866 0.059944 0.061480 0.061383 0.0615413 2 80 0.123464 0.124114 0.124577 0.124002 0.126946 0.126100 0.124136 0.124722 0.123968 0.00418461 0.119759 0.120507 0.120907 0.120627 0.123361 0.122480 0.121216 0.121453 0.120846 4 320 0.545528 0.547630 0.548184 0.53858 0.556751 0.552576 0.544482 0.553054 0.55573 0.00418461 0.545846 0.548778 0.547022 0.540428 0.557797 0.552197 0.544378 0.552576 0.555509 8 1280 2.175465 2.161101 2.183961 2.20155 2.21936 2.205510 2.200173 2.214569 2.22917 0.00418461 2.191026 2.176429 2.200684 2.21215 2.23766 2.216435 2.216916 2.226358 2.24151 16 5120 8.347375 8.175633 8.279888 8.36449 8.55286 8.299832 8.381256 8.338521 8.56242 0.00418461 8.434543 8.257122 8.368382 8.44681 8.68141 8.418962 8.470152 8.415954 8.64199 32 20480 31.289151 31.086102 30.612794 31.4156 31.1073 30.733905 31.441326 31.169267 31.8369 0.00418461 31.916297 31.431039 31.213340 31.8739 31.9563 31.367105 31.880803 31.562384 32.3351 P(X,Y,Z) = X^2 Y^4 Z^8 1 20 0.021393 0.021449 0.021402 0.021417 0.0212323 0.021345 0.021825 0.021794 0.021846 0.00195282 0.019471 0.019533 0.019484 0.0194949 0.019305 0.019424 0.019937 0.019905 0.0199576 2 80 0.045817 0.045686 0.046559 0.0455091 0.0475762 0.046608 0.046805 0.047152 0.0465597 0.00195282 0.044039 0.044086 0.044908 0.0441792 0.0459859 0.045168 0.045171 0.045468 0.0448805 4 320 0.256898 0.255519 0.254955 0.257766 0.262537 0.259141 0.259407 0.262701 0.260293 0.00195282 0.256653 0.254870 0.254705 0.258166 0.263556 0.260594 0.259446 0.263608 0.260821 8 1280 1.035233 1.025872 1.007792 1.04218 1.05498 0.999289 1.044645 1.050923 1.03935 0.00195282 1.040572 1.032049 1.014822 1.05181 1.06392 1.008575 1.050887 1.056953 1.0473 16 5120 3.964834 3.879027 3.791794 3.90832 3.93602 3.772441 3.934880 3.928793 3.96701 0.00195282 4.004518 3.923444 3.835998 3.95743 3.98114 3.815838 3.994189 3.974130 4.03508 32 20480 14.687189 14.398359 14.054603 14.3213 14.6219 14.235452 14.325337 14.567542 14.2463 0.00195282 14.950594 14.623447 14.253553 14.6597 14.951 14.407216 14.659935 14.833494 14.6852 P(X,Y,Z) = X^16 1 20 7.120389 7.413451 7.396381 6.47193 7.20128 6.446998 5.281892 7.028100 6.84586 0.739198 6.734083 7.006837 6.918552 6.65462 6.73731 6.108064 4.720293 6.385730 6.20015 2 80 22.687035 22.447873 22.540473 21.3007 24.5407 22.273675 21.235235 21.199884 23.5746 0.739198 22.779351 22.552853 22.186419 21.2307 24.3811 21.838956 21.156591 20.785320 23.1289 4 320 97.006838 103.281284 105.194816 92.6117 98.5849 99.971925 97.225759 98.098417 102.114 0.739198 97.812695 103.163165 105.039318 94.2095 98.8719 100.005587 99.257576 97.917236 102.371 8 1280 385.930972 427.670288 426.394488 360.778 412.622 409.709343 365.125300 414.769818 415.025 0.739198 392.285834 428.435829 427.176932 365.955 414.156 411.457814 372.533213 416.206485 416.685 16 5120 1422.090316 1674.936652 1672.766789 1374.4 1600.03 1581.667308 1349.010202 1609.055219 1616.58 0.739198 1470.187427 1683.115862 1681.022187 1406.91 1616.02 1597.477736 1386.701362 1622.026799 1629.67 32 20480 4926.826598 6437.184477 6422.383318 5042.52 5943.68 5873.634265 4953.702978 5926.516555 5978.82 0.739198 5253.476277 6507.419204 6494.954267 5260.13 6072.02 5983.286593 5217.801980 6041.909892 6094.86 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 60 109.357705 106.564418 108.570581 108.465 109.295 102.719624 104.655060 110.542222 110.792 12.5664 98.254896 95.656572 98.287187 98.0986 98.1212 92.041912 94.391274 100.743965 100.202 2 240 434.489858 421.745011 422.054651 418.911 441.805 426.360622 422.320927 422.925602 431.995 12.5664 427.133699 416.116811 414.153171 412.305 435.638 420.857298 417.524926 414.620257 426.303 4 960 1718.877938 1723.877326 1727.908979 1717.63 1722.97 1729.007389 1727.451865 1734.438035 1739.6 12.5664 1725.240881 1730.786883 1733.139806 1727.82 1732.74 1739.384294 1737.886611 1741.153195 1747.04 8 3840 6779.838460 6762.399123 6778.255813 6792.69 6828.64 6766.405202 6786.552398 6817.801097 6859.56 12.5664 6855.665364 6840.952922 6844.542370 6863.25 6915.25 6846.695687 6868.836279 6883.723482 6931.67 16 15360 25376.214268 24827.937354 25158.639944 25217.2 25267.8 24968.561866 24983.175234 25197.951851 25446.7 12.5664 25960.509224 25388.362890 25660.977174 25721.3 25896.9 25516.278978 25548.774330 25703.796666 26045.1 32 61440 89505.962526 88925.697939 90213.639856 90299 88933.7 89743.756773 89190.428983 89929.479285 89265.5 12.5664 93673.571831 92084.040768 93402.302294 93524.5 93144.3 92903.244310 92469.983952 93234.822123 93411.9 P(X,Y,Z) = X 1 60 2.479789 1.909004 1.971707 1.34367 -2.07604 1.490300 -0.048517 2.173541 1.45752 0 3.743238 3.359902 2.785481 5.21924 3.08427 2.971715 1.828672 4.080797 2.03892 2 240 -4.159202 -3.721165 -5.516978 -7.07337 0.791021 -5.908666 2.046943 4.981200 6.10788 0 5.376765 3.973002 6.016678 7.85212 2.31894 6.959701 2.547526 4.981402 6.6393 4 960 1.189977 4.426491 0.911412 7.28222 -0.1753 -3.407283 -0.182755 -7.370708 0.338101 0 10.706858 6.541172 1.087363 8.49283 2.28868 4.608433 2.040094 11.347385 13.5238 8 3840 -26.228820 -7.058660 -35.659528 20.4267 12.773 -2.943504 10.978618 -3.031605 -19.7646 0 31.111182 27.218779 35.703736 43.5316 18.3364 20.904182 29.981553 3.738540 20.1048 16 15360 -89.225661 -57.016691 -48.874152 -100.78 12.4801 5.400206 -79.006011 25.131156 56.219 0 120.768565 94.642066 101.408841 123.581 110.229 19.556454 148.100590 28.792150 144.234 32 61440 -524.802301 21.738175 164.675159 -296.398 168.482 -29.806385 -227.001615 19.568801 44.0506 0 524.885718 440.288544 208.671642 297.136 208.995 172.882740 267.269583 186.007195 528.733 P(X,Y,Z) = Y 1 60 0.827924 2.075687 1.566541 1.48625 2.21245 0.383477 2.008936 2.165444 -1.57765 0 0.893757 2.204074 2.387758 2.43002 3.31697 2.933973 2.795614 4.778933 2.12877 2 240 5.191400 2.892707 -1.873225 -4.10428 0.163864 -1.202730 -2.429789 -0.158986 0.113511 0 5.902549 4.572956 1.954096 5.50228 3.41832 5.172598 2.759102 0.858439 3.39052 4 960 -8.785660 -5.262003 -15.666118 1.47948 -4.98851 -1.682994 -3.443181 1.122574 -0.372596 0 19.071470 5.314144 15.934871 4.23772 15.3916 4.072619 7.875135 8.020733 6.11162 8 3840 5.931942 -0.879067 19.550546 -54.8569 -71.9827 -35.363066 -61.102034 -41.050154 -43.5551 0 7.020632 52.161468 29.787047 54.9169 72.0879 41.143873 61.279049 46.131238 52.7133 16 15360 -62.930558 -200.032786 -76.031690 -247.428 -416.83 -183.714716 -373.145732 -353.155719 -349.412 0 191.915934 318.489140 255.364119 271.939 417.244 184.907268 375.418486 360.599655 353.419 32 61440 -572.152186 -1040.585912 -848.025144 -553.288 -1646.35 -472.460883 -1074.341189 -1220.627673 -1612.02 0 846.413243 1113.925873 1169.962189 604.291 1652.7 511.303961 1183.757307 1245.931171 1612.03 P(X,Y,Z) = Z 1 60 -2.275331 1.428239 1.221021 1.99192 1.0499 0.204132 1.360893 2.102737 3.16033 0 3.547574 3.281534 6.221653 3.78811 1.42071 1.235966 4.528787 3.592137 4.91111 2 240 -0.136779 -7.461806 -3.836663 -6.56323 1.70742 -2.099410 -7.588376 -5.648710 2.31783 0 4.597131 7.547199 4.528728 7.40715 2.41274 3.731256 11.099885 5.747431 5.78089 4 960 3.481379 4.053025 15.933780 -10.1417 3.32278 4.302117 11.958077 4.614902 9.57481 0 8.147309 9.472155 16.040491 12.7678 13.5377 4.303520 13.526615 5.264288 11.1029 8 3840 9.952016 37.871292 22.377893 61.8468 78.4623 72.383343 55.001002 42.498103 67.6441 0 68.335550 77.604017 88.803251 65.1377 85.0399 73.275802 55.606783 57.009380 77.0221 16 15360 232.182904 240.758708 208.768314 461.457 571.39 266.029115 398.770945 287.733823 394.877 0 407.817828 366.252281 463.872708 465.132 571.39 270.975984 423.734647 359.537988 400.801 32 61440 1557.972486 1845.954322 1265.095078 1600.07 2191.39 1028.351629 1961.448057 1913.934383 2105.14 0 1676.766806 1938.480696 1519.658030 1710.65 2208 1030.365873 1961.485209 2019.774025 2139.19 P(X,Y,Z) = X^2 1 60 36.610056 36.929292 37.195198 35.3635 36.7738 34.892751 32.594798 36.668610 36.5155 4.18879 33.055878 33.386146 33.585243 32.6041 33.1645 31.484221 28.970933 33.008629 32.7308 2 240 143.919534 141.485692 141.059684 138.551 149.994 141.304537 139.597146 138.825257 144.434 4.18879 142.099212 140.043196 138.341038 136.384 147.916 139.245762 138.436077 136.005357 141.973 4 960 570.190669 584.421354 588.477730 562.224 574.192 574.423635 566.968610 573.042971 581.192 4.18879 573.696419 585.965527 589.910014 566.68 576.535 576.196956 572.980760 573.732749 582.739 8 3840 2227.475543 2341.935663 2321.138397 2179.66 2320.18 2280.338312 2182.429550 2321.367951 2302.47 4.18879 2258.817358 2361.438408 2339.042113 2205.2 2342.87 2305.321623 2214.990906 2340.614365 2323.22 16 15360 8238.074422 8694.152409 8690.403522 8059.95 8686.94 8412.250667 7983.837610 8616.633343 8644.97 4.18879 8482.828322 8845.379011 8827.305384 8234.14 8869.86 8596.890297 8172.805647 8779.702111 8794.74 32 61440 28601.031884 31603.821950 31595.875737 29001.3 30854.1 29945.312480 28744.484625 30321.211088 30992.8 4.18879 30378.927946 32532.150196 32515.925569 30021.3 32090.2 31005.055331 29814.766286 31479.554110 32024 P(X,Y,Z) = Y^2 Z^2 1 60 7.378616 7.088642 7.182826 7.35669 7.29784 6.747649 7.423592 7.549957 7.50486 0.837758 6.624275 6.351828 6.533359 6.5852 6.51716 5.992322 6.719926 6.860897 6.79918 2 240 29.071482 28.335942 28.668484 27.9704 29.1326 29.306870 28.319862 28.690812 29.5275 0.837758 28.456453 27.945493 28.066608 27.5781 28.6386 28.916732 27.938937 28.143901 29.1472 4 960 114.431098 113.109794 114.285482 115.153 115.712 117.542725 116.326523 117.770366 118.002 0.837758 114.430292 113.359641 114.390408 115.928 116.647 118.369090 116.828819 118.490154 118.653 8 3840 447.628691 442.336897 449.556083 459.042 453.695 453.172771 457.215583 447.784196 463.638 0.837758 452.395176 447.697837 454.227481 465.129 460.56 458.312937 463.836210 452.412644 468.392 16 15360 1671.245545 1617.546995 1664.091042 1662.42 1646.07 1674.238066 1635.703922 1639.230680 1715.94 0.837758 1701.469823 1652.275610 1698.864188 1704.8 1688.99 1706.567707 1685.578199 1668.466298 1762.49 32 61440 5992.386490 5832.123722 5944.149260 5776.18 5792.28 6078.132914 5637.128090 5972.477275 5931.48 0.837758 6163.946288 6004.189913 6135.813159 6046.94 6087.26 6259.654101 5899.364436 6140.953333 6270.57 P(X,Y,Z) = X^2 Y^2 Z^2 1 60 1.382819 1.354367 1.374729 1.37379 1.38034 1.313128 1.338752 1.399734 1.40292 0.11968 1.277122 1.250508 1.276408 1.27461 1.27386 1.211091 1.241372 1.306663 1.30274 2 240 3.928478 3.895379 3.933861 3.8807 4.02462 3.960994 3.921571 3.937884 3.95047 0.11968 3.831858 3.809246 3.839332 3.80241 3.93782 3.883400 3.845215 3.846784 3.86868 4 960 15.768104 15.760988 15.783713 15.6378 15.9816 15.898366 15.821098 15.961688 15.9657 0.11968 15.774828 15.755498 15.770135 15.6726 16.0161 15.926533 15.839788 15.972037 15.9712 8 3840 62.930810 62.725405 62.694335 63.4551 64.2718 62.844559 63.535003 63.881971 64.1511 0.11968 63.356443 63.097402 63.080824 63.8939 64.8146 63.278152 63.961333 64.236220 64.5166 16 15360 242.497007 236.700632 238.439025 240.397 243.839 238.136341 240.175332 240.211122 245.293 0.11968 245.252001 239.400804 240.788258 243.001 247.01 241.091826 242.976940 242.703919 248.229 32 61440 897.992740 886.404624 889.817718 896.061 897.999 889.576293 891.890750 892.279529 901.213 0.11968 917.620474 900.043461 903.797895 910.954 918.254 904.145444 906.492070 907.285755 921.043 P(X,Y,Z) = Y^2 Z^4 1 60 3.522480 3.359473 3.377358 3.48425 3.45236 3.090762 3.598296 3.636860 3.56774 0.359039 3.212899 3.061266 3.147532 3.1504 3.1157 2.767452 3.300309 3.332434 3.27355 2 240 12.213305 11.847262 11.940714 11.8479 12.3179 12.276048 11.794806 11.933065 12.3583 0.359039 11.948675 11.675402 11.685593 11.6694 12.0866 12.149587 11.650729 11.687876 12.2044 4 960 47.992827 47.663572 47.871648 48.065 48.9056 49.030225 48.829285 50.009790 49.4915 0.359039 47.965764 47.671525 47.935035 48.3924 49.3353 49.534477 49.055533 50.292648 49.7823 8 3840 188.530936 189.162156 186.436576 191.905 192.856 184.647834 193.204103 192.485538 192.023 0.359039 190.357963 191.119063 188.589062 194.646 195.432 187.267895 195.715454 194.232530 194.245 16 15360 701.845584 700.835460 677.282415 687.41 703.026 676.529420 691.940957 709.435649 704.983 0.359039 714.802041 714.724518 695.014826 706.514 718.909 690.008642 711.740708 721.543764 725.883 32 61440 2506.663663 2515.833308 2398.283299 2353.12 2510.83 2453.602420 2397.989641 2582.008882 2412.28 0.359039 2578.375909 2590.446420 2482.460627 2477.61 2627.53 2522.591342 2507.290659 2657.431706 2562.41 P(X,Y,Z) = Z^6 1 60 15.798115 14.612347 14.707526 15.502 15.3239 12.668851 16.303274 16.486092 15.9205 1.7952 14.424043 13.354451 14.178031 13.8695 13.6831 11.155101 14.962730 15.067034 14.6312 2 240 62.443253 58.053430 57.701317 60.772 63.3013 58.325574 60.099310 59.906713 58.2368 1.7952 61.490622 56.878592 57.227648 59.7772 62.3174 58.142918 59.473365 58.775548 58.1043 4 960 244.252591 245.237062 237.765691 244.679 248.42 241.640692 253.054060 256.623546 244.537 1.7952 244.755138 245.447278 239.770209 245.296 249.344 245.994137 253.558119 257.354178 246.276 8 3840 988.681836 978.546329 900.486110 988.319 985.405 886.931287 1019.005880 1015.466408 932.898 1.7952 996.059083 987.471095 913.878478 996.651 994.556 905.397197 1025.702509 1022.114149 949.948 16 15360 3758.709624 3652.092494 3262.975544 3708.79 3701.3 3217.433239 3868.551559 3852.247241 3336.26 1.7952 3837.111236 3736.688258 3370.935214 3774.16 3763.45 3320.334909 3926.017435 3910.185729 3475.69 32 61440 13242.601190 12673.160830 11638.088108 13202.9 13377.2 11530.682630 14184.204710 14088.113094 11099.6 1.7952 13831.140124 13183.855467 12240.498042 13682.9 13826.6 12106.766298 14602.075481 14521.715392 12065.1 P(X,Y,Z) = X Y^2 Z^4 1 60 -0.004008 -0.003104 -0.000870 0.0137542 0.00397827 0.017634 0.002672 0.012197 0.00853394 0 0.004016 0.004691 0.005259 0.0162885 0.00414258 0.017774 0.008652 0.019087 0.00960678 2 240 -0.014824 0.058548 0.019972 -0.0633474 0.0818417 0.028386 0.028754 -0.000461 -0.041519 0 0.036161 0.086870 0.030820 0.069055 0.0822413 0.032068 0.042425 0.081787 0.0833227 4 960 0.032847 0.323319 0.025659 0.0849678 0.271442 0.037160 -0.169234 -0.182561 -0.11957 0 0.066911 0.348297 0.036419 0.0855402 0.39107 0.047536 0.319667 0.535904 0.195241 8 3840 0.364645 0.247022 -0.817129 0.971865 0.746492 1.045304 -0.201155 -0.373074 -0.771349 0 0.378696 0.292069 0.826972 1.59862 1.35417 1.119860 0.380880 1.110473 0.901529 16 15360 1.832691 2.339063 0.271665 2.98582 4.52778 0.671068 0.626629 2.267547 0.876326 0 2.429780 2.527009 2.148357 3.02497 5.48027 2.995833 1.176396 4.640525 3.69504 32 61440 2.293387 10.351383 0.262309 4.05722 14.7643 -9.074098 6.985463 14.565986 -5.8448 0 7.594020 12.811519 1.401626 13.6725 14.9368 14.008896 10.763119 17.780613 18.0442 P(X,Y,Z) = X^2 Y^4 Z^2 1 60 0.458567 0.444020 0.457310 0.465905 0.460885 0.450233 0.453013 0.461935 0.471242 0.0398932 0.421479 0.407468 0.421998 0.430813 0.425457 0.415816 0.422169 0.436437 0.439272 2 240 1.305180 1.304733 1.314105 1.27941 1.33774 1.324892 1.308964 1.323795 1.32623 0.0398932 1.272278 1.277289 1.282486 1.25573 1.31014 1.296881 1.284083 1.294837 1.29948 4 960 5.253459 5.227084 5.249116 5.21403 5.31653 5.331404 5.279785 5.322233 5.35623 0.0398932 5.254171 5.234304 5.242741 5.23366 5.33324 5.340423 5.279339 5.327615 5.36113 8 3840 20.874610 20.575229 20.949063 21.2338 21.3108 21.226945 21.172203 21.090574 21.5231 0.0398932 21.018761 20.719807 21.093995 21.37 21.5134 21.350097 21.339856 21.222387 21.6437 16 15360 80.477027 77.770571 79.942580 80.6928 80.8052 80.252695 79.979215 78.756570 82.4979 0.0398932 81.294605 78.600372 80.734099 81.59 82.0563 81.313443 81.033268 79.554612 83.464 32 61440 300.554978 294.133641 296.600745 300.753 295.017 299.304962 295.501227 294.675413 302.751 0.0398932 306.291876 297.862738 301.675679 306.204 303.073 304.798141 300.830586 298.760158 309.291 P(X,Y,Z) = X^6 Y^2 1 60 1.100041 1.106770 1.117970 1.0766 1.10598 1.071863 1.006941 1.102246 1.10594 0.199466 0.914440 0.921556 0.930401 0.909982 0.921266 0.891489 0.823397 0.920080 0.918116 2 240 7.200181 7.462701 7.209442 6.99298 7.69545 7.201891 6.949529 7.024997 7.42179 0.199466 7.108526 7.382998 7.071045 6.90832 7.61121 7.086896 6.931849 6.904121 7.33011 4 960 28.508105 29.925511 29.629409 28.6221 29.1519 29.405752 27.847462 28.848731 29.0369 0.199466 28.712953 30.048820 29.727316 28.9565 29.3696 29.540519 28.140394 28.846982 29.0376 8 3840 107.619318 119.651539 116.259170 105.734 118.657 114.396545 106.380742 116.926724 113.453 0.199466 109.647944 120.720473 117.742664 107.138 120.124 116.332834 108.434469 117.925728 114.916 16 15360 389.089964 442.808928 421.002132 383.339 438.811 399.073660 380.426869 435.887683 419.82 0.199466 403.413189 451.635716 432.314174 391.764 452.97 414.971177 392.878433 444.337233 428.715 32 61440 1324.972194 1601.523470 1464.956900 1381.45 1499.15 1337.243812 1335.446155 1530.296523 1480.22 0.199466 1424.890632 1659.551635 1536.429412 1427.18 1604.82 1424.248776 1394.568050 1589.313723 1526.37 P(X,Y,Z) = Z^8 1 60 12.558955 11.512368 11.597663 12.3102 12.1502 9.833057 13.014701 13.142346 12.647 1.39626 11.540817 10.603933 11.374178 11.0502 10.8879 8.688734 12.023011 12.079883 11.7058 2 240 48.269515 44.722842 44.242518 46.9842 49.0608 44.648893 46.355971 46.266616 44.5728 1.39626 47.567631 43.772094 44.002284 46.2214 48.3243 44.524589 45.909860 45.420747 44.6102 4 960 188.944896 190.036925 182.951027 189.693 192.551 186.963646 196.552749 199.490454 188.777 1.39626 189.363037 190.219264 184.760041 190.066 193.16 190.656688 196.817072 199.917130 190.202 8 3840 768.210997 761.448375 694.407945 767.421 766.637 683.209650 793.492859 792.173588 719.482 1.39626 773.502129 767.706429 705.232205 773.073 772.927 697.906584 798.024800 796.653337 733.249 16 15360 2937.320454 2866.373201 2521.513556 2904.85 2903.31 2481.768377 3042.240135 3035.687142 2571.07 1.39626 2994.752384 2927.369626 2608.679668 2950.74 2948.1 2564.768557 3081.431287 3075.510967 2682.35 32 61440 10402.241787 10003.147126 9010.133623 10417.9 10532 8915.857623 11270.511942 11213.181743 8534.92 1.39626 10841.058194 10380.821474 9509.429309 10766.3 10869.3 9398.896529 11566.153454 11522.414561 9304.78 P(X,Y,Z) = X^6 Z^4 1 60 0.535534 0.545740 0.544765 0.513342 0.536109 0.510174 0.477479 0.537841 0.532085 0.0543999 0.489627 0.499796 0.497414 0.477837 0.488402 0.464922 0.428507 0.487369 0.481508 2 240 1.908368 1.729115 1.771812 1.83221 1.88225 1.819525 1.874979 1.807146 1.80544 0.0543999 1.880581 1.707572 1.733405 1.79078 1.84546 1.813527 1.849626 1.763624 1.76435 4 960 7.432264 7.338622 7.559892 7.24722 7.30878 7.189922 7.472763 7.385683 7.47159 0.0543999 7.467753 7.362297 7.608230 7.27126 7.32322 7.224309 7.550094 7.428495 7.52169 8 3840 29.283062 29.218832 29.225624 29.0501 28.7251 28.781759 28.958655 29.345232 29.5036 0.0543999 29.641336 29.680567 29.440800 29.4164 29.1063 29.163549 29.342368 29.756214 29.795 16 15360 109.207737 101.680832 109.240980 105.948 104.505 108.322570 105.096801 102.928693 109.23 0.0543999 112.641096 105.324213 111.097441 108.873 106.771 110.547164 107.337953 106.683247 111.677 32 61440 370.931268 345.186243 395.752739 367.25 371.115 388.679936 373.758081 337.171699 388.303 0.0543999 398.107413 364.825006 408.061223 382.628 381.513 401.864209 386.513702 362.963116 409.102 P(X,Y,Z) = X^4 Y^6 Z^2 1 60 0.054390 0.052737 0.054867 0.0559693 0.0551358 0.055420 0.053483 0.054342 0.056293 0.00418461 0.050410 0.048797 0.050940 0.0523522 0.0515365 0.051897 0.050454 0.052347 0.0530699 2 240 0.128784 0.130449 0.130025 0.127279 0.133344 0.130672 0.129279 0.130706 0.13053 0.00418461 0.125225 0.127226 0.126524 0.124288 0.130158 0.127430 0.126787 0.127550 0.127624 4 960 0.546054 0.548033 0.548268 0.540449 0.556833 0.553163 0.544791 0.553073 0.555952 0.00418461 0.546502 0.549282 0.547319 0.542485 0.558078 0.553049 0.544801 0.552764 0.555797 8 3840 2.175492 2.160661 2.184149 2.20167 2.21933 2.205962 2.199782 2.213682 2.22879 0.00418461 2.191217 2.176154 2.201004 2.21249 2.23786 2.217186 2.216639 2.225638 2.24127 16 15360 8.346803 8.174116 8.278634 8.36402 8.55079 8.298633 8.379730 8.336420 8.56076 0.00418461 8.434286 8.255952 8.367511 8.44658 8.67978 8.418076 8.469002 8.414209 8.64073 32 61440 31.287048 31.082767 30.609584 31.4139 31.1039 30.731270 31.437911 31.165558 31.8333 0.00418461 31.914814 31.428225 31.210656 31.8727 31.9537 31.364899 31.877921 31.559190 32.332 P(X,Y,Z) = X^2 Y^4 Z^8 1 60 0.033381 0.031740 0.031859 0.0329841 0.0326373 0.028970 0.034303 0.034552 0.0337932 0.00195282 0.031896 0.030365 0.031183 0.0312365 0.0308748 0.027328 0.032905 0.033072 0.0324421 2 240 0.053247 0.052397 0.053491 0.0524535 0.0545324 0.053750 0.053329 0.053523 0.0537677 0.00195282 0.051574 0.050967 0.051935 0.0511773 0.0530206 0.052522 0.051870 0.051917 0.0522998 4 960 0.257311 0.255800 0.255381 0.25746 0.262491 0.259326 0.259826 0.263120 0.260615 0.00195282 0.257093 0.255194 0.255197 0.25797 0.263535 0.260826 0.259973 0.264019 0.261191 8 3840 1.034921 1.025788 1.007725 1.04211 1.05469 0.999320 1.044968 1.050825 1.03938 0.00195282 1.040340 1.032020 1.014817 1.05179 1.06373 1.008668 1.051315 1.056918 1.04738 16 15360 3.964248 3.878610 3.791094 3.90763 3.93558 3.771938 3.934367 3.928590 3.966 0.00195282 4.004094 3.923181 3.835466 3.95692 3.98087 3.815473 3.993780 3.974006 4.03421 32 61440 14.685772 14.397186 14.053483 14.3198 14.6209 14.234184 14.324449 14.567073 14.2449 0.00195282 14.949399 14.622507 14.252639 14.6584 14.9502 14.406169 14.659214 14.833207 14.684 P(X,Y,Z) = X^16 1 60 8.049185 8.360506 8.341333 7.36393 8.13086 7.335811 6.115087 7.961292 7.76981 0.739198 7.663869 7.956460 7.866003 7.54006 7.66802 6.995111 5.554122 7.322785 7.12785 2 240 23.479818 23.199356 23.242645 22.1066 25.286 23.046605 22.026583 21.958203 24.2799 0.739198 23.559739 23.288656 22.883701 22.0176 25.1173 22.625749 21.961466 21.549187 23.8468 4 960 97.184796 103.322208 105.205531 92.9229 98.6098 100.092564 97.363133 98.214306 102.177 0.739198 97.997432 103.227874 105.069128 94.4703 98.9052 100.131173 99.384658 98.046756 102.45 8 3840 385.866807 427.631655 426.338456 360.771 412.601 409.612494 365.045511 414.723043 414.974 0.739198 392.239000 428.417447 427.141291 365.945 414.159 411.390255 372.462937 416.183434 416.658 16 15360 1421.920884 1674.727726 1672.563652 1374.17 1599.82 1581.376590 1348.746178 1608.813421 1616.37 0.739198 1470.053927 1682.943722 1680.854106 1406.69 1615.87 1597.242593 1386.455722 1621.832072 1629.5 32 61440 4926.549797 6436.793262 6421.997584 5042.15 5943.22 5873.118605 4953.314456 5926.027804 5978.45 0.739198 5253.269364 6507.097050 6494.636263 5259.77 6071.67 5982.859594 5217.396491 6041.520228 6094.57 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 60 109.357705 106.564418 108.570581 108.465 109.295 102.719624 104.655060 110.542222 110.792 12.5664 98.254896 95.656572 98.287187 98.0986 98.1212 92.041912 94.391274 100.743965 100.202 2 240 434.489858 421.745011 422.054651 418.911 441.805 426.360622 422.320927 422.925602 431.995 12.5664 427.133699 416.116811 414.153171 412.305 435.638 420.857298 417.524926 414.620257 426.303 4 960 1718.877938 1723.877326 1727.908979 1717.63 1722.97 1729.007389 1727.451865 1734.438035 1739.6 12.5664 1725.240881 1730.786883 1733.139806 1727.82 1732.74 1739.384294 1737.886611 1741.153195 1747.04 8 3840 6779.838460 6762.399123 6778.255813 6792.69 6828.64 6766.405202 6786.552398 6817.801097 6859.56 12.5664 6855.665364 6840.952922 6844.542370 6863.25 6915.25 6846.695687 6868.836279 6883.723482 6931.67 16 15360 25376.214268 24827.937354 25158.639944 25217.2 25267.8 24968.561866 24983.175234 25197.951851 25446.7 12.5664 25960.509224 25388.362890 25660.977174 25721.3 25896.9 25516.278978 25548.774330 25703.796666 26045.1 32 61440 89505.962526 88925.697939 90213.639856 90299 88933.7 89743.756773 89190.428983 89929.479285 89265.5 12.5664 93673.571831 92084.040768 93402.302294 93524.5 93144.3 92903.244310 92469.983952 93234.822123 93411.9 P(X,Y,Z) = X 1 60 2.109434 1.623895 1.677234 1.14299 -1.76599 1.267725 -0.041271 1.848924 1.23984 0 3.184188 2.858103 2.369472 4.43975 2.62363 2.527892 1.555562 3.471334 1.73441 2 240 -4.025269 -3.608632 -5.393757 -6.83057 0.760967 -5.654969 1.906922 4.704119 5.81175 0 5.181191 3.855766 5.866064 7.57594 2.15731 6.649198 2.445235 4.704929 6.34519 4 960 1.175334 4.370247 0.872389 7.16316 -0.225511 -3.385400 -0.166168 -7.282928 0.325491 0 10.595888 6.493367 1.046480 8.34125 2.22193 4.568518 2.022094 11.235202 13.395 8 3840 -26.148397 -7.005237 -35.498806 20.369 12.747 -2.920306 10.921839 -2.993371 -19.7326 0 31.022790 27.227239 35.540803 43.4329 18.343 20.856301 29.924692 3.692674 20.0805 16 15360 -89.181937 -56.935094 -48.803110 -100.703 12.5074 5.430093 -78.964927 25.181703 56.2061 0 120.690811 94.593961 101.294312 123.474 110.224 19.573982 148.046917 28.826317 144.098 32 61440 -524.735581 21.745458 164.654138 -296.366 168.509 -29.802682 -226.993203 19.598290 44.0635 0 524.819474 440.245174 208.609892 297.105 208.979 172.888355 267.254020 185.988614 528.622 P(X,Y,Z) = Y 1 60 0.704275 1.765685 1.332579 1.26428 1.88202 0.326205 1.708903 1.842037 -1.34203 0 0.760275 1.874897 2.031149 2.0671 2.82158 2.495787 2.378092 4.065203 1.81084 2 240 4.936839 2.731159 -1.884045 -4.00028 0.14514 -1.223669 -2.320606 -0.067766 0.121244 0 5.630488 4.387983 1.958992 5.29669 3.27562 5.039147 2.627720 0.802068 3.19395 4 960 -8.694720 -5.193930 -15.493372 1.47664 -4.90947 -1.640902 -3.417387 1.103682 -0.382546 0 18.877058 5.241863 15.756673 4.18574 15.194 4.044570 7.833886 7.966108 5.99006 8 3840 5.924374 -0.877719 19.524232 -54.6396 -71.7799 -35.238887 -60.920608 -40.936277 -43.4326 0 6.988398 52.051171 29.735026 54.6987 71.8832 41.051991 61.097627 46.011910 52.5484 16 15360 -62.831252 -199.882458 -75.935033 -247.217 -416.541 -183.548535 -372.878454 -352.894364 -349.162 0 191.733481 318.313894 255.183287 271.713 416.954 184.732595 375.146944 360.330197 353.173 32 61440 -572.033460 -1040.428864 -847.877422 -553.175 -1646.05 -472.376730 -1074.145768 -1220.417213 -1611.72 0 846.253709 1113.764657 1169.779730 604.161 1652.4 511.228176 1183.538212 1245.715065 1611.73 P(X,Y,Z) = Z 1 60 -1.935512 1.214933 1.038663 1.69442 0.893098 0.173645 1.157644 1.788695 2.68834 0 3.017747 2.791440 5.292454 3.22236 1.20853 1.051376 3.852417 3.055654 4.17764 2 240 -0.164030 -7.175611 -3.691764 -6.38356 1.62695 -2.076794 -7.332626 -5.481431 2.14513 0 4.313297 7.263863 4.329469 7.18079 2.32164 3.581837 10.712094 5.570292 5.55097 4 960 3.442354 3.978135 15.729183 -10.027 3.24448 4.266254 11.864279 4.577872 9.47197 0 8.016382 9.371945 15.842476 12.6182 13.3902 4.268560 13.420882 5.227106 10.9768 8 3840 9.930970 37.787763 22.312589 61.6964 78.2317 72.170730 54.901529 42.462536 67.4985 0 68.231412 77.426263 88.613043 64.978 84.8041 73.057245 55.487868 56.895916 76.8438 16 15360 232.087713 240.635802 208.662510 461.196 571.056 265.873396 398.541114 287.597866 394.633 0 407.621849 366.029397 463.580809 464.868 571.056 270.825480 423.456124 359.330049 400.551 32 61440 1557.764222 1845.664758 1264.884876 1599.83 2191.06 1028.185218 1961.132592 1913.653465 2104.8 0 1676.543443 1938.166454 1519.396521 1710.4 2207.67 1030.200760 1961.170057 2019.458533 2138.84 P(X,Y,Z) = X^2 1 60 36.539625 36.299696 36.745746 35.7174 36.6207 34.600776 33.619017 36.748571 36.7011 4.18879 32.917580 32.714604 33.213563 32.6176 32.9585 31.123287 30.083685 33.251957 33.0233 2 240 144.055277 141.362768 141.001062 138.769 149.584 141.517263 139.693573 139.041342 144.454 4.18879 142.147937 139.868049 138.278164 136.605 147.513 139.498338 138.462042 136.225629 142.057 4 960 570.330560 584.124831 588.123705 562.544 574.137 574.475683 567.268658 573.177865 581.148 4.18879 573.786938 585.699268 589.567155 566.971 576.515 576.307077 573.181676 573.917095 582.726 8 3840 2227.713642 2341.197028 2320.664568 2180.31 2319.8 2280.142336 2183.090635 2320.981040 2302.4 4.18879 2258.999556 2360.753967 2338.598964 2205.83 2342.54 2305.139817 2215.604697 2340.253210 2323.17 16 15360 8238.509471 8693.255922 8689.850228 8060.65 8686.36 8412.142970 7984.525428 8616.142855 8644.72 4.18879 8483.141962 8844.548338 8826.807069 8234.81 8869.33 8596.773752 8173.494735 8779.228512 8794.58 32 61440 28601.652151 31602.813219 31595.169746 29001.9 30853.4 29945.386858 28744.960789 30320.960050 30992.3 4.18879 30379.311442 32531.195988 32515.286575 30021.9 32089.6 31005.128888 29815.246211 31479.277037 32023.6 P(X,Y,Z) = Y^2 Z^2 1 60 7.241063 6.898785 7.166467 7.41165 7.28068 7.026960 7.219736 7.299628 7.47091 0.837758 6.457677 6.128537 6.438278 6.65386 6.53106 6.298717 6.579655 6.787694 6.81021 2 240 29.036695 28.224541 28.465810 27.9273 29.1535 28.954806 28.264898 28.591518 29.2471 0.837758 28.445107 27.829022 27.892970 27.511 28.6958 28.593080 27.908868 28.041454 28.8928 4 960 114.499349 113.216406 114.231522 115.214 115.638 117.302421 116.307008 117.608387 117.785 0.837758 114.528579 113.501585 114.366140 115.965 116.549 118.128965 116.808035 118.317046 118.433 8 3840 447.826131 442.321942 449.449394 459.107 453.592 453.055093 457.308557 447.822652 463.444 0.837758 452.588549 447.703953 454.129049 465.147 460.447 458.203080 463.883875 452.452555 468.209 16 15360 1671.492203 1617.483999 1663.965389 1662.76 1646.12 1674.121589 1636.140259 1639.344748 1715.72 0.837758 1701.745216 1652.255424 1698.755276 1705.08 1689.06 1706.479469 1685.923609 1668.615444 1762.26 32 61440 5992.520877 5831.927692 5944.001623 5776.73 5792.25 6077.957858 5637.811840 5972.425330 5931.32 0.837758 6164.187013 6004.072632 6135.734134 6047.4 6087.25 6259.535780 5899.971693 6140.978425 6270.39 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 0.11968 0.119680 0.119680 0.119680 0.11968 0.11968 0.119680 0.119680 0.119680 0.11968 2 240 4.091415 3.997149 4.013566 3.9867 4.18044 4.061091 4.015210 4.020989 4.09828 0.11968 4.008903 3.935805 3.927682 3.9147 4.10912 4.002806 3.963184 3.935031 4.02987 4 960 15.836719 15.832689 15.865568 15.7357 16.0393 15.960561 15.884475 16.031815 16.0396 0.11968 15.851167 15.838341 15.863310 15.7822 16.0831 16.000420 15.916640 16.051686 16.0545 8 3840 62.919801 62.726149 62.700905 63.4411 64.2329 62.841327 63.511574 63.858646 64.1264 0.11968 63.360478 63.116742 63.101119 63.8935 64.7913 63.292612 63.956041 64.227331 64.5068 16 15360 242.373209 236.577825 238.329283 240.271 243.692 238.011835 240.032060 240.084856 245.151 0.11968 245.159656 239.308890 240.708148 242.904 246.895 240.996066 242.865236 242.607084 248.119 32 61440 897.730352 886.140590 889.573325 895.798 897.72 889.320003 891.615718 892.014321 900.939 0.11968 917.411549 899.821554 903.597280 910.735 918.028 903.931001 906.261407 907.066210 920.822 P(X,Y,Z) = Y^2 Z^4 1 60 2.001381 1.906777 1.980763 2.04853 2.01233 1.942204 1.995486 2.017567 2.06491 0.359039 1.658525 1.567915 1.654343 1.71324 1.6795 1.615824 1.695197 1.755138 1.75836 2 240 12.413524 12.001390 12.122159 12.0333 12.4999 12.368671 12.045036 12.169989 12.4446 0.359039 12.155641 11.814213 11.879941 11.85 12.2815 12.237330 11.887622 11.926131 12.2934 4 960 48.160632 47.817417 47.968364 48.2594 48.9829 49.103054 49.016914 50.084904 49.5735 0.359039 48.145202 47.842119 48.046509 48.5724 49.3869 49.593336 49.230365 50.361547 49.864 8 3840 188.722024 189.210520 186.515706 192.107 192.906 184.848284 193.396983 192.556312 192.141 0.359039 190.552634 191.179202 188.668798 194.823 195.483 187.462165 195.898551 194.305430 194.37 16 15360 702.086550 700.784971 677.481117 687.779 703.12 676.754965 692.263007 709.517537 705.082 0.359039 715.052939 714.694675 695.190555 706.844 719.008 690.260027 712.033506 721.628094 725.99 32 61440 2506.872679 2515.727246 2398.554975 2353.61 2510.85 2453.776918 2398.387714 2582.075840 2412.38 0.359039 2578.624488 2590.358368 2482.748281 2478.04 2627.54 2522.821476 2507.655621 2657.501473 2562.53 P(X,Y,Z) = Z^6 1 60 14.653629 14.157509 14.217233 14.2979 14.4291 12.860453 14.308174 15.029443 14.7156 1.7952 13.145076 12.695138 13.003021 12.7582 12.7855 11.302953 12.797280 13.470307 13.194 2 240 62.650223 58.590322 58.420581 60.9457 63.5221 59.102523 60.655784 60.391692 59.0347 1.7952 61.640553 57.453364 57.795112 59.9563 62.5057 58.829445 59.942363 59.219366 58.6772 4 960 244.332992 245.249320 238.264659 244.724 248.463 241.873470 252.921318 256.457735 244.897 1.7952 244.826747 245.455249 240.178582 245.371 249.411 246.059012 253.473216 257.224471 246.603 8 3840 988.474071 978.323623 901.046161 988.288 985.317 887.683354 1018.636840 1015.001328 933.43 1.7952 995.890143 987.290857 914.380157 996.679 994.521 906.071802 1025.396589 1021.700171 950.398 16 15360 3758.219648 3651.484286 3263.589643 3708.27 3700.78 3218.172777 3867.530030 3851.223979 3336.98 1.7952 3836.664283 3736.137734 3371.412611 3773.72 3762.99 3320.969494 3925.101165 3909.245230 3476.26 32 61440 13242.027925 12672.568920 11638.731655 13202.2 13376.6 11531.368810 14182.737772 14086.753372 11100.5 1.7952 13830.587888 13183.302494 12240.894928 13682.2 13826 12107.230475 14600.707935 14520.451385 12065.8 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 -0.012354 0.057216 0.037002 -0.0720105 0.0628103 -0.011929 0.033218 0.025691 -0.0223537 0 0.035068 0.077841 0.047912 0.0754144 0.0628438 0.029408 0.045870 0.061017 0.0640479 4 960 0.030544 0.293266 0.043089 0.0777158 0.241537 0.052505 -0.164521 -0.163015 -0.091074 0 0.035922 0.322452 0.045080 0.0781909 0.330891 0.052708 0.301891 0.475750 0.174794 8 3840 0.353528 0.233939 -0.785559 0.958962 0.725915 1.012188 -0.193991 -0.356083 -0.747068 0 0.371150 0.296078 0.790958 1.551 1.31852 1.076550 0.368158 1.062895 0.861139 16 15360 1.811973 2.319294 0.263173 2.95282 4.48496 0.679610 0.612494 2.247570 0.881208 0 2.402586 2.509384 2.129751 2.99265 5.44443 2.958584 1.147600 4.591093 3.66659 32 61440 2.295759 10.333080 0.266666 4.0371 14.7448 -9.049052 6.962863 14.530760 -5.81314 0 7.563988 12.792280 1.393796 13.6357 14.9192 13.973808 10.739946 17.738385 18.0071 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 0.0398932 0.039893 0.039893 0.039893 0.0398932 0.0398932 0.039893 0.039893 0.039893 0.0398932 2 240 1.353791 1.349802 1.342632 1.32028 1.39119 1.352542 1.338863 1.351717 1.37337 0.0398932 1.323639 1.328935 1.313431 1.29745 1.37013 1.330708 1.320905 1.323230 1.35163 4 960 5.277928 5.250313 5.272976 5.26034 5.34177 5.355131 5.296185 5.338599 5.37007 0.0398932 5.281651 5.260648 5.270366 5.28209 5.36184 5.367254 5.301426 5.347025 5.37682 8 3840 20.877741 20.571678 20.954484 21.2359 21.2952 21.226633 21.167264 21.070991 21.5132 0.0398932 21.026969 20.722616 21.103769 21.377 21.5037 21.355976 21.340043 21.207055 21.6381 16 15360 80.443909 77.722904 79.902496 80.6572 80.7479 80.215801 79.932330 78.714134 82.4498 0.0398932 81.271006 78.563412 80.704885 81.5629 82.0111 81.284682 80.997092 79.521877 83.4268 32 61440 300.476778 294.036518 296.511715 300.675 294.914 299.227929 295.409020 294.588375 302.659 0.0398932 306.229453 297.780251 301.602597 306.14 302.991 304.733932 300.753101 298.688495 309.216 P(X,Y,Z) = X^6 Y^2 1 60 3.821746 3.835585 3.896816 3.74222 3.85764 3.728077 3.435304 3.812961 3.84114 0.199466 3.671846 3.687026 3.739289 3.66863 3.71615 3.602737 3.297970 3.687461 3.68639 2 240 6.906002 7.010056 6.826987 6.66688 7.27565 6.848046 6.689965 6.723154 7.03227 0.199466 6.808259 6.931558 6.686711 6.56846 7.1846 6.744976 6.656791 6.594049 6.92841 4 960 28.338837 29.618336 29.399765 28.3839 28.9171 29.126554 27.737112 28.613272 28.8618 0.199466 28.540413 29.735620 29.489375 28.7044 29.1193 29.251657 28.031169 28.615047 28.8724 8 3840 107.640573 119.363284 116.123313 105.756 118.408 114.291316 106.369061 116.723396 113.385 0.199466 109.642034 120.425760 117.581501 107.146 119.856 116.187863 108.400308 117.715901 114.824 16 15360 389.221155 442.600870 421.000166 383.487 438.697 399.220136 380.551527 435.720112 419.84 0.199466 403.496548 451.397294 432.260428 391.906 452.793 415.028419 392.955488 444.154311 428.705 32 61440 1325.226306 1601.422771 1465.093775 1381.61 1499.21 1337.606089 1335.691931 1530.206828 1480.35 0.199466 1425.070220 1659.388251 1536.491715 1427.35 1604.75 1424.492872 1394.776682 1589.193090 1526.48 P(X,Y,Z) = Z^8 1 60 10.261589 9.918753 9.949332 9.9961 10.0972 8.974143 10.012622 10.530766 10.2956 1.39626 9.074270 8.764839 8.976746 8.78416 8.80815 7.747709 8.815991 9.294786 9.09191 2 240 48.657244 45.331437 45.001869 47.349 49.4347 45.493510 47.042013 46.860684 45.4143 1.39626 47.905490 44.413767 44.620978 46.587 48.6675 45.312244 46.519308 45.974372 45.2419 4 960 189.097325 190.153153 183.538074 189.806 192.731 187.222651 196.512190 199.429063 189.163 1.39626 189.504640 190.320180 185.240669 190.217 193.378 190.768091 196.834740 199.905980 190.555 8 3840 768.086879 761.214068 694.800556 767.416 766.524 683.723537 793.216383 791.760909 719.897 1.39626 773.421991 767.529367 705.578891 773.144 772.885 698.373267 797.813387 796.302300 733.608 16 15360 2936.771229 2865.626892 2521.733758 2904.2 2902.64 2482.107427 3041.209918 3034.600014 2571.49 1.39626 2994.297514 2926.739382 2608.807230 2950.21 2947.51 2565.024115 3080.530207 3074.540953 2682.69 32 61440 10401.389714 10002.143806 9010.268076 10416.9 10531.2 8916.052399 11268.884032 11211.588731 8535.4 1.39626 10840.337457 10379.954449 9509.337915 10765.4 10868.6 9398.852940 11564.694959 11520.988972 9305.12 P(X,Y,Z) = X^6 Z^4 1 60 0.405281 0.391858 0.392776 0.394374 0.398605 0.353616 0.395266 0.416066 0.40638 0.0543999 0.359249 0.347154 0.355348 0.347303 0.348414 0.305917 0.348667 0.367795 0.359522 2 240 1.998517 1.877387 1.911672 1.93157 2.0195 1.930410 1.951064 1.907639 1.9314 0.0543999 1.973513 1.854087 1.877749 1.89567 1.9859 1.911437 1.929608 1.868778 1.89803 4 960 7.451344 7.383310 7.577325 7.27159 7.3458 7.228013 7.498938 7.419907 7.49212 0.0543999 7.487462 7.404630 7.620839 7.29602 7.36149 7.262451 7.575119 7.458705 7.53865 8 3840 29.318705 29.265260 29.232649 29.0631 28.7788 28.787674 28.987851 29.394029 29.5137 0.0543999 29.675882 29.718155 29.447730 29.4283 29.1568 29.167613 29.368484 29.799154 29.8063 16 15360 109.241424 101.783450 109.255250 105.976 104.587 108.314981 105.143489 103.025264 109.233 0.0543999 112.671335 105.411298 111.107353 108.894 106.848 110.538148 107.382762 106.763205 111.682 32 61440 370.986790 345.319648 395.789399 367.309 371.207 388.677011 373.815358 337.313640 388.292 0.0543999 398.152656 364.939742 408.088777 382.683 381.607 401.853765 386.572821 363.075882 409.083 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 0.00418461 0.004185 0.004185 0.004185 0.00418461 0.00418461 0.004185 0.004185 0.004185 0.00418461 2 240 0.160409 0.161990 0.160213 0.156242 0.165547 0.160669 0.159688 0.161615 0.163897 0.00418461 0.157287 0.160121 0.157220 0.154088 0.163866 0.158330 0.158096 0.158792 0.1618 4 960 0.548061 0.548854 0.549923 0.545964 0.557956 0.556125 0.545596 0.553130 0.556666 0.00418461 0.548818 0.550236 0.549534 0.548247 0.559661 0.556746 0.546081 0.553261 0.556678 8 3840 2.175705 2.159216 2.185152 2.20208 2.21925 2.207382 2.198641 2.211005 2.22767 0.00418461 2.191920 2.175185 2.202391 2.2135 2.23845 2.219520 2.215888 2.223444 2.2405 16 15360 8.345187 8.169586 8.275050 8.36273 8.54452 8.295008 8.375193 8.330108 8.55586 0.00418461 8.433617 8.252439 8.365085 8.44605 8.67482 8.415433 8.465609 8.408972 8.637 32 61440 31.280821 31.072790 30.600002 31.409 31.0936 30.723384 31.427607 31.154467 31.8224 0.00418461 31.910449 31.419813 31.202673 31.8692 31.9457 31.358314 31.869232 31.549656 32.3228 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 0.00195282 0.001953 0.001953 0.001953 0.00195282 0.00195282 0.001953 0.001953 0.001953 0.00195282 2 240 0.098710 0.095514 0.096278 0.096841 0.100324 0.098310 0.095854 0.096663 0.0986285 0.00195282 0.097490 0.094749 0.095241 0.0961842 0.0993261 0.098275 0.095443 0.095516 0.0982313 4 960 0.257676 0.256278 0.255664 0.257336 0.262133 0.259375 0.260667 0.264174 0.26161 0.00195282 0.257526 0.255870 0.255614 0.2581 0.263195 0.260879 0.261013 0.265014 0.262314 8 3840 1.034166 1.025729 1.007461 1.04202 1.05391 0.999253 1.045881 1.050588 1.03942 0.00195282 1.039832 1.032148 1.014734 1.05182 1.06323 1.008778 1.052539 1.056861 1.04759 16 15360 3.962607 3.877510 3.789056 3.90564 3.9344 3.770492 3.932920 3.928141 3.96305 0.00195282 4.002936 3.922571 3.833936 3.95549 3.98021 3.814441 3.992657 3.973804 4.03168 32 61440 14.681571 14.393677 14.050163 14.3153 14.6179 14.230395 14.321835 14.565735 14.2406 0.00195282 14.945864 14.619703 14.249942 14.6546 14.9479 14.403049 14.657110 14.832418 14.6806 P(X,Y,Z) = X^16 1 60 2.744386 2.754278 2.798231 2.68727 2.77013 2.676994 2.466979 2.738114 2.75831 0.739198 2.051158 2.062240 2.097753 2.06469 2.08449 2.006889 1.787339 2.067390 2.06054 2 240 26.651318 26.411691 26.460073 25.1158 28.6887 26.183517 25.098040 25.068843 27.5798 0.739198 26.774477 26.563981 26.130412 25.0731 28.5721 25.803857 25.104634 24.684288 27.1787 4 960 97.632187 103.602651 105.279861 93.7604 98.709 100.361628 97.728355 98.695927 102.385 0.739198 98.445895 103.590045 105.214423 95.1872 99.0313 100.414805 99.685120 98.558061 102.685 8 3840 385.663335 427.535110 426.152460 360.812 412.527 409.320991 364.827745 414.612400 414.808 0.739198 392.069025 428.383776 427.018443 365.985 414.155 411.181467 372.262097 416.146183 416.567 16 15360 1421.395483 1674.099320 1671.948042 1373.48 1599.17 1580.489528 1347.956346 1608.104753 1615.72 0.739198 1469.629175 1682.428282 1680.345502 1406.04 1615.4 1596.522182 1385.718803 1621.267293 1628.98 32 61440 4925.712775 6435.619206 6420.841179 5041.04 5941.83 5871.564382 4952.149608 5924.565839 5977.37 0.739198 5252.635046 6506.132347 6493.684990 5258.67 6070.61 5981.570332 5216.179730 6040.359038 6093.73 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. 08-Oct-2025 17:15:18