04 May 2020 08:04:50 PM TRIANGLE_WANDZURA_RULE_TEST: C++ version Test the TRIANGLE_WANDZURA_RULE library. TEST01 WANDZURA_RULE_NUM returns the number of rules; WANDZURA_DEGREE returns the degree of a rule; WANDZURA_ORDER_NUM returns the order of a rule. Number of available rules = 6 Rule Degree Order 1 5 7 2 10 25 3 15 54 4 20 85 5 25 126 6 30 175 TEST02 WANDZURA_RULE returns the points and weights of a Wandzura rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 6 Rule Sum of weights 1 1 2 1 3 1 4 1 5 1 6 1 TEST03 WANDZURA_RULE returns the points and weights of a Wandzura rule for the triangle. In this test, we simply check that, for each quadrature point, the barycentric coordinates add up to 1. Number of available rules = 6 Rule Suborder Sum of coordinates 1 3 0.99999999999999 1.00000000000001 1.00000000000001 2 7 0.99999999999999 0.99999999999999 1.00000000000001 0.9999999999999899 0.9999999999999999 0.99999999999999 1 3 12 1 1 1.00000000000001 0.9999999999999899 0.99999999999999 1 1 1 0.99999999999999 1 1 1 4 19 0.99999999999999 1.00000000000001 0.99999999999999 1.00000000000001 1.00000000000001 1.00000000000001 0.9999999999999999 0.99999999999999 1 1 1 0.99999999999999 1 1 1 0.99999999999999 1 0.99999999999999 1 5 26 0.99999999999999 0.99999999999999 0.99999999999999 0.99999999999999 0.9999999999999999 1 0.99999999999999 1.00000000000001 1.00000000000001 0.9999999999999899 0.99999999999999 1 1 1 0.99999999999999 1 1 1 1 1 1 1 1 0.99999999999999 1 1 6 36 0.99999999999999 1.00000000000001 1 0.99999999999999 1.00000000000001 1.00000000000001 0.99999999999999 1 1.00000000000001 1.00000000000001 1 1 1.00000000000001 1 1 1 1 1 1 0.99999999999999 0.99999999999999 1 1 1 0.99999999999999 1.00000000000001 0.99999999999999 1 1 0.99999999999999 1 1 1 1 0.99999999999999 1 TEST04 WANDZURA_RULE returns the points and weights of a Wandzura 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 0.9999999999999999 1.110223024625157e-16 2 1 4.440892098500626e-16 3 0.9999999999999996 4.440892098500626e-16 4 1 0 5 1.000000000000001 6.661338147750939e-16 6 0.9999999999999996 4.440892098500626e-16 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 1.000000000000005 5.329070518200751e-15 2 0.9999999999999969 3.108624468950438e-15 3 0.9999999999999998 2.220446049250313e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999978 2.220446049250313e-15 6 0.9999999999999991 8.881784197001252e-16 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 1.000000000000008 8.43769498715119e-15 2 0.9999999999999976 2.442490654175344e-15 3 1 2.220446049250313e-16 4 0.9999999999999989 1.110223024625157e-15 5 0.9999999999999949 5.10702591327572e-15 6 0.9999999999999971 2.886579864025407e-15 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 1.000000000000012 1.243449787580175e-14 2 0.9999999999999952 4.773959005888173e-15 3 1.000000000000001 1.332267629550188e-15 4 0.9999999999999979 2.109423746787797e-15 5 0.9999999999999934 6.550315845288424e-15 6 0.9999999999999953 4.662936703425657e-15 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 1.000000000000016 1.643130076445232e-14 2 0.9999999999999913 8.659739592076221e-15 3 1.000000000000002 2.220446049250313e-15 4 0.9999999999999968 3.219646771412954e-15 5 0.9999999999999941 5.88418203051333e-15 6 0.9999999999999956 4.440892098500626e-15 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 1.00000000000002 1.953992523340276e-14 2 0.9999999999999857 1.432187701766452e-14 3 1.000000000000001 1.110223024625157e-15 4 0.9999999999999951 4.884981308350689e-15 5 0.9999999999999946 5.440092820663267e-15 6 0.9999999999999958 4.218847493575595e-15 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 0.9954144620811511 0.004585537918848859 2 0.9999999999999795 2.05391259555654e-14 3 1 0 4 0.9999999999999936 6.439293542825908e-15 5 0.9999999999999944 5.551115123125783e-15 6 0.9999999999999963 3.663735981263017e-15 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 0.9817082388511208 0.0182917611488792 2 0.9999999999999725 2.753353101070388e-14 3 0.9999999999999981 1.887379141862766e-15 4 0.9999999999999917 8.326672684688674e-15 5 0.9999999999999942 5.773159728050814e-15 6 0.9999999999999978 2.220446049250313e-15 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 0.9566024444547547 0.04339755554524527 2 0.999999999999966 3.397282455352979e-14 3 0.9999999999999961 3.885780586188048e-15 4 0.9999999999999902 9.769962616701378e-15 5 0.9999999999999938 6.217248937900877e-15 6 0.9999999999999983 1.665334536937735e-15 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 0.9200840310049203 0.07991596899507969 2 0.9999999999999591 4.085620730620576e-14 3 0.9999999999999938 6.217248937900877e-15 4 0.9999999999999875 1.254552017826427e-14 5 0.9999999999999934 6.550315845288424e-15 6 1 2.220446049250313e-16 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 0.8736711916041516 0.1263288083958484 2 0.9999999999999529 4.707345624410664e-14 3 0.9999999999999911 8.881784197001252e-15 4 0.999999999999986 1.398881011027697e-14 5 0.9999999999999944 5.551115123125783e-15 6 1.000000000000003 2.664535259100376e-15 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 1.000000000000005 5.329070518200751e-15 2 0.999999999999997 2.997602166487923e-15 3 0.9999999999999997 3.33066907387547e-16 4 0.9999999999999992 7.771561172376096e-16 5 0.9999999999999978 2.220446049250313e-15 6 0.9999999999999991 8.881784197001252e-16 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1.000000000000013 1.332267629550188e-14 2 0.9999999999999911 8.881784197001252e-15 3 0.9999999999999978 2.220446049250313e-15 4 0.9999999999999961 3.885780586188048e-15 5 0.9999999999999949 5.10702591327572e-15 6 0.9999999999999982 1.77635683940025e-15 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1.00000000000002 1.976196983832779e-14 2 0.999999999999991 8.992806499463768e-15 3 0.9999999999999961 3.885780586188048e-15 4 0.9999999999999957 4.329869796038111e-15 5 0.9999999999999905 9.547918011776346e-15 6 0.9999999999999952 4.773959005888173e-15 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 1.00000000000003 2.97539770599542e-14 2 0.9999999999999893 1.06581410364015e-14 3 0.9999999999999962 3.774758283725532e-15 4 0.9999999999999936 6.439293542825908e-15 5 0.9999999999999891 1.088018564132653e-14 6 0.9999999999999944 5.551115123125783e-15 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 1.00000000000004 4.04121180963557e-14 2 0.9999999999999853 1.465494392505207e-14 3 0.9999999999999954 4.551914400963142e-15 4 0.9999999999999913 8.659739592076221e-15 5 0.9999999999999892 1.076916333886402e-14 6 0.9999999999999936 6.439293542825908e-15 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 1.013756613756664 0.01375661375666359 2 0.9999999999999797 2.031708135064036e-14 3 0.9999999999999936 6.439293542825908e-15 4 0.9999999999999889 1.110223024625157e-14 5 0.99999999999999 9.992007221626409e-15 6 0.9999999999999933 6.661338147750939e-15 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 1.043386243386302 0.0433862433863017 2 0.9999999999999731 2.686739719592879e-14 3 0.9999999999999911 8.881784197001252e-15 4 0.9999999999999868 1.321165399303936e-14 5 0.9999999999999912 8.770761894538737e-15 6 0.9999999999999937 6.328271240363392e-15 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 1.082131416436632 0.08213141643663247 2 0.999999999999966 3.397282455352979e-14 3 0.9999999999999877 1.232347557333924e-14 4 0.9999999999999852 1.476596622751458e-14 5 0.9999999999999911 8.881784197001252e-15 6 0.9999999999999948 5.218048215738236e-15 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 1.120935304979062 0.120935304979062 2 0.9999999999999594 4.063416270128073e-14 3 0.9999999999999837 1.63202784619898e-14 4 0.9999999999999835 1.654232306691483e-14 5 0.9999999999999922 7.771561172376096e-15 6 0.9999999999999963 3.663735981263017e-15 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 1.152148228008819 0.1521482280088191 2 0.9999999999999524 4.762856775641922e-14 3 0.9999999999999791 2.087219286295294e-14 4 0.9999999999999811 1.887379141862766e-14 5 0.9999999999999931 6.883382752675971e-15 6 0.9999999999999971 2.886579864025407e-15 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 1.000000000000008 8.43769498715119e-15 2 0.9999999999999973 2.664535259100376e-15 3 1 2.220446049250313e-16 4 0.9999999999999989 1.110223024625157e-15 5 0.9999999999999949 5.10702591327572e-15 6 0.999999999999997 2.997602166487923e-15 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1.00000000000002 1.998401444325282e-14 2 0.9999999999999913 8.659739592076221e-15 3 0.9999999999999946 5.440092820663267e-15 4 0.9999999999999957 4.329869796038111e-15 5 0.9999999999999905 9.547918011776346e-15 6 0.9999999999999953 4.662936703425657e-15 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.000000000000026 2.642330798607873e-14 2 0.999999999999993 6.994405055138486e-15 3 0.9999999999999899 1.010302952408892e-14 4 0.9999999999999957 4.329869796038111e-15 5 0.999999999999984 1.598721155460225e-14 6 0.9999999999999916 8.43769498715119e-15 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 1.000000000000037 3.730349362740526e-14 2 0.9999999999999942 5.773159728050814e-15 3 0.9999999999999889 1.110223024625157e-14 4 0.999999999999994 5.995204332975845e-15 5 0.9999999999999793 2.065014825802791e-14 6 0.9999999999999882 1.176836406102666e-14 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 0.9629629629630125 0.03703703703698746 2 0.9999999999999918 8.215650382226158e-15 3 0.9999999999999876 1.243449787580175e-14 4 0.9999999999999915 8.548717289613705e-15 5 0.9999999999999787 2.131628207280301e-14 6 0.9999999999999861 1.387778780781446e-14 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 0.9097505668934843 0.09024943310651568 2 0.9999999999999868 1.321165399303936e-14 3 0.9999999999999862 1.376676550535194e-14 4 0.999999999999989 1.099120794378905e-14 5 0.999999999999979 2.098321516541546e-14 6 0.999999999999985 1.498801083243961e-14 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 0.8665010977936836 0.1334989022063164 2 0.9999999999999792 2.076117056049043e-14 3 0.9999999999999828 1.720845688168993e-14 4 0.9999999999999879 1.210143096841421e-14 5 0.99999999999998 1.998401444325282e-14 6 0.9999999999999847 1.532107773982716e-14 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 0.8460902411571876 0.1539097588428124 2 0.9999999999999708 2.919886554764162e-14 3 0.999999999999979 2.098321516541546e-14 4 0.9999999999999859 1.409983241273949e-14 5 0.9999999999999816 1.84297022087776e-14 6 0.999999999999985 1.498801083243961e-14 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 0.8495227503644138 0.1504772496355862 2 0.9999999999999611 3.885780586188048e-14 3 0.9999999999999742 2.575717417130363e-14 4 0.9999999999999847 1.532107773982716e-14 5 0.9999999999999846 1.543210004228968e-14 6 0.9999999999999859 1.409983241273949e-14 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 1.000000000000012 1.243449787580175e-14 2 0.9999999999999952 4.773959005888173e-15 3 1.000000000000001 1.332267629550188e-15 4 0.9999999999999979 2.109423746787797e-15 5 0.9999999999999934 6.550315845288424e-15 6 0.9999999999999953 4.662936703425657e-15 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 1.00000000000003 2.997602166487923e-14 2 0.9999999999999895 1.054711873393899e-14 3 0.9999999999999936 6.439293542825908e-15 4 0.9999999999999936 6.439293542825908e-15 5 0.999999999999989 1.099120794378905e-14 6 0.9999999999999944 5.551115123125783e-15 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 1.000000000000037 3.730349362740526e-14 2 0.9999999999999941 5.88418203051333e-15 3 0.9999999999999861 1.387778780781446e-14 4 0.9999999999999939 6.106226635438361e-15 5 0.9999999999999795 2.05391259555654e-14 6 0.9999999999999885 1.154631945610163e-14 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 1.051146384479767 0.0511463844797666 2 0.9999999999999993 6.661338147750939e-16 3 0.9999999999999837 1.63202784619898e-14 4 0.999999999999992 7.993605777301127e-15 5 0.9999999999999722 2.775557561562891e-14 6 0.9999999999999832 1.676436767183986e-14 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 1.05366591080883 0.05366591080883043 2 1.000000000000002 1.554312234475219e-15 3 0.9999999999999826 1.743050148661496e-14 4 0.9999999999999893 1.06581410364015e-14 5 0.9999999999999688 3.11972669919669e-14 6 0.9999999999999787 2.131628207280301e-14 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 0.9924774142461951 0.007522585753804933 2 0.9999999999999993 6.661338147750939e-16 3 0.9999999999999816 1.84297022087776e-14 4 0.9999999999999871 1.287858708565182e-14 5 0.9999999999999672 3.275157922644212e-14 6 0.9999999999999759 2.40918396343659e-14 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 0.8963880504751619 0.1036119495248381 2 0.9999999999999941 5.88418203051333e-15 3 0.9999999999999797 2.031708135064036e-14 4 0.9999999999999855 1.454392162258955e-14 5 0.9999999999999675 3.252953462151709e-14 6 0.9999999999999737 2.631228568361621e-14 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 0.7970803762945871 0.2029196237054129 2 0.9999999999999866 1.343369859796439e-14 3 0.9999999999999764 2.364775042451583e-14 4 0.9999999999999848 1.521005543736464e-14 5 0.9999999999999679 3.208544541166702e-14 6 0.9999999999999727 2.731148640577885e-14 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 1.000000000000016 1.643130076445232e-14 2 0.9999999999999913 8.659739592076221e-15 3 1.000000000000002 2.220446049250313e-15 4 0.9999999999999969 3.108624468950438e-15 5 0.9999999999999941 5.88418203051333e-15 6 0.9999999999999956 4.440892098500626e-15 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 1.00000000000004 4.04121180963557e-14 2 0.9999999999999851 1.48769885299771e-14 3 0.9999999999999921 7.882583474838611e-15 4 0.9999999999999912 8.770761894538737e-15 5 0.9999999999999892 1.076916333886402e-14 6 0.9999999999999936 6.439293542825908e-15 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 0.9629629629630126 0.03703703703698735 2 0.9999999999999919 8.104628079763643e-15 3 0.9999999999999823 1.765254609153999e-14 4 0.9999999999999915 8.548717289613705e-15 5 0.9999999999999785 2.153832667772804e-14 6 0.9999999999999861 1.387778780781446e-14 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 1.05366591080883 0.05366591080883021 2 1.000000000000002 1.554312234475219e-15 3 0.9999999999999788 2.120525977034049e-14 4 0.9999999999999893 1.06581410364015e-14 5 0.9999999999999687 3.130828929442941e-14 6 0.9999999999999788 2.120525977034049e-14 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 1.137746103732578 0.1377461037325778 2 1.000000000000008 8.215650382226158e-15 3 0.9999999999999778 2.220446049250313e-14 4 0.9999999999999858 1.4210854715202e-14 5 0.9999999999999619 3.808064974464287e-14 6 0.9999999999999735 2.653433028854124e-14 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 1.14249035467056 0.1424903546705603 2 1.00000000000001 1.021405182655144e-14 3 0.9999999999999778 2.220446049250313e-14 4 0.9999999999999828 1.720845688168993e-14 5 0.9999999999999593 4.074518500374325e-14 6 0.9999999999999697 3.030908857226677e-14 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 1.069173199520227 0.06917319952022694 2 1.000000000000008 8.215650382226158e-15 3 0.9999999999999768 2.320366121466577e-14 4 0.9999999999999811 1.887379141862766e-14 5 0.999999999999956 4.39648317751562e-14 6 0.9999999999999659 3.408384685599231e-14 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 1.00000000000002 1.953992523340276e-14 2 0.9999999999999856 1.443289932012704e-14 3 1.000000000000001 1.110223024625157e-15 4 0.9999999999999951 4.884981308350689e-15 5 0.9999999999999946 5.440092820663267e-15 6 0.9999999999999957 4.329869796038111e-15 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 1.013756613756664 0.01375661375666382 2 0.9999999999999796 2.042810365310288e-14 3 0.9999999999999902 9.769962616701378e-15 4 0.9999999999999889 1.110223024625157e-14 5 0.9999999999999901 9.880984919163893e-15 6 0.9999999999999934 6.550315845288424e-15 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 0.9097505668934844 0.09024943310651556 2 0.9999999999999867 1.332267629550188e-14 3 0.9999999999999798 2.020605904817785e-14 4 0.9999999999999891 1.088018564132653e-14 5 0.999999999999979 2.098321516541546e-14 6 0.999999999999985 1.498801083243961e-14 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 0.9924774142461951 0.007522585753804933 2 0.9999999999999994 5.551115123125783e-16 3 0.9999999999999747 2.531308496145357e-14 4 0.9999999999999872 1.27675647831893e-14 5 0.9999999999999671 3.286260152890463e-14 6 0.9999999999999761 2.386979502944087e-14 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 1.14249035467056 0.14249035467056 2 1.00000000000001 9.992007221626409e-15 3 0.9999999999999736 2.642330798607873e-14 4 0.9999999999999828 1.720845688168993e-14 5 0.9999999999999593 4.074518500374325e-14 6 0.9999999999999695 3.05311331771918e-14 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 1.239578844891564 0.2395788448915641 2 1.000000000000016 1.598721155460225e-14 3 0.9999999999999737 2.631228568361621e-14 4 0.999999999999979 2.098321516541546e-14 5 0.9999999999999527 4.729550084903167e-14 6 0.9999999999999648 3.519406988061746e-14 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 0.9954144620811511 0.004585537918848859 2 0.9999999999999795 2.05391259555654e-14 3 1 0 4 0.9999999999999936 6.439293542825908e-15 5 0.9999999999999944 5.551115123125783e-15 6 0.9999999999999962 3.774758283725532e-15 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 1.043386243386301 0.04338624338630148 2 0.9999999999999732 2.675637489346627e-14 3 0.9999999999999882 1.176836406102666e-14 4 0.999999999999987 1.298960938811433e-14 5 0.9999999999999912 8.770761894538737e-15 6 0.9999999999999938 6.217248937900877e-15 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 0.8665010977936838 0.1334989022063162 2 0.9999999999999792 2.076117056049043e-14 3 0.9999999999999761 2.386979502944087e-14 4 0.9999999999999878 1.221245327087672e-14 5 0.99999999999998 1.998401444325282e-14 6 0.9999999999999843 1.565414464721471e-14 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 0.896388050475162 0.103611949524838 2 0.9999999999999941 5.88418203051333e-15 3 0.999999999999971 2.897682094271659e-14 4 0.9999999999999853 1.465494392505207e-14 5 0.9999999999999672 3.275157922644212e-14 6 0.9999999999999737 2.631228568361621e-14 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 1.069173199520227 0.06917319952022694 2 1.000000000000008 8.215650382226158e-15 3 0.9999999999999688 3.11972669919669e-14 4 0.9999999999999809 1.909583602355269e-14 5 0.999999999999956 4.39648317751562e-14 6 0.9999999999999658 3.419486915845482e-14 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 0.9817082388511207 0.01829176114887932 2 0.9999999999999726 2.742250870824137e-14 3 0.9999999999999981 1.887379141862766e-15 4 0.9999999999999917 8.326672684688674e-15 5 0.9999999999999941 5.88418203051333e-15 6 0.9999999999999978 2.220446049250313e-15 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 1.082131416436632 0.08213141643663247 2 0.999999999999966 3.397282455352979e-14 3 0.9999999999999853 1.465494392505207e-14 4 0.9999999999999853 1.465494392505207e-14 5 0.9999999999999911 8.881784197001252e-15 6 0.9999999999999947 5.329070518200751e-15 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 0.8460902411571875 0.1539097588428125 2 0.9999999999999707 2.930988785010413e-14 3 0.999999999999973 2.69784194983913e-14 4 0.9999999999999858 1.4210854715202e-14 5 0.9999999999999816 1.84297022087776e-14 6 0.999999999999985 1.498801083243961e-14 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 0.7970803762945873 0.2029196237054127 2 0.9999999999999866 1.343369859796439e-14 3 0.9999999999999671 3.286260152890463e-14 4 0.9999999999999847 1.532107773982716e-14 5 0.9999999999999678 3.219646771412954e-14 6 0.9999999999999727 2.731148640577885e-14 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 0.9566024444547547 0.04339755554524527 2 0.999999999999966 3.397282455352979e-14 3 0.9999999999999961 3.885780586188048e-15 4 0.9999999999999902 9.769962616701378e-15 5 0.9999999999999939 6.106226635438361e-15 6 0.9999999999999983 1.665334536937735e-15 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 1.120935304979062 0.120935304979062 2 0.9999999999999591 4.085620730620576e-14 3 0.9999999999999819 1.809663530139005e-14 4 0.9999999999999833 1.665334536937735e-14 5 0.9999999999999922 7.771561172376096e-15 6 0.9999999999999962 3.774758283725532e-15 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 0.8495227503644138 0.1504772496355862 2 0.9999999999999614 3.863576125695545e-14 3 0.9999999999999695 3.05311331771918e-14 4 0.9999999999999849 1.509903313490213e-14 5 0.9999999999999846 1.543210004228968e-14 6 0.9999999999999859 1.409983241273949e-14 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 0.9200840310049204 0.07991596899507958 2 0.9999999999999591 4.085620730620576e-14 3 0.9999999999999939 6.106226635438361e-15 4 0.9999999999999873 1.265654248072678e-14 5 0.9999999999999934 6.550315845288424e-15 6 1 2.220446049250313e-16 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 1.152148228008819 0.1521482280088191 2 0.9999999999999524 4.762856775641922e-14 3 0.9999999999999779 2.209343819004062e-14 4 0.9999999999999812 1.876276911616515e-14 5 0.9999999999999931 6.883382752675971e-15 6 0.9999999999999971 2.886579864025407e-15 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 0.8736711916041517 0.1263288083958483 2 0.9999999999999529 4.707345624410664e-14 3 0.9999999999999912 8.770761894538737e-15 4 0.9999999999999859 1.409983241273949e-14 5 0.9999999999999944 5.551115123125783e-15 6 1.000000000000003 2.664535259100376e-15 TEST05 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 0.33333333333333 0.33333333333333 0.08352339980519638 1 0.00426913409105 0.49786543295447 0.007229850592056743 2 0.49786543295447 0.49786543295447 0.007229850592056743 3 0.49786543295447 0.00426913409105 0.007229850592056743 4 0.14397510054189 0.42801244972906 0.07449217792098051 5 0.42801244972906 0.42801244972906 0.07449217792098051 6 0.42801244972906 0.14397510054189 0.07449217792098051 7 0.63048717451355 0.18475641274322 0.07864647340310853 8 0.18475641274322 0.18475641274322 0.07864647340310853 9 0.18475641274322 0.63048717451355 0.07864647340310853 10 0.95903756285664 0.02048121857168 0.006928323087107504 11 0.02048121857168 0.02048121857168 0.006928323087107504 12 0.02048121857168 0.95903756285664 0.006928323087107504 13 0.03500298989727 0.13657357625603 0.0295183203347794 14 0.13657357625603 0.82842343384669 0.0295183203347794 15 0.82842343384669 0.03500298989727 0.0295183203347794 16 0.13657357625603 0.03500298989727 0.0295183203347794 17 0.82842343384669 0.13657357625603 0.0295183203347794 18 0.03500298989727 0.82842343384669 0.0295183203347794 19 0.03754907025844 0.33274360058864 0.03957936719606124 20 0.33274360058864 0.62970732915292 0.03957936719606124 21 0.62970732915292 0.03754907025844 0.03957936719606124 22 0.33274360058864 0.03754907025844 0.03957936719606124 23 0.62970732915292 0.33274360058864 0.03957936719606124 24 0.03754907025844 0.62970732915292 0.03957936719606124 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 2 for physical triangle with area = 1 X Y W 0 1.66666666666666 1.66666666666667 0.08352339980519638 1 1.99573086590894 1.99573086590895 0.007229850592056743 2 1.99573086590894 1.50213456704553 0.007229850592056743 3 1.0085382681821 1.50213456704553 0.007229850592056743 4 1.85602489945812 1.85602489945811 0.07449217792098051 5 1.85602489945812 1.57198755027094 0.07449217792098051 6 1.28795020108378 1.57198755027094 0.07449217792098051 7 1.36951282548644 1.36951282548645 0.07864647340310853 8 1.36951282548644 1.81524358725678 0.07864647340310853 9 2.2609743490271 1.81524358725678 0.07864647340310853 10 1.04096243714336 1.04096243714336 0.006928323087107504 11 1.04096243714336 1.97951878142832 0.006928323087107504 12 2.91807512571328 1.97951878142832 0.006928323087107504 13 1.27314715251206 1.96499701010273 0.0295183203347794 14 2.65684686769338 1.86342642374397 0.0295183203347794 15 1.07000597979454 1.17157656615331 0.0295183203347794 16 1.07000597979454 1.86342642374397 0.0295183203347794 17 1.27314715251206 1.17157656615331 0.0295183203347794 18 2.65684686769338 1.96499701010273 0.0295183203347794 19 1.66548720117728 1.96245092974156 0.03957936719606124 20 2.25941465830584 1.66725639941136 0.03957936719606124 21 1.07509814051688 1.37029267084708 0.03957936719606124 22 1.07509814051688 1.66725639941136 0.03957936719606124 23 1.66548720117728 1.37029267084708 0.03957936719606124 24 2.25941465830584 1.96245092974156 0.03957936719606124 TRIANGLE_WANDZURA_RULE_TEST: Normal end of execution. 04 May 2020 08:04:50 PM