03 March 2022 09:12:38 AM TRIANGLE_NCO_RULE_TEST: C++ version Test the TRIANGLE_NCO_RULE library. TEST01 TRIANGLE_NCO_RULE_NUM returns the number of rules; TRIANGLE_NCO_DEGREE returns the degree of a rule; TRIANGLE_NCO_ORDER_NUM returns the order of a rule. Number of available rules = 9 Rule Degree Order 1 0 1 2 1 3 3 2 6 4 3 10 5 4 15 6 5 21 7 6 28 8 7 36 9 8 45 TEST02 TRIANGLE_NCO_RULE returns the points and weights of an NCO rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 9 Rule Order Sum of weights 1 1 1 2 3 1 3 6 1 4 10 1 5 15 1 6 21 1 7 28 1 8 36 1 9 45 1 TEST03 TRIANGLE_NCO_RULE returns the points and weights of an NCO 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 1 2 1 1 3 2 1 1 4 3 0.9999999999999999 0.9999999999999999 1 5 4 1 1 1 0.9999999999999999 6 5 1 1 1 1 1 7 7 1 1 1 1 1 0.9999999999999999 1 8 8 1 0.9999999999999999 0.9999999999999999 1 1 1 1 1 9 10 1 1 1 1 1 1 1 1 1 1 TEST04 TRIANGLE_NCO_RULE returns the points and weights of an NCO 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 1 0 3 1 0 4 1 4.440892098500626e-16 5 1 2.220446049250313e-16 6 1 2.220446049250313e-16 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999998 2.220446049250313e-16 9 1.000000000000001 1.110223024625157e-15 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 1 0 2 1 0 3 1 2.220446049250313e-16 4 1 0 5 1 0 6 0.9999999999999994 5.551115123125783e-16 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999993 6.661338147750939e-16 9 1.000000000000004 3.552713678800501e-15 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 0.6666666666666666 0.3333333333333334 2 0.75 0.25 3 1 2.220446049250313e-16 4 0.9999999999999998 2.220446049250313e-16 5 1 0 6 0.9999999999999998 2.220446049250313e-16 7 1.000000000000002 2.442490654175344e-15 8 1 0 9 0.9999999999999989 1.110223024625157e-15 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 0.3703703703703703 0.6296296296296298 2 0.5208333333333333 0.4791666666666667 3 1.013333333333333 0.0133333333333332 4 0.9999999999999998 2.220446049250313e-16 5 1 2.220446049250313e-16 6 1 2.220446049250313e-16 7 1.000000000000002 2.220446049250313e-15 8 0.9999999999999994 5.551115123125783e-16 9 1.000000000000001 8.881784197001252e-16 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 0.1851851851851851 0.8148148148148149 2 0.3515625 0.6484375 3 0.9640000000000001 0.03599999999999992 4 0.9490740740740741 0.05092592592592593 5 1 0 6 0.9999999999999999 1.110223024625157e-16 7 1.000000000000002 2.220446049250313e-15 8 1 0 9 0.9999999999999996 4.440892098500626e-16 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 0.08641975308641972 0.9135802469135803 2 0.232421875 0.767578125 3 0.8511999999999996 0.1488000000000004 4 0.8533950617283949 0.1466049382716051 5 1.004164931278634 0.004164931278634487 6 0.9999999999999998 2.220446049250313e-16 7 1.000000000000003 2.664535259100376e-15 8 1 0 9 1.000000000000003 3.108624468950438e-15 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 0.03840877914951987 0.9615912208504801 2 0.150390625 0.849609375 3 0.7063466666666666 0.2936533333333334 4 0.7357681755829901 0.2642318244170099 5 1.001765137541897 0.001765137541897444 6 0.9906412760416662 0.009358723958333814 7 1.000000000000002 2.220446049250313e-15 8 1.000000000000001 1.110223024625157e-15 9 1.000000000000002 1.77635683940025e-15 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 0.01646090534979423 0.9835390946502057 2 0.09521484375 0.90478515625 3 0.5587968 0.4412032 4 0.6149176954732508 0.3850823045267492 5 0.9801732271417528 0.01982677285824719 6 0.963922119140625 0.03607788085937502 7 1.000938203864589 0.0009382038645893154 8 1.000000000000001 8.881784197001252e-16 9 1 4.440892098500626e-16 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 0.006858710562414262 0.9931412894375857 2 0.059051513671875 0.940948486328125 3 0.4262591999999998 0.5737408000000002 4 0.5020254629629627 0.4979745370370373 5 0.9339330186766209 0.06606698132337907 6 0.9178333282470701 0.08216667175292991 7 1.002003044552454 0.002003044552454147 8 0.9983820000000013 0.001617999999998676 9 1.000000000000002 1.77635683940025e-15 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 0.002794289488390996 0.997205710511609 2 0.03594716389973958 0.9640528361002604 3 0.3161429333333333 0.6838570666666668 4 0.4024431774881875 0.5975568225118124 5 0.8651851122007511 0.1348148877992489 6 0.8552181720733643 0.1447818279266357 7 0.999979998476541 2.00015234590456e-05 8 0.9921721333333342 0.007827866666665795 9 1.000183768142239 0.0001837681422389714 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 0.001117715795356398 0.9988822842046436 2 0.02152633666992188 0.9784736633300781 3 0.2293406719999999 0.770659328 4 0.3178788088070923 0.6821211911929077 5 0.7804757824994433 0.2195242175005567 6 0.7812086045742037 0.2187913954257963 7 0.9907131021663661 0.0092868978336339 8 0.9783752000000012 0.02162479999999878 9 1.000642152285982 0.0006421522859818563 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 1 0 2 1 0 3 1 0 4 1 4.440892098500626e-16 5 1 0 6 0.9999999999999996 4.440892098500626e-16 7 1.000000000000001 8.881784197001252e-16 8 0.9999999999999992 7.771561172376096e-16 9 1.000000000000002 1.998401444325282e-15 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1.333333333333333 0.3333333333333333 2 1.25 0.25 3 1 4.440892098500626e-16 4 1 0 5 0.9999999999999998 2.220446049250313e-16 6 1 0 7 1 4.440892098500626e-16 8 0.999999999999999 9.992007221626409e-16 9 0.9999999999999951 4.884981308350689e-15 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1.111111111111111 0.1111111111111112 2 1.09375 0.09375 3 0.9800000000000002 0.0199999999999998 4 1 0 5 0.9999999999999991 8.881784197001252e-16 6 0.9999999999999999 1.110223024625157e-16 7 1.000000000000003 3.33066907387547e-15 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000001 6.661338147750939e-16 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 0.7407407407407406 0.2592592592592594 2 0.859375 0.140625 3 1.112 0.1119999999999997 4 1.101851851851852 0.1018518518518516 5 0.9999999999999997 3.33066907387547e-16 6 0.9999999999999999 1.110223024625157e-16 7 1.000000000000003 2.664535259100376e-15 8 0.9999999999999993 6.661338147750939e-16 9 0.9999999999999996 4.440892098500626e-16 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 0.4320987654320987 0.5679012345679013 2 0.6494140625 0.3505859375 3 1.246 0.2460000000000002 4 1.188271604938271 0.1882716049382713 5 0.9895876718034158 0.01041232819658422 6 0.9999999999999999 1.110223024625157e-16 7 1.000000000000003 3.33066907387547e-15 8 0.9999999999999998 2.220446049250313e-16 9 1.000000000000005 5.329070518200751e-15 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 0.2304526748971193 0.7695473251028807 2 0.478515625 0.521484375 3 1.28576 0.2857599999999998 4 1.206275720164609 0.2062757201646088 5 1.011364312488844 0.01136431248884362 6 1.028076171875 0.028076171875 7 1.000000000000006 5.773159728050814e-15 8 1 0 9 1.000000000000002 1.77635683940025e-15 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 0.1152263374485596 0.8847736625514404 2 0.343505859375 0.656494140625 3 1.2227712 0.2227711999999997 4 1.158744855967078 0.1587448559670781 5 1.077336823942405 0.07733682394240504 6 1.084158325195313 0.08415832519531263 7 0.9967162864739501 0.003283713526049947 8 1 4.440892098500626e-16 9 1.000000000000001 1.332267629550188e-15 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 0.05486968449931411 0.9451303155006859 2 0.2398681640625 0.7601318359375 3 1.0889472 0.0889472 4 1.066486625514403 0.06648662551440276 5 1.16513406100228 0.1651340610022798 6 1.148277282714844 0.1482772827148438 7 0.9966788411131287 0.003321158886871345 8 1.006472 0.006472000000000477 9 1.000000000000002 1.77635683940025e-15 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 0.02514860539551896 0.974851394604481 2 0.1630210876464844 0.8369789123535156 3 0.9217823999999997 0.07821760000000033 4 0.9501457475994509 0.04985425240054908 5 1.243298597818034 0.2432985978180344 6 1.199601531028748 0.1996015310287476 7 1.011106751894068 0.01110675189406773 8 1.026326400000001 0.02632640000000119 9 0.9991730433599375 0.0008269566400624928 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 0.01117715795356398 0.988822842046436 2 0.1080513000488281 0.8919486999511719 3 0.7501542399999999 0.2498457600000001 4 0.8252650208936643 0.1747349791063357 5 1.28873176070729 0.2887317607072901 6 1.225266009569168 0.2252660095691683 7 1.046314480027415 0.04631448002741467 8 1.061156800000001 0.06115680000000112 9 0.9978918474235154 0.002108152576484557 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 0.6666666666666666 0.3333333333333334 2 0.75 0.25 3 1 4.440892098500626e-16 4 1 0 5 0.9999999999999996 4.440892098500626e-16 6 1 0 7 1.000000000000004 3.552713678800501e-15 8 1 4.440892098500626e-16 9 0.9999999999999972 2.775557561562891e-15 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1.111111111111111 0.1111111111111109 2 1.09375 0.09375 3 0.9800000000000003 0.01999999999999968 4 1 0 5 1 0 6 1 0 7 1.000000000000004 3.552713678800501e-15 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000001 8.881784197001252e-16 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.111111111111111 0.1111111111111112 2 1.0546875 0.0546875 3 0.7320000000000004 0.2679999999999996 4 0.8472222222222221 0.1527777777777779 5 1 2.220446049250313e-16 6 0.9999999999999997 3.33066907387547e-16 7 1.000000000000002 1.554312234475219e-15 8 0.9999999999999991 8.881784197001252e-16 9 1.000000000000005 5.329070518200751e-15 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 0.8641975308641973 0.1358024691358027 2 0.888671875 0.111328125 3 0.7111999999999999 0.2888000000000001 4 0.853395061728395 0.146604938271605 5 1.004164931278634 0.004164931278633599 6 1 2.220446049250313e-16 7 1.000000000000004 3.996802888650564e-15 8 0.999999999999997 2.997602166487923e-15 9 0.9999999999999958 4.218847493575595e-15 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 0.5761316872427982 0.4238683127572018 2 0.7177734375 0.2822265625 3 0.8624000000000001 0.1375999999999999 4 0.9452160493827161 0.05478395061728392 5 0.913349596398326 0.08665040360167398 6 0.9403483072916666 0.05965169270833337 7 1.000000000000003 2.664535259100376e-15 8 0.9999999999999979 2.109423746787797e-15 9 0.9999999999999978 2.220446049250313e-15 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 0.3456790123456789 0.6543209876543211 2 0.569091796875 0.430908203125 3 1.0313856 0.03138559999999968 4 1.029475308641975 0.02947530864197501 5 0.7860398303427989 0.2139601696572011 6 0.8692657470703125 0.1307342529296875 7 1.004221917390646 0.004221917390646368 8 0.9999999999999986 1.443289932012704e-15 9 0.9999999999999996 4.440892098500626e-16 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 0.1920438957475994 0.8079561042524006 2 0.44219970703125 0.55780029296875 3 1.1292288 0.1292287999999999 4 1.068394204389574 0.06839420438957444 5 0.7085993081114168 0.2914006918885832 6 0.8359470367431641 0.1640529632568359 7 0.985276822826997 0.01472317717300298 8 0.9820319999999986 0.01796800000000143 9 1.000000000000006 6.217248937900877e-15 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 0.1005944215820759 0.8994055784179241 2 0.3348541259765625 0.6651458740234375 3 1.13600256 0.1360025599999999 4 1.059306412894375 0.05930641289437544 5 0.7160417159239327 0.2839582840760673 6 0.8517222404479983 0.1482777595520017 7 0.9262713180871591 0.07372868191284088 8 0.9402550666666663 0.05974493333333375 9 1.001695386563748 0.001695386563747903 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 0.05029721079103792 0.9497027892089621 2 0.2464199066162109 0.7535800933837891 3 1.06812288 0.06812287999999977 4 1.012280485539551 0.0122804855395513 5 0.7941600858629574 0.2058399141370426 6 0.9023201465606693 0.09767985343933072 7 0.8396989401353055 0.1603010598646945 8 0.8870611200000003 0.1129388799999997 9 1.000067908419095 6.790841909531942e-05 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 0.3703703703703703 0.6296296296296298 2 0.5208333333333333 0.4791666666666667 3 1.013333333333333 0.0133333333333332 4 0.9999999999999996 4.440892098500626e-16 5 1 0 6 1 2.220446049250313e-16 7 1.000000000000002 2.220446049250313e-15 8 1 4.440892098500626e-16 9 1 4.440892098500626e-16 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 0.7407407407407406 0.2592592592592594 2 0.859375 0.140625 3 1.112 0.1119999999999997 4 1.101851851851852 0.1018518518518516 5 1 0 6 1 2.220446049250313e-16 7 1.000000000000004 3.774758283725532e-15 8 0.9999999999999986 1.443289932012704e-15 9 0.9999999999999997 3.33066907387547e-16 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 0.8641975308641973 0.1358024691358027 2 0.888671875 0.111328125 3 0.7111999999999998 0.2888000000000002 4 0.853395061728395 0.146604938271605 5 1.004164931278634 0.004164931278634265 6 1 2.220446049250313e-16 7 1.000000000000006 6.217248937900877e-15 8 0.9999999999999987 1.332267629550188e-15 9 0.9999999999999991 8.881784197001252e-16 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 0.7681755829903975 0.2318244170096025 2 0.7747395833333333 0.2252604166666667 3 0.4330666666666664 0.5669333333333335 4 0.708161865569273 0.291838134430727 5 1.115487594454691 0.1154875944546914 6 1.072509765625 0.07250976562499978 7 1.000000000000005 4.884981308350689e-15 8 0.9999999999999973 2.664535259100376e-15 9 0.9999999999999941 5.88418203051333e-15 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 0.5761316872427982 0.4238683127572018 2 0.640869140625 0.359130859375 3 0.4126079999999999 0.5873920000000001 4 0.7003600823045267 0.2996399176954733 5 1.099337860925295 0.09933786092529462 6 1.058578491210938 0.0585784912109375 7 0.9976544903385363 0.002345509661463741 8 0.999999999999998 1.998401444325282e-15 9 1.000000000000006 6.439293542825908e-15 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 0.3840877914951987 0.6159122085048013 2 0.5255126953125 0.4744873046875 3 0.5424384 0.4575616 4 0.7498713991769544 0.2501286008230456 5 0.9145679096294909 0.08543209037050914 6 0.9505290985107422 0.04947090148925781 7 1.044066039315752 0.04406603931575193 8 1.031251999999998 0.03125199999999828 9 1.000000000000002 2.220446049250313e-15 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 0.2347203170248436 0.7652796829751564 2 0.4288482666015625 0.5711517333984375 3 0.6991846399999997 0.3008153600000003 4 0.7993327046181978 0.2006672953818022 5 0.6660562957854057 0.3339437042145943 6 0.8166475296020509 0.1833524703979491 7 1.112720571678391 0.1127205716783912 8 1.070484066666665 0.07048406666666462 9 0.9979252780138722 0.002074721986127792 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 0.1341258954427678 0.8658741045572322 2 0.3449249267578125 0.6550750732421875 3 0.8126975999999999 0.1873024000000001 4 0.8261054907788443 0.1738945092211557 5 0.4635222819115031 0.5364777180884969 6 0.712031185626984 0.287968814373016 7 1.135186045877926 0.1351860458779257 8 1.076375519999999 0.07637551999999936 9 1.009318294923953 0.00931829492395253 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 0.1851851851851851 0.8148148148148149 2 0.3515625 0.6484375 3 0.9640000000000001 0.03599999999999992 4 0.9490740740740738 0.05092592592592615 5 1 2.220446049250313e-16 6 0.9999999999999999 1.110223024625157e-16 7 1.000000000000002 1.77635683940025e-15 8 0.9999999999999998 2.220446049250313e-16 9 1.000000000000001 1.332267629550188e-15 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 0.4320987654320987 0.5679012345679013 2 0.6494140625 0.3505859375 3 1.246 0.246 4 1.188271604938271 0.1882716049382713 5 0.9895876718034151 0.01041232819658489 6 1 0 7 1.000000000000001 1.332267629550188e-15 8 0.9999999999999996 4.440892098500626e-16 9 0.9999999999999993 6.661338147750939e-16 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 0.5761316872427982 0.4238683127572018 2 0.7177734375 0.2822265625 3 0.8623999999999998 0.1376000000000002 4 0.9452160493827161 0.05478395061728392 5 0.9133495963983256 0.08665040360167442 6 0.9403483072916667 0.05965169270833326 7 1.000000000000004 3.774758283725532e-15 8 0.9999999999999979 2.109423746787797e-15 9 0.9999999999999996 4.440892098500626e-16 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 0.5761316872427981 0.4238683127572019 2 0.640869140625 0.359130859375 3 0.4126079999999999 0.5873920000000001 4 0.7003600823045266 0.2996399176954734 5 1.099337860925295 0.09933786092529506 6 1.058578491210938 0.0585784912109375 7 0.9976544903385365 0.002345509661463518 8 0.9999999999999986 1.443289932012704e-15 9 0.9999999999999954 4.551914400963142e-15 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 0.4801097393689984 0.5198902606310016 2 0.528717041015625 0.471282958984375 3 0.1861439999999999 0.8138560000000001 4 0.5870091735253771 0.4129908264746229 5 1.267371588368792 0.2673715883687919 6 1.15229606628418 0.1522960662841797 7 0.9365715102899494 0.06342848971005055 8 0.9621059999999982 0.03789400000000176 9 0.9999999999999963 3.663735981263017e-15 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 0.3520804755372655 0.6479195244627345 2 0.4317855834960938 0.5682144165039062 3 0.1759295999999998 0.8240704000000002 4 0.5652542009602194 0.4347457990397806 5 1.217103764726656 0.2171037647266565 6 1.117331743240356 0.1173317432403564 7 0.9351474993879378 0.06485250061206216 8 0.9657772666666646 0.03422273333333536 9 1.000930639849094 0.0009306398490942502 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 0.2347203170248436 0.7652796829751564 2 0.3568840026855469 0.6431159973144531 3 0.2797132799999998 0.7202867200000003 4 0.5787781254762994 0.4212218745237006 5 0.9683310837616075 0.03166891623839252 6 0.9830717742443085 0.01692822575569153 7 1.049505617396506 0.0495056173965065 8 1.035955359999998 0.03595535999999799 9 0.975146202469342 0.02485379753065797 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 0.08641975308641972 0.9135802469135803 2 0.232421875 0.767578125 3 0.8511999999999997 0.1488000000000003 4 0.853395061728395 0.146604938271605 5 1.004164931278634 0.004164931278634265 6 1 0 7 1.000000000000003 2.664535259100376e-15 8 1 2.220446049250313e-16 9 1.000000000000002 2.442490654175344e-15 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 0.2304526748971192 0.7695473251028808 2 0.478515625 0.521484375 3 1.28576 0.2857599999999996 4 1.206275720164609 0.2062757201646086 5 1.011364312488844 0.01136431248884406 6 1.028076171875 0.02807617187499978 7 1.000000000000005 4.884981308350689e-15 8 1 0 9 1.000000000000001 8.881784197001252e-16 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 0.3456790123456789 0.6543209876543211 2 0.569091796875 0.430908203125 3 1.0313856 0.03138559999999968 4 1.029475308641975 0.02947530864197501 5 0.7860398303427996 0.2139601696572004 6 0.8692657470703125 0.1307342529296875 7 1.004221917390645 0.004221917390645258 8 0.9999999999999986 1.443289932012704e-15 9 1.000000000000002 1.554312234475219e-15 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 0.3840877914951987 0.6159122085048013 2 0.5255126953125 0.4744873046875 3 0.5424383999999999 0.4575616000000001 4 0.7498713991769546 0.2501286008230454 5 0.9145679096294912 0.08543209037050881 6 0.9505290985107422 0.04947090148925781 7 1.044066039315754 0.04406603931575415 8 1.031251999999998 0.03125199999999828 9 0.9999999999999916 8.43769498715119e-15 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 0.3520804755372655 0.6479195244627345 2 0.4317855834960938 0.5682144165039062 3 0.1759295999999998 0.8240704000000002 4 0.5652542009602194 0.4347457990397806 5 1.217103764726657 0.2171037647266567 6 1.117331743240356 0.1173317432403564 7 0.9351474993879346 0.06485250061206538 8 0.965777266666665 0.03422273333333503 9 1.000930639849094 0.0009306398490942502 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 0.2816643804298123 0.7183356195701878 2 0.3436660766601562 0.6563339233398438 3 0.02057932799999984 0.9794206720000002 4 0.4805348365340646 0.5194651634659353 5 1.384399218637381 0.384399218637381 6 1.192360192537308 0.1923601925373077 7 0.7939128394936328 0.2060871605063672 8 0.8876735999999975 0.1123264000000025 9 1.032304123535361 0.03230412353536138 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 0.03840877914951987 0.9615912208504801 2 0.150390625 0.849609375 3 0.7063466666666666 0.2936533333333334 4 0.7357681755829901 0.2642318244170099 5 1.001765137541897 0.001765137541897444 6 0.9906412760416666 0.00935872395833337 7 1.000000000000002 1.77635683940025e-15 8 1.000000000000001 6.661338147750939e-16 9 1.000000000000001 1.332267629550188e-15 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 0.1152263374485596 0.8847736625514404 2 0.343505859375 0.656494140625 3 1.2227712 0.2227711999999997 4 1.158744855967078 0.1587448559670779 5 1.077336823942405 0.07733682394240482 6 1.084158325195312 0.08415832519531219 7 0.9967162864739496 0.003283713526050391 8 1 4.440892098500626e-16 9 0.9999999999999991 8.881784197001252e-16 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 0.1920438957475994 0.8079561042524006 2 0.44219970703125 0.55780029296875 3 1.1292288 0.1292287999999999 4 1.068394204389574 0.06839420438957444 5 0.7085993081114164 0.2914006918885836 6 0.8359470367431641 0.1640529632568359 7 0.9852768228269964 0.01472317717300364 8 0.9820319999999987 0.01796800000000132 9 0.9999999999999992 7.771561172376096e-16 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 0.2347203170248436 0.7652796829751564 2 0.4288482666015625 0.5711517333984375 3 0.6991846399999999 0.3008153600000001 4 0.7993327046181979 0.2006672953818021 5 0.6660562957854057 0.3339437042145943 6 0.8166475296020508 0.1833524703979492 7 1.11272057167839 0.1127205716783903 8 1.070484066666665 0.07048406666666462 9 0.9979252780138705 0.002074721986129457 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 0.2347203170248436 0.7652796829751564 2 0.3568840026855469 0.6431159973144531 3 0.2797132799999998 0.7202867200000003 4 0.5787781254762991 0.4212218745237009 5 0.9683310837616076 0.03166891623839241 6 0.9830717742443085 0.01692822575569153 7 1.049505617396506 0.04950561739650583 8 1.035955359999999 0.03595535999999888 9 0.9751462024693422 0.02485379753065775 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 0.01646090534979423 0.9835390946502057 2 0.09521484375 0.90478515625 3 0.5587967999999999 0.4412032000000001 4 0.6149176954732507 0.3850823045267493 5 0.9801732271417527 0.0198267728582473 6 0.963922119140625 0.03607788085937502 7 1.00093820386459 0.0009382038645895374 8 1.000000000000001 8.881784197001252e-16 9 1 2.220446049250313e-16 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 0.05486968449931411 0.9451303155006859 2 0.2398681640625 0.7601318359375 3 1.0889472 0.08894719999999978 4 1.066486625514403 0.06648662551440276 5 1.16513406100228 0.1651340610022798 6 1.148277282714844 0.1482772827148438 7 0.9966788411131287 0.003321158886871345 8 1.006472000000001 0.006472000000000699 9 1.000000000000003 3.33066907387547e-15 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 0.1005944215820759 0.8994055784179241 2 0.3348541259765625 0.6651458740234375 3 1.13600256 0.1360025599999999 4 1.059306412894375 0.05930641289437544 5 0.7160417159239325 0.2839582840760675 6 0.851722240447998 0.148277759552002 7 0.9262713180871596 0.07372868191284043 8 0.9402550666666659 0.05974493333333408 9 1.001695386563741 0.001695386563740797 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 0.1341258954427678 0.8658741045572322 2 0.3449249267578125 0.6550750732421875 3 0.8126975999999999 0.1873024000000001 4 0.8261054907788443 0.1738945092211557 5 0.4635222819115034 0.5364777180884965 6 0.7120311856269838 0.2879688143730162 7 1.135186045877926 0.1351860458779259 8 1.076375519999999 0.07637551999999914 9 1.009318294923954 0.009318294923954307 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 0.006858710562414262 0.9931412894375857 2 0.059051513671875 0.940948486328125 3 0.4262591999999998 0.5737408000000002 4 0.5020254629629627 0.4979745370370373 5 0.9339330186766209 0.06606698132337907 6 0.91783332824707 0.08216667175293002 7 1.002003044552455 0.002003044552455036 8 0.998382000000001 0.001617999999999009 9 1.000000000000003 3.108624468950438e-15 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 0.02514860539551896 0.974851394604481 2 0.1630210876464844 0.8369789123535156 3 0.9217823999999999 0.07821760000000011 4 0.9501457475994509 0.04985425240054908 5 1.243298597818035 0.2432985978180349 6 1.199601531028748 0.1996015310287478 7 1.011106751894066 0.01110675189406618 8 1.026326400000001 0.02632640000000097 9 0.9991730433599395 0.0008269566400604944 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 0.05029721079103792 0.9497027892089621 2 0.2464199066162109 0.7535800933837891 3 1.06812288 0.06812288 4 1.012280485539552 0.01228048553955152 5 0.7941600858629565 0.2058399141370435 6 0.9023201465606694 0.09767985343933061 7 0.8396989401353062 0.1603010598646938 8 0.8870611200000003 0.1129388799999997 9 1.000067908419095 6.790841909531942e-05 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 0.002794289488390996 0.997205710511609 2 0.03594716389973959 0.9640528361002604 3 0.3161429333333333 0.6838570666666668 4 0.4024431774881876 0.5975568225118124 5 0.8651851122007509 0.1348148877992491 6 0.8552181720733644 0.1447818279266356 7 0.999979998476541 2.00015234590456e-05 8 0.9921721333333342 0.007827866666665795 9 1.000183768142239 0.0001837681422387494 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 0.01117715795356398 0.988822842046436 2 0.1080513000488281 0.8919486999511719 3 0.75015424 0.24984576 4 0.8252650208936643 0.1747349791063357 5 1.28873176070729 0.2887317607072903 6 1.225266009569168 0.2252660095691683 7 1.046314480027413 0.04631448002741334 8 1.061156800000001 0.0611568000000009 9 0.9978918474235171 0.002108152576482891 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 0.001117715795356398 0.9988822842046436 2 0.02152633666992188 0.9784736633300781 3 0.229340672 0.770659328 4 0.3178788088070923 0.6821211911929077 5 0.7804757824994432 0.2195242175005568 6 0.7812086045742036 0.2187913954257964 7 0.9907131021663654 0.009286897833634566 8 0.9783752000000012 0.02162479999999878 9 1.000642152285982 0.0006421522859820783 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 3 for reference triangle with area = 0.5 X Y W 0 0.6 0.2 0.5833333333333334 1 0.2 0.2 0.5833333333333334 2 0.2 0.6 0.5833333333333334 3 0.4 0.4 -0.25 4 0.4 0.2 -0.25 5 0.2 0.4 -0.25 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 3 for physical triangle with area = 1 X Y W 0 1.4 1.4 0.5833333333333334 1 1.4 1.8 0.5833333333333334 2 2.2 1.8 0.5833333333333334 3 1.8 1.6 -0.25 4 1.4 1.6 -0.25 5 1.8 1.8 -0.25 TRIANGLE_NCO_RULE_TEST: Normal end of execution. 03 March 2022 09:12:38 AM