21 December 2011 04:36:06 PM DUNAVANT_PRB: C++ version Test the DUNAVANT library. TEST01 DUNAVANT_RULE_NUM returns the number of rules; DUNAVANT_DEGREE returns the degree of a rule; DUNAVANT_ORDER_NUM returns the order of a rule. Number of available rules = 20 Rule Degree Order 1 1 1 2 2 3 3 3 4 4 4 6 5 5 7 6 6 12 7 7 13 8 8 16 9 9 19 10 10 25 11 11 27 12 12 33 13 13 37 14 14 42 15 15 48 16 16 52 17 17 61 18 18 70 19 19 73 20 20 79 TEST02 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 20 Rule Order Sum of weights 1 1 1 2 3 1 3 4 1 4 6 1 5 7 1 6 12 1 7 13 1 8 16 1 9 19 1 10 25 1 11 27 1 12 33 1 13 37 1 14 42 1 15 48 1 16 52 1 17 61 1 18 70 1 19 73 1 20 79 1 TEST03 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the triangle. In this test, we simply check that, for each quadrature point, the barycentric coordinates add up to 1. Rule Suborder Sum of coordinates 1 1 0.9999999999999989 2 1 1.000000000000001 3 2 0.9999999999999989 1 4 2 1 1.000000000000001 5 3 0.9999999999999989 1 0.999999999999999 6 3 0.999999999999999 1 1 7 4 0.9999999999999989 1 1 1 8 5 0.9999999999999989 1 1 0.9999999999999999 1 9 6 0.9999999999999989 1.000000000000001 1.000000000000001 1.000000000000001 1.000000000000001 1 10 6 0.9999999999999989 0.999999999999999 1 1 1 0.999999999999999 11 7 0.999999999999999 1 0.9999999999999989 0.999999999999999 1 1.000000000000001 1 12 8 1 0.9999999999999989 1 1 0.9999999999999991 1 1 1 13 10 0.9999999999999989 1.000000000000001 1 1.000000000000001 0.999999999999999 1 1 1 1 1 14 10 1.000000000000001 1 1.000000000000001 0.999999999999999 1.000000000000001 1 1 1 1 1 15 11 1 1.000000000000001 0.999999999999999 1 1 0.999999999999999 0.999999999999999 1 1 1 1.000000000000001 16 13 0.9999999999999989 0.9999999999999991 0.9999999999999989 0.9999999999999989 1 1 1 1 1 1 1 1.000000000000001 0.999999999999999 17 15 0.9999999999999989 1 1.000000000000001 1.000000000000001 1 1.000000000000001 0.999999999999999 1 1 1 1 1.000000000000001 1 0.999999999999999 1 18 17 0.9999999999999989 0.999999999999999 1 1.000000000000001 1 1 1.000000000000001 0.9999999999999991 1 1.000000000000001 1 1 1.000000000000001 0.999999999999999 1 1 0.9999999999999999 19 17 0.9999999999999989 0.9999999999999991 1.000000000000001 1 1.000000000000001 1.000000000000001 1 1.000000000000001 1.000000000000001 1 1 1 1 1.000000000000001 1 1 1 20 19 0.9999999999999989 1 1.000000000000001 1.000000000000001 0.999999999999999 0.9999999999999989 1 0.9999999999999989 0.9999999999999999 1 1 1 1 1 1 1 0.9999999999999989 1 1.000000000000001 TEST04 DUNAVANT_RULE returns the points and weights of a Dunavant rule for the unit triangle. This routine uses those rules to estimate the integral of monomomials in the unit triangle. Integrate 2 * X^0 * Y^0 Rule QUAD ERROR 1 1 0 2 0.9999999999999989 1.110223024625157e-15 3 0.9999999999999991 8.881784197001252e-16 4 0.999999999999999 9.992007221626409e-16 5 0.999999999999999 9.992007221626409e-16 6 1.000000000000002 1.998401444325282e-15 7 0.9999999999999981 1.887379141862766e-15 8 1 0 9 0.9999999999999959 4.107825191113079e-15 10 0.9999999999999992 7.771561172376096e-16 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 0.9999999999999989 1.110223024625157e-15 2 1 0 3 0.9999999999999998 2.220446049250313e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999983 1.665334536937735e-15 6 1.000000000000002 1.77635683940025e-15 7 0.9999999999999982 1.77635683940025e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999963 3.663735981263017e-15 10 0.999999999999999 9.992007221626409e-16 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 0.6666666666666653 0.3333333333333347 2 1 2.220446049250313e-16 3 1 0 4 1 2.220446049250313e-16 5 0.9999999999999978 2.220446049250313e-15 6 1.000000000000002 2.442490654175344e-15 7 0.9999999999999973 2.664535259100376e-15 8 0.9999999999999997 3.33066907387547e-16 9 0.9999999999999966 3.441691376337985e-15 10 0.9999999999999989 1.110223024625157e-15 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 0.3703703703703692 0.6296296296296308 2 1.018518518518519 0.01851851851851904 3 1 0 4 1.000000000000001 1.332267629550188e-15 5 0.9999999999999976 2.442490654175344e-15 6 1.000000000000004 3.996802888650564e-15 7 0.999999999999996 3.996802888650564e-15 8 0.9999999999999992 7.771561172376096e-16 9 0.9999999999999962 3.774758283725532e-15 10 0.9999999999999996 4.440892098500626e-16 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 0.1851851851851844 0.8148148148148155 2 0.9953703703703712 0.004629629629628762 3 0.933333333333333 0.06666666666666698 4 1.000000000000002 2.220446049250313e-15 5 0.999999999999997 2.997602166487923e-15 6 1.000000000000005 4.884981308350689e-15 7 0.9999999999999947 5.329070518200751e-15 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999964 3.552713678800501e-15 10 1 2.220446049250313e-16 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 0.0864197530864193 0.9135802469135808 2 0.9236111111111124 0.07638888888888762 3 0.8088888888888887 0.1911111111111113 4 1.005273934867111 0.005273934867110697 5 0.9999999999999964 3.552713678800501e-15 6 1.000000000000006 5.773159728050814e-15 7 0.9999999999999936 6.439293542825908e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999967 3.33066907387547e-15 10 1.000000000000001 8.881784197001252e-16 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 0.03840877914951965 0.9615912208504803 2 0.8197873799725668 0.1802126200274332 3 0.6606617283950614 0.3393382716049386 4 1.012949494765379 0.01294949476537877 5 0.9954144620811248 0.004585537918875171 6 1.000000000000007 6.661338147750939e-15 7 0.9999999999999922 7.771561172376096e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999971 2.886579864025407e-15 10 1.000000000000002 2.442490654175344e-15 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 0.01646090534979412 0.9835390946502058 2 0.7024176954732527 0.2975823045267473 3 0.5161007407407404 0.4838992592592596 4 1.016901624524834 0.0169016245248339 5 0.9817082388510918 0.01829176114890818 6 1.000198039172351 0.0001980391723512831 7 0.9999999999999913 8.659739592076221e-15 8 0.9999999999999983 1.665334536937735e-15 9 0.9999999999999978 2.220446049250313e-15 10 1.000000000000004 3.552713678800501e-15 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 0.006858710562414209 0.9931412894375858 2 0.5852944958847752 0.4147055041152248 3 0.3899219753086418 0.6100780246913582 4 1.012161388071187 0.01216138807118661 5 0.9566024444547235 0.04339755554527647 6 1.000439376969608 0.0004393769696080518 7 0.9995720416471456 0.0004279583528543629 8 0.9999999999999978 2.220446049250313e-15 9 0.999999999999998 1.998401444325282e-15 10 1.000000000000004 4.440892098500626e-15 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 0.002794289488390971 0.997205710511609 2 0.4768957110831697 0.5231042889168303 3 0.2871415454961133 0.7128584545038867 4 0.9962554029129934 0.003744597087006585 5 0.9200840310048873 0.07991596899511266 6 1.000085816069184 8.581606918389717e-05 7 0.9978864157721259 0.00211358422787411 8 0.9999421173630614 5.788263693862206e-05 9 0.9999999999999988 1.221245327087672e-15 10 1.000000000000006 5.773159728050814e-15 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 0.001117715795356387 0.9988822842046436 2 0.3815143858278732 0.6184856141721269 3 0.2072308048651119 0.7927691951348881 4 0.9689180401081767 0.03108195989182327 5 0.8736711916041171 0.1263288083958829 6 0.9982193656077571 0.001780634392242852 7 0.9939749176968413 0.00602508230315868 8 0.9996616764904406 0.0003383235095594239 9 0.9999697359697354 3.026403026462621e-05 10 1.000000000000007 7.105427357601002e-15 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 0.9999999999999989 1.110223024625157e-15 2 1 0 3 0.9999999999999998 2.220446049250313e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999983 1.665334536937735e-15 6 1.000000000000002 1.77635683940025e-15 7 0.9999999999999982 1.77635683940025e-15 8 1 0 9 0.9999999999999963 3.663735981263017e-15 10 0.999999999999999 9.992007221626409e-16 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1.33333333333333 0.3333333333333304 2 1.000000000000002 1.554312234475219e-15 3 1.000000000000001 8.881784197001252e-16 4 0.9999999999999991 8.881784197001252e-16 5 0.9999999999999973 2.664535259100376e-15 6 1 2.220446049250313e-16 7 0.9999999999999992 7.771561172376096e-16 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999978 2.220446049250313e-15 10 0.9999999999999978 2.220446049250313e-15 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1.111111111111108 0.1111111111111076 2 0.9722222222222243 0.02777777777777568 3 1.000000000000001 1.110223024625157e-15 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999969 3.108624468950438e-15 6 1 0 7 0.9999999999999993 6.661338147750939e-16 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999981 1.887379141862766e-15 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 0.7407407407407377 0.2592592592592623 2 1.064814814814818 0.06481481481481755 3 1.133333333333334 0.1333333333333342 4 1.000000000000001 8.881784197001252e-16 5 0.9999999999999962 3.774758283725532e-15 6 1.000000000000001 1.332267629550188e-15 7 0.9999999999999988 1.221245327087672e-15 8 0.9999999999999997 3.33066907387547e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999976 2.442490654175344e-15 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 0.4320987654320965 0.5679012345679035 2 1.174768518518522 0.1747685185185222 3 1.244444444444445 0.2444444444444447 4 0.9868151628322327 0.0131848371677673 5 0.9999999999999954 4.551914400963142e-15 6 1.000000000000002 2.220446049250313e-15 7 0.999999999999998 1.998401444325282e-15 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999979 2.109423746787797e-15 10 0.9999999999999966 3.441691376337985e-15 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 0.2304526748971179 0.7695473251028822 2 1.235082304526753 0.2350823045267532 3 1.25357037037037 0.2535703703703702 4 0.98224725517231 0.01775274482768996 5 1.013756613756608 0.01375661375660808 6 1.000000000000003 3.33066907387547e-15 7 0.9999999999999971 2.886579864025407e-15 8 0.9999999999999994 5.551115123125783e-16 9 0.9999999999999979 2.109423746787797e-15 10 0.9999999999999964 3.552713678800501e-15 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 0.1152263374485588 0.8847736625514412 2 1.230581275720169 0.2305812757201691 3 1.166625185185185 0.166625185185185 4 0.9991170406072902 0.0008829593927097701 5 1.043386243386237 0.04338624338623664 6 0.9993068628967992 0.0006931371032008471 7 0.9999999999999962 3.774758283725532e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999963 3.663735981263017e-15 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 0.05486968449931368 0.9451303155006863 2 1.170910493827165 0.1709104938271655 3 1.020815802469135 0.02081580246913517 4 1.035862570339427 0.03586257033942686 5 1.082131416436559 0.08213141643655941 6 0.999232687983325 0.0007673120166750147 7 1.001711833411374 0.001711833411374153 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999963 3.663735981263017e-15 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 0.02514860539551874 0.9748513946044812 2 1.073089027492003 0.07308902749200308 3 0.8524339094650201 0.1475660905349799 4 1.083738321283062 0.08373832128306158 5 1.120935304978982 0.1209353049789816 6 1.002030401021518 0.002030401021517969 7 1.007157358084734 0.007157358084733723 8 1.000260471866212 0.0002604718662115868 9 0.9999999999999988 1.221245327087672e-15 10 0.9999999999999968 3.219646771412954e-15 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 0.01117715795356387 0.9888228420464361 2 0.9538023373596553 0.04619766264034475 3 0.68669524865112 0.31330475134888 4 1.132942216937082 0.1329422169370815 5 1.152148228008732 0.1521482280087321 6 1.009418068376315 0.009418068376315425 7 1.017443906148548 0.01744390614854785 8 1.001344321726166 0.001344321726165942 9 1.000151320151319 0.0001513201513192453 10 0.9999999999999974 2.55351295663786e-15 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 0.6666666666666653 0.3333333333333347 2 1 2.220446049250313e-16 3 1 0 4 1 2.220446049250313e-16 5 0.9999999999999979 2.109423746787797e-15 6 1.000000000000003 2.664535259100376e-15 7 0.9999999999999973 2.664535259100376e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.9999999999999966 3.441691376337985e-15 10 0.9999999999999989 1.110223024625157e-15 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1.111111111111108 0.1111111111111076 2 0.9722222222222243 0.02777777777777568 3 1.000000000000001 8.881784197001252e-16 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999968 3.219646771412954e-15 6 1 2.220446049250313e-16 7 0.9999999999999993 6.661338147750939e-16 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999981 1.887379141862766e-15 10 0.999999999999998 1.998401444325282e-15 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.111111111111106 0.1111111111111065 2 0.7638888888888919 0.2361111111111081 3 0.8000000000000018 0.1999999999999982 4 0.9999999999999996 4.440892098500626e-16 5 0.9999999999999964 3.552713678800501e-15 6 0.9999999999999996 4.440892098500626e-16 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999992 7.771561172376096e-16 9 0.9999999999999989 1.110223024625157e-15 10 0.9999999999999979 2.109423746787797e-15 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 0.8641975308641932 0.1358024691358068 2 0.7291666666666701 0.2708333333333299 3 0.808888888888891 0.191111111111109 4 1.005273934867108 0.00527393486710781 5 0.999999999999996 3.996802888650564e-15 6 1 0 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999978 2.220446049250313e-15 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 0.5761316872427948 0.4238683127572052 2 0.819187242798358 0.180812757201642 3 0.9499259259259276 0.05007407407407238 4 0.9584343448152447 0.0415656551847553 5 0.9629629629629586 0.03703703703704142 6 1.000000000000001 6.661338147750939e-16 7 1 4.440892098500626e-16 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999996 4.440892098500626e-16 10 0.9999999999999969 3.108624468950438e-15 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 0.3456790123456765 0.6543209876543234 2 0.9371141975308692 0.06288580246913078 3 1.080675555555556 0.0806755555555565 4 0.8815019770050568 0.1184980229949432 5 0.9097505668934189 0.09024943310658107 6 1.000891176275551 0.00089117627555102 7 1 2.220446049250313e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999998 2.220446049250313e-16 10 0.9999999999999963 3.663735981263017e-15 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 0.1920438957475979 0.8079561042524022 2 1.028485082304533 0.02848508230453262 3 1.133495308641976 0.1334953086419759 4 0.8113921072273262 0.1886078927726738 5 0.866501097793609 0.133498902206391 6 0.9962244428697231 0.003775557130276885 7 0.9941169905707082 0.005883009429291763 8 0.9999999999999988 1.221245327087672e-15 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999956 4.440892098500626e-15 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 0.100594421582075 0.899405578417925 2 1.074120513260181 0.07412051326018076 3 1.103431637860082 0.1034316378600824 4 0.7696828411439617 0.2303171588560383 5 0.8460902411571047 0.1539097588428953 6 0.9816781406020066 0.01832185939799336 7 0.9792225441811699 0.02077745581883006 8 0.9992094022584869 0.0007905977415131327 9 0.9999999999999991 8.881784197001252e-16 10 0.9999999999999952 4.773959005888173e-15 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 0.05029721079103743 0.9497027892089626 2 1.073285500971658 0.07328550097165776 3 1.012554218930041 0.01255421893004094 4 0.7613180219665322 0.2386819780334678 5 0.8495227503643228 0.1504772496356772 6 0.9579452617335611 0.04205473826643891 7 0.9567540055313334 0.04324599446866662 8 0.9963061209271791 0.003693879072820927 9 0.9993026793026781 0.0006973206973218682 10 0.9999999999999949 5.10702591327572e-15 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 0.3703703703703692 0.6296296296296308 2 1.018518518518519 0.01851851851851904 3 0.9999999999999999 1.110223024625157e-16 4 1.000000000000001 1.110223024625157e-15 5 0.9999999999999976 2.442490654175344e-15 6 1.000000000000004 3.996802888650564e-15 7 0.999999999999996 3.996802888650564e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999963 3.663735981263017e-15 10 0.9999999999999996 4.440892098500626e-16 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 0.7407407407407376 0.2592592592592624 2 1.064814814814818 0.06481481481481755 3 1.133333333333334 0.1333333333333342 4 1.000000000000001 8.881784197001252e-16 5 0.9999999999999962 3.774758283725532e-15 6 1.000000000000001 1.110223024625157e-15 7 0.9999999999999989 1.110223024625157e-15 8 0.9999999999999998 2.220446049250313e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999972 2.775557561562891e-15 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 0.864197530864193 0.135802469135807 2 0.7291666666666703 0.2708333333333297 3 0.8088888888888909 0.1911111111111091 4 1.005273934867108 0.00527393486710781 5 0.9999999999999962 3.774758283725532e-15 6 1 0 7 1.000000000000001 6.661338147750939e-16 8 0.9999999999999991 8.881784197001252e-16 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999978 2.220446049250313e-15 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 0.7681755829903931 0.2318244170096069 2 0.5161179698216769 0.4838820301783231 3 0.5945679012345702 0.4054320987654298 4 1.063495826322662 0.06349582632266215 5 1.051146384479714 0.05114638447971398 6 0.9999999999999998 2.220446049250313e-16 7 1.000000000000001 1.332267629550188e-15 8 0.999999999999999 9.992007221626409e-16 9 1.000000000000001 6.661338147750939e-16 10 0.9999999999999979 2.109423746787797e-15 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 0.5761316872427942 0.4238683127572058 2 0.4816100823045302 0.5183899176954698 3 0.5915259259259279 0.4084740740740721 4 1.057370444436663 0.05737044443666339 5 1.053665910808764 0.05366591080876382 6 0.9995049020691392 0.0004950979308607772 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000001 1.110223024625157e-15 10 0.9999999999999977 2.331468351712829e-15 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 0.3840877914951957 0.6159122085048043 2 0.5446244855967119 0.4553755144032881 3 0.694510617283952 0.305489382716048 4 0.9721305594358866 0.02786944056411345 5 0.9924774142461171 0.007522585753882871 6 1.011536773794916 0.01153677379491591 7 1.011657611348051 0.01165761134805088 8 0.9999999999999988 1.221245327087672e-15 9 1.000000000000001 1.332267629550188e-15 10 0.9999999999999972 2.775557561562891e-15 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 0.2347203170248416 0.7652796829751584 2 0.6358536713153532 0.3641463286846468 3 0.8005938216735262 0.1994061783264738 4 0.8463179268812919 0.1536820731187081 5 0.8963880504750774 0.1036119495249226 6 1.030392324808048 0.03039232480804777 7 1.028932067888712 0.02893206788871172 8 1.001551556719631 0.001551556719631364 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999959 4.107825191113079e-15 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 0.1341258954427665 0.8658741045572335 2 0.7181760592897484 0.2818239407102516 3 0.8601701838134433 0.1398298161865567 4 0.7204965241704401 0.2795034758295599 5 0.7970803762944993 0.2029196237055007 6 1.042706234947614 0.04270623494761439 7 1.039343367901022 0.03934336790102244 8 1.006133549344604 0.006133549344604416 9 1.001881361881362 0.001881361881362453 10 0.9999999999999951 4.884981308350689e-15 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 0.1851851851851844 0.8148148148148155 2 0.9953703703703713 0.004629629629628651 3 0.9333333333333329 0.0666666666666671 4 1.000000000000002 1.998401444325282e-15 5 0.999999999999997 2.997602166487923e-15 6 1.000000000000005 5.10702591327572e-15 7 0.9999999999999947 5.329070518200751e-15 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999964 3.552713678800501e-15 10 1 0 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 0.4320987654320965 0.5679012345679035 2 1.174768518518522 0.1747685185185217 3 1.244444444444445 0.2444444444444449 4 0.9868151628322328 0.01318483716776719 5 0.9999999999999954 4.551914400963142e-15 6 1.000000000000002 2.220446049250313e-15 7 0.999999999999998 1.998401444325282e-15 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999978 2.220446049250313e-15 10 0.9999999999999967 3.33066907387547e-15 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 0.5761316872427948 0.4238683127572052 2 0.819187242798358 0.180812757201642 3 0.9499259259259274 0.05007407407407261 4 0.9584343448152447 0.0415656551847553 5 0.9629629629629585 0.03703703703704153 6 1.000000000000001 6.661338147750939e-16 7 1 4.440892098500626e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999968 3.219646771412954e-15 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 0.5761316872427942 0.4238683127572058 2 0.4816100823045302 0.5183899176954698 3 0.5915259259259279 0.4084740740740721 4 1.057370444436664 0.05737044443666361 5 1.053665910808764 0.05366591080876382 6 0.9995049020691392 0.0004950979308607772 7 1.000000000000001 1.332267629550188e-15 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000001 8.881784197001252e-16 10 0.9999999999999977 2.331468351712829e-15 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 0.4801097393689947 0.5198902606310053 2 0.3206983024691386 0.6793016975308614 3 0.4145382716049403 0.5854617283950597 4 1.129906973064206 0.1299069730642055 5 1.137746103732494 0.1377461037324936 6 0.9835924220110452 0.01640757798895476 7 0.9854550876925736 0.01454491230742638 8 0.9999999999999992 7.771561172376096e-16 9 1.000000000000002 2.220446049250313e-15 10 0.999999999999998 1.998401444325282e-15 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 0.3520804755372624 0.6479195244627376 2 0.2936296153406521 0.7063703846593479 3 0.4025547325102898 0.5974452674897102 4 1.106104831351558 0.1061048313515578 5 1.142490354670461 0.1424903546704606 6 0.9827409055580099 0.01725909444199014 7 0.9855046352465318 0.01449536475346824 8 0.9990653931110699 0.0009346068889301007 9 1.000000000000003 3.108624468950438e-15 10 0.9999999999999973 2.664535259100376e-15 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 0.2347203170248413 0.7652796829751587 2 0.3325968554717302 0.6674031445282698 3 0.4674610216735267 0.5325389783264733 4 0.9988283998579236 0.001171600142076401 5 1.069173199520119 0.06917319952011858 6 1.007858145127857 0.007858145127857208 7 1.01024311940511 0.0102431194051098 8 0.9978902668857513 0.002109733114248669 9 0.9966912366912397 0.003308763308760287 10 0.9999999999999971 2.886579864025407e-15 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 0.0864197530864193 0.9135802469135808 2 0.9236111111111124 0.07638888888888762 3 0.8088888888888885 0.1911111111111115 4 1.005273934867111 0.005273934867110697 5 0.9999999999999964 3.552713678800501e-15 6 1.000000000000006 5.773159728050814e-15 7 0.9999999999999934 6.550315845288424e-15 8 0.9999999999999989 1.110223024625157e-15 9 0.9999999999999967 3.33066907387547e-15 10 1.000000000000001 8.881784197001252e-16 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 0.2304526748971179 0.7695473251028822 2 1.235082304526753 0.2350823045267529 3 1.25357037037037 0.2535703703703702 4 0.9822472551723103 0.01775274482768974 5 1.013756613756608 0.01375661375660808 6 1.000000000000003 3.33066907387547e-15 7 0.999999999999997 2.997602166487923e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.999999999999998 1.998401444325282e-15 10 0.9999999999999962 3.774758283725532e-15 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 0.3456790123456766 0.6543209876543234 2 0.9371141975308692 0.06288580246913078 3 1.080675555555556 0.0806755555555565 4 0.8815019770050568 0.1184980229949432 5 0.9097505668934188 0.09024943310658118 6 1.000891176275551 0.0008911762755507979 7 1 2.220446049250313e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999998 2.220446049250313e-16 10 0.9999999999999962 3.774758283725532e-15 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 0.3840877914951957 0.6159122085048043 2 0.5446244855967119 0.4553755144032881 3 0.6945106172839521 0.3054893827160479 4 0.9721305594358866 0.02786944056411345 5 0.9924774142461171 0.007522585753882871 6 1.011536773794916 0.01153677379491591 7 1.011657611348051 0.01165761134805088 8 0.9999999999999989 1.110223024625157e-15 9 1.000000000000001 1.332267629550188e-15 10 0.9999999999999972 2.775557561562891e-15 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 0.3520804755372623 0.6479195244627376 2 0.2936296153406521 0.7063703846593479 3 0.4025547325102899 0.5974452674897102 4 1.106104831351558 0.1061048313515578 5 1.14249035467046 0.1424903546704603 6 0.9827409055580097 0.01725909444199025 7 0.9855046352465318 0.01449536475346824 8 0.9990653931110698 0.0009346068889302117 9 1.000000000000003 2.886579864025407e-15 10 0.9999999999999976 2.442490654175344e-15 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 0.2816643804298096 0.7183356195701904 2 0.1878679412437149 0.812132058756285 3 0.2735522660082321 0.7264477339917679 4 1.166184510418822 0.1661845104188222 5 1.239578844891442 0.2395788448914415 6 0.9503256832693606 0.04967431673063938 7 0.9555740437777276 0.04442595622227241 8 0.9976843973853775 0.002315602614622492 9 1.003977067977072 0.003977067977072091 10 0.999999999999998 1.998401444325282e-15 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 0.03840877914951965 0.9615912208504803 2 0.8197873799725668 0.1802126200274332 3 0.6606617283950614 0.3393382716049386 4 1.012949494765379 0.01294949476537877 5 0.9954144620811248 0.004585537918875171 6 1.000000000000007 6.661338147750939e-15 7 0.9999999999999923 7.66053886991358e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999973 2.664535259100376e-15 10 1.000000000000002 2.442490654175344e-15 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 0.1152263374485588 0.8847736625514412 2 1.230581275720169 0.2305812757201693 3 1.166625185185185 0.1666251851851848 4 0.9991170406072901 0.0008829593927098811 5 1.043386243386237 0.04338624338623664 6 0.9993068628967993 0.0006931371032007361 7 0.9999999999999963 3.663735981263017e-15 8 0.9999999999999994 5.551115123125783e-16 9 0.9999999999999982 1.77635683940025e-15 10 0.9999999999999962 3.774758283725532e-15 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 0.1920438957475979 0.8079561042524022 2 1.028485082304533 0.02848508230453262 3 1.133495308641976 0.1334953086419757 4 0.8113921072273262 0.1886078927726738 5 0.866501097793609 0.133498902206391 6 0.9962244428697228 0.003775557130277218 7 0.9941169905707083 0.005883009429291652 8 0.9999999999999988 1.221245327087672e-15 9 0.9999999999999994 5.551115123125783e-16 10 0.9999999999999953 4.662936703425657e-15 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 0.2347203170248416 0.7652796829751585 2 0.6358536713153532 0.3641463286846468 3 0.8005938216735261 0.1994061783264739 4 0.8463179268812918 0.1536820731187082 5 0.8963880504750775 0.1036119495249225 6 1.030392324808048 0.03039232480804799 7 1.028932067888711 0.0289320678887115 8 1.001551556719632 0.001551556719631586 9 1.000000000000001 1.110223024625157e-15 10 0.999999999999996 3.996802888650564e-15 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 0.2347203170248413 0.7652796829751587 2 0.3325968554717301 0.6674031445282699 3 0.4674610216735267 0.5325389783264733 4 0.9988283998579234 0.001171600142076623 5 1.069173199520119 0.06917319952011858 6 1.007858145127857 0.007858145127857208 7 1.01024311940511 0.0102431194051098 8 0.9978902668857513 0.002109733114248669 9 0.9966912366912397 0.003308763308760287 10 0.999999999999997 2.997602166487923e-15 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 0.01646090534979412 0.9835390946502058 2 0.7024176954732527 0.2975823045267473 3 0.5161007407407404 0.4838992592592596 4 1.016901624524834 0.0169016245248339 5 0.9817082388510917 0.01829176114890829 6 1.000198039172352 0.0001980391723515051 7 0.9999999999999912 8.770761894538737e-15 8 0.9999999999999982 1.77635683940025e-15 9 0.9999999999999979 2.109423746787797e-15 10 1.000000000000004 3.552713678800501e-15 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 0.05486968449931368 0.9451303155006863 2 1.170910493827165 0.1709104938271655 3 1.020815802469136 0.02081580246913561 4 1.035862570339427 0.03586257033942686 5 1.082131416436559 0.08213141643655919 6 0.999232687983325 0.0007673120166750147 7 1.001711833411374 0.001711833411374153 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999983 1.665334536937735e-15 10 0.9999999999999963 3.663735981263017e-15 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 0.100594421582075 0.899405578417925 2 1.07412051326018 0.07412051326018032 3 1.103431637860083 0.1034316378600826 4 0.7696828411439616 0.2303171588560384 5 0.8460902411571045 0.1539097588428955 6 0.9816781406020066 0.01832185939799336 7 0.9792225441811699 0.02077745581883006 8 0.9992094022584865 0.0007905977415134657 9 0.9999999999999989 1.110223024625157e-15 10 0.9999999999999951 4.884981308350689e-15 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 0.1341258954427665 0.8658741045572335 2 0.7181760592897484 0.2818239407102516 3 0.8601701838134436 0.1398298161865564 4 0.7204965241704401 0.2795034758295599 5 0.7970803762944993 0.2029196237055007 6 1.042706234947614 0.04270623494761439 7 1.039343367901022 0.03934336790102244 8 1.006133549344604 0.006133549344604194 9 1.001881361881363 0.001881361881362675 10 0.9999999999999952 4.773959005888173e-15 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 0.006858710562414209 0.9931412894375858 2 0.5852944958847752 0.4147055041152248 3 0.3899219753086418 0.6100780246913582 4 1.012161388071187 0.01216138807118683 5 0.9566024444547235 0.04339755554527647 6 1.000439376969608 0.0004393769696080518 7 0.9995720416471456 0.0004279583528543629 8 0.9999999999999978 2.220446049250313e-15 9 0.999999999999998 1.998401444325282e-15 10 1.000000000000005 4.662936703425657e-15 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 0.02514860539551874 0.9748513946044812 2 1.073089027492003 0.07308902749200308 3 0.8524339094650202 0.1475660905349798 4 1.083738321283062 0.08373832128306158 5 1.120935304978981 0.1209353049789814 6 1.002030401021518 0.002030401021518191 7 1.007157358084734 0.007157358084733501 8 1.000260471866212 0.0002604718662118088 9 0.9999999999999984 1.554312234475219e-15 10 0.999999999999997 2.997602166487923e-15 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 0.05029721079103742 0.9497027892089626 2 1.073285500971658 0.07328550097165798 3 1.012554218930041 0.01255421893004072 4 0.7613180219665323 0.2386819780334677 5 0.849522750364323 0.150477249635677 6 0.9579452617335612 0.0420547382664388 7 0.9567540055313337 0.04324599446866628 8 0.9963061209271792 0.003693879072820816 9 0.999302679302678 0.0006973206973219792 10 0.9999999999999949 5.10702591327572e-15 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 0.002794289488390971 0.997205710511609 2 0.4768957110831697 0.5231042889168303 3 0.2871415454961133 0.7128584545038867 4 0.9962554029129934 0.003744597087006585 5 0.9200840310048873 0.07991596899511266 6 1.000085816069184 8.581606918367513e-05 7 0.9978864157721259 0.00211358422787411 8 0.9999421173630614 5.788263693862206e-05 9 0.9999999999999989 1.110223024625157e-15 10 1.000000000000006 5.773159728050814e-15 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 0.01117715795356387 0.9888228420464361 2 0.9538023373596553 0.04619766264034475 3 0.68669524865112 0.31330475134888 4 1.132942216937081 0.1329422169370813 5 1.152148228008732 0.1521482280087321 6 1.009418068376315 0.009418068376315425 7 1.017443906148548 0.01744390614854807 8 1.001344321726166 0.00134432172616572 9 1.000151320151319 0.0001513201513194673 10 0.9999999999999973 2.664535259100376e-15 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 0.001117715795356387 0.9988822842046436 2 0.3815143858278732 0.6184856141721269 3 0.2072308048651119 0.7927691951348881 4 0.9689180401081767 0.03108195989182327 5 0.8736711916041171 0.1263288083958829 6 0.9982193656077571 0.001780634392242852 7 0.9939749176968414 0.006025082303158569 8 0.9996616764904406 0.0003383235095594239 9 0.9999697359697353 3.026403026473723e-05 10 1.000000000000007 7.105427357601002e-15 TEST05 This routine creates an EPS plot of each set of Dunavant points. Rule 1 plotted in "dunavant_rule_01.eps". Rule 2 plotted in "dunavant_rule_02.eps". Rule 3 plotted in "dunavant_rule_03.eps". Rule 4 plotted in "dunavant_rule_04.eps". Rule 5 plotted in "dunavant_rule_05.eps". Rule 6 plotted in "dunavant_rule_06.eps". Rule 7 plotted in "dunavant_rule_07.eps". Rule 8 plotted in "dunavant_rule_08.eps". Rule 9 plotted in "dunavant_rule_09.eps". Rule 10 plotted in "dunavant_rule_10.eps". TEST06 REFERENCE_TO_PHYSICAL_T3 transforms a rule on the unit (reference) triangle to a rule on an arbitrary (physical) triangle. The reference triangle: 1 0 0 2 1 0 3 0 1 Rule 2 for reference triangle with area = 0.5 X Y W 0 0.666666666666667 0.166666666666667 0.333333333333333 1 0.166666666666667 0.166666666666667 0.333333333333333 2 0.166666666666667 0.666666666666667 0.333333333333333 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 2 for physical triangle with area = 1 X Y W 0 1.333333333333334 1.333333333333333 0.333333333333333 1 1.333333333333334 1.833333333333333 0.333333333333333 2 2.333333333333334 1.833333333333333 0.333333333333333 DUNAVANT_PRB: Normal end of execution. 21 December 2011 04:36:06 PM