08-Jan-2022 10:38:20 triangle_dunavant_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test triangle_dunavant_rule(). TRIANGLE_DUNAVANT_RULE_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 TRIANGLE_DUNAVANT_RULE_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 1.000000 2 3 1.000000 3 4 1.000000 4 6 1.000000 5 7 1.000000 6 12 1.000000 7 13 1.000000 8 16 1.000000 9 19 1.000000 10 25 1.000000 11 27 1.000000 12 33 1.000000 13 37 1.000000 14 42 1.000000 15 48 1.000000 16 52 1.000000 17 61 1.000000 18 70 1.000000 19 73 1.000000 20 79 1.000000 TRIANGLE_DUNAVANT_RULE_TEST025 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 sum to 1. Rule Suborder Sum of coordinates 1 1 1.000000e+00 2 1 1.000000e+00 3 2 1.000000e+00 1.000000e+00 4 2 1.000000e+00 1.000000e+00 5 3 1.000000e+00 1.000000e+00 1.000000e+00 6 3 1.000000e+00 1.000000e+00 1.000000e+00 7 4 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 8 5 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 9 6 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 10 6 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 11 7 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 12 8 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 13 10 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 14 10 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 15 11 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 16 13 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 17 15 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 18 17 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 19 17 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 20 19 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 TRIANGLE_DUNAVANT_RULE_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 sum to 1. Rule Suborder Sum of coordinates 1 1 1.000000e+00 2 1 1.000000e+00 3 2 1.000000e+00 1.000000e+00 4 2 1.000000e+00 1.000000e+00 5 3 1.000000e+00 1.000000e+00 1.000000e+00 6 3 1.000000e+00 1.000000e+00 1.000000e+00 7 4 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 8 5 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 9 6 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 10 6 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 11 7 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 12 8 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 13 10 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 14 10 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 15 11 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 16 13 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 17 15 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 18 17 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 19 17 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 20 19 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 TRIANGLE_DUNAVANT_RULE_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 2.000000 * X^0 * Y^0 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 6.000000 * X^0 * Y^1 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 12.000000 * X^0 * Y^2 Rule QUAD ERROR 1 0.666667 0.333333 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 20.000000 * X^0 * Y^3 Rule QUAD ERROR 1 0.370370 0.629630 2 1.018519 0.018519 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 30.000000 * X^0 * Y^4 Rule QUAD ERROR 1 0.185185 0.814815 2 0.995370 0.004630 3 0.933333 0.066667 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 42.000000 * X^0 * Y^5 Rule QUAD ERROR 1 0.086420 0.913580 2 0.923611 0.076389 3 0.808889 0.191111 4 1.005274 0.005274 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 56.000000 * X^0 * Y^6 Rule QUAD ERROR 1 0.038409 0.961591 2 0.819787 0.180213 3 0.660662 0.339338 4 1.012949 0.012949 5 0.995414 0.004586 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 72.000000 * X^0 * Y^7 Rule QUAD ERROR 1 0.016461 0.983539 2 0.702418 0.297582 3 0.516101 0.483899 4 1.016902 0.016902 5 0.981708 0.018292 6 1.000198 0.000198 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 90.000000 * X^0 * Y^8 Rule QUAD ERROR 1 0.006859 0.993141 2 0.585294 0.414706 3 0.389922 0.610078 4 1.012161 0.012161 5 0.956602 0.043398 6 1.000439 0.000439 7 0.999572 0.000428 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 110.000000 * X^0 * Y^9 Rule QUAD ERROR 1 0.002794 0.997206 2 0.476896 0.523104 3 0.287142 0.712858 4 0.996255 0.003745 5 0.920084 0.079916 6 1.000086 0.000086 7 0.997886 0.002114 8 0.999942 0.000058 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 132.000000 * X^0 * Y^10 Rule QUAD ERROR 1 0.001118 0.998882 2 0.381514 0.618486 3 0.207231 0.792769 4 0.968918 0.031082 5 0.873671 0.126329 6 0.998219 0.001781 7 0.993975 0.006025 8 0.999662 0.000338 9 0.999970 0.000030 10 1.000000 0.000000 Integrate 6.000000 * X^1 * Y^0 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 24.000000 * X^1 * Y^1 Rule QUAD ERROR 1 1.333333 0.333333 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 60.000000 * X^1 * Y^2 Rule QUAD ERROR 1 1.111111 0.111111 2 0.972222 0.027778 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 120.000000 * X^1 * Y^3 Rule QUAD ERROR 1 0.740741 0.259259 2 1.064815 0.064815 3 1.133333 0.133333 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 210.000000 * X^1 * Y^4 Rule QUAD ERROR 1 0.432099 0.567901 2 1.174769 0.174769 3 1.244444 0.244444 4 0.986815 0.013185 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 336.000000 * X^1 * Y^5 Rule QUAD ERROR 1 0.230453 0.769547 2 1.235082 0.235082 3 1.253570 0.253570 4 0.982247 0.017753 5 1.013757 0.013757 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 504.000000 * X^1 * Y^6 Rule QUAD ERROR 1 0.115226 0.884774 2 1.230581 0.230581 3 1.166625 0.166625 4 0.999117 0.000883 5 1.043386 0.043386 6 0.999307 0.000693 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 720.000000 * X^1 * Y^7 Rule QUAD ERROR 1 0.054870 0.945130 2 1.170910 0.170910 3 1.020816 0.020816 4 1.035863 0.035863 5 1.082131 0.082131 6 0.999233 0.000767 7 1.001712 0.001712 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 990.000000 * X^1 * Y^8 Rule QUAD ERROR 1 0.025149 0.974851 2 1.073089 0.073089 3 0.852434 0.147566 4 1.083738 0.083738 5 1.120935 0.120935 6 1.002030 0.002030 7 1.007157 0.007157 8 1.000260 0.000260 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 1320.000000 * X^1 * Y^9 Rule QUAD ERROR 1 0.011177 0.988823 2 0.953802 0.046198 3 0.686695 0.313305 4 1.132942 0.132942 5 1.152148 0.152148 6 1.009418 0.009418 7 1.017444 0.017444 8 1.001344 0.001344 9 1.000151 0.000151 10 1.000000 0.000000 Integrate 12.000000 * X^2 * Y^0 Rule QUAD ERROR 1 0.666667 0.333333 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 60.000000 * X^2 * Y^1 Rule QUAD ERROR 1 1.111111 0.111111 2 0.972222 0.027778 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 180.000000 * X^2 * Y^2 Rule QUAD ERROR 1 1.111111 0.111111 2 0.763889 0.236111 3 0.800000 0.200000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 420.000000 * X^2 * Y^3 Rule QUAD ERROR 1 0.864198 0.135802 2 0.729167 0.270833 3 0.808889 0.191111 4 1.005274 0.005274 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 840.000000 * X^2 * Y^4 Rule QUAD ERROR 1 0.576132 0.423868 2 0.819187 0.180813 3 0.949926 0.050074 4 0.958434 0.041566 5 0.962963 0.037037 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 1512.000000 * X^2 * Y^5 Rule QUAD ERROR 1 0.345679 0.654321 2 0.937114 0.062886 3 1.080676 0.080676 4 0.881502 0.118498 5 0.909751 0.090249 6 1.000891 0.000891 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 2520.000000 * X^2 * Y^6 Rule QUAD ERROR 1 0.192044 0.807956 2 1.028485 0.028485 3 1.133495 0.133495 4 0.811392 0.188608 5 0.866501 0.133499 6 0.996224 0.003776 7 0.994117 0.005883 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 3960.000000 * X^2 * Y^7 Rule QUAD ERROR 1 0.100594 0.899406 2 1.074121 0.074121 3 1.103432 0.103432 4 0.769683 0.230317 5 0.846090 0.153910 6 0.981678 0.018322 7 0.979223 0.020777 8 0.999209 0.000791 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 5940.000000 * X^2 * Y^8 Rule QUAD ERROR 1 0.050297 0.949703 2 1.073286 0.073286 3 1.012554 0.012554 4 0.761318 0.238682 5 0.849523 0.150477 6 0.957945 0.042055 7 0.956754 0.043246 8 0.996306 0.003694 9 0.999303 0.000697 10 1.000000 0.000000 Integrate 20.000000 * X^3 * Y^0 Rule QUAD ERROR 1 0.370370 0.629630 2 1.018519 0.018519 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 120.000000 * X^3 * Y^1 Rule QUAD ERROR 1 0.740741 0.259259 2 1.064815 0.064815 3 1.133333 0.133333 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 420.000000 * X^3 * Y^2 Rule QUAD ERROR 1 0.864198 0.135802 2 0.729167 0.270833 3 0.808889 0.191111 4 1.005274 0.005274 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 1120.000000 * X^3 * Y^3 Rule QUAD ERROR 1 0.768176 0.231824 2 0.516118 0.483882 3 0.594568 0.405432 4 1.063496 0.063496 5 1.051146 0.051146 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 2520.000000 * X^3 * Y^4 Rule QUAD ERROR 1 0.576132 0.423868 2 0.481610 0.518390 3 0.591526 0.408474 4 1.057370 0.057370 5 1.053666 0.053666 6 0.999505 0.000495 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 5040.000000 * X^3 * Y^5 Rule QUAD ERROR 1 0.384088 0.615912 2 0.544624 0.455376 3 0.694511 0.305489 4 0.972131 0.027869 5 0.992477 0.007523 6 1.011537 0.011537 7 1.011658 0.011658 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 9240.000000 * X^3 * Y^6 Rule QUAD ERROR 1 0.234720 0.765280 2 0.635854 0.364146 3 0.800594 0.199406 4 0.846318 0.153682 5 0.896388 0.103612 6 1.030392 0.030392 7 1.028932 0.028932 8 1.001552 0.001552 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 15840.000000 * X^3 * Y^7 Rule QUAD ERROR 1 0.134126 0.865874 2 0.718176 0.281824 3 0.860170 0.139830 4 0.720497 0.279503 5 0.797080 0.202920 6 1.042706 0.042706 7 1.039343 0.039343 8 1.006134 0.006134 9 1.001881 0.001881 10 1.000000 0.000000 Integrate 30.000000 * X^4 * Y^0 Rule QUAD ERROR 1 0.185185 0.814815 2 0.995370 0.004630 3 0.933333 0.066667 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 210.000000 * X^4 * Y^1 Rule QUAD ERROR 1 0.432099 0.567901 2 1.174769 0.174769 3 1.244444 0.244444 4 0.986815 0.013185 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 840.000000 * X^4 * Y^2 Rule QUAD ERROR 1 0.576132 0.423868 2 0.819187 0.180813 3 0.949926 0.050074 4 0.958434 0.041566 5 0.962963 0.037037 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 2520.000000 * X^4 * Y^3 Rule QUAD ERROR 1 0.576132 0.423868 2 0.481610 0.518390 3 0.591526 0.408474 4 1.057370 0.057370 5 1.053666 0.053666 6 0.999505 0.000495 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 6300.000000 * X^4 * Y^4 Rule QUAD ERROR 1 0.480110 0.519890 2 0.320698 0.679302 3 0.414538 0.585462 4 1.129907 0.129907 5 1.137746 0.137746 6 0.983592 0.016408 7 0.985455 0.014545 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 13860.000000 * X^4 * Y^5 Rule QUAD ERROR 1 0.352080 0.647920 2 0.293630 0.706370 3 0.402555 0.597445 4 1.106105 0.106105 5 1.142490 0.142490 6 0.982741 0.017259 7 0.985505 0.014495 8 0.999065 0.000935 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 27720.000000 * X^4 * Y^6 Rule QUAD ERROR 1 0.234720 0.765280 2 0.332597 0.667403 3 0.467461 0.532539 4 0.998828 0.001172 5 1.069173 0.069173 6 1.007858 0.007858 7 1.010243 0.010243 8 0.997890 0.002110 9 0.996691 0.003309 10 1.000000 0.000000 Integrate 42.000000 * X^5 * Y^0 Rule QUAD ERROR 1 0.086420 0.913580 2 0.923611 0.076389 3 0.808889 0.191111 4 1.005274 0.005274 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 336.000000 * X^5 * Y^1 Rule QUAD ERROR 1 0.230453 0.769547 2 1.235082 0.235082 3 1.253570 0.253570 4 0.982247 0.017753 5 1.013757 0.013757 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 1512.000000 * X^5 * Y^2 Rule QUAD ERROR 1 0.345679 0.654321 2 0.937114 0.062886 3 1.080676 0.080676 4 0.881502 0.118498 5 0.909751 0.090249 6 1.000891 0.000891 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 5040.000000 * X^5 * Y^3 Rule QUAD ERROR 1 0.384088 0.615912 2 0.544624 0.455376 3 0.694511 0.305489 4 0.972131 0.027869 5 0.992477 0.007523 6 1.011537 0.011537 7 1.011658 0.011658 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 13860.000000 * X^5 * Y^4 Rule QUAD ERROR 1 0.352080 0.647920 2 0.293630 0.706370 3 0.402555 0.597445 4 1.106105 0.106105 5 1.142490 0.142490 6 0.982741 0.017259 7 0.985505 0.014495 8 0.999065 0.000935 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 33264.000000 * X^5 * Y^5 Rule QUAD ERROR 1 0.281664 0.718336 2 0.187868 0.812132 3 0.273552 0.726448 4 1.166185 0.166185 5 1.239579 0.239579 6 0.950326 0.049674 7 0.955574 0.044426 8 0.997684 0.002316 9 1.003977 0.003977 10 1.000000 0.000000 Integrate 56.000000 * X^6 * Y^0 Rule QUAD ERROR 1 0.038409 0.961591 2 0.819787 0.180213 3 0.660662 0.339338 4 1.012949 0.012949 5 0.995414 0.004586 6 1.000000 0.000000 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 504.000000 * X^6 * Y^1 Rule QUAD ERROR 1 0.115226 0.884774 2 1.230581 0.230581 3 1.166625 0.166625 4 0.999117 0.000883 5 1.043386 0.043386 6 0.999307 0.000693 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 2520.000000 * X^6 * Y^2 Rule QUAD ERROR 1 0.192044 0.807956 2 1.028485 0.028485 3 1.133495 0.133495 4 0.811392 0.188608 5 0.866501 0.133499 6 0.996224 0.003776 7 0.994117 0.005883 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 9240.000000 * X^6 * Y^3 Rule QUAD ERROR 1 0.234720 0.765280 2 0.635854 0.364146 3 0.800594 0.199406 4 0.846318 0.153682 5 0.896388 0.103612 6 1.030392 0.030392 7 1.028932 0.028932 8 1.001552 0.001552 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 27720.000000 * X^6 * Y^4 Rule QUAD ERROR 1 0.234720 0.765280 2 0.332597 0.667403 3 0.467461 0.532539 4 0.998828 0.001172 5 1.069173 0.069173 6 1.007858 0.007858 7 1.010243 0.010243 8 0.997890 0.002110 9 0.996691 0.003309 10 1.000000 0.000000 Integrate 72.000000 * X^7 * Y^0 Rule QUAD ERROR 1 0.016461 0.983539 2 0.702418 0.297582 3 0.516101 0.483899 4 1.016902 0.016902 5 0.981708 0.018292 6 1.000198 0.000198 7 1.000000 0.000000 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 720.000000 * X^7 * Y^1 Rule QUAD ERROR 1 0.054870 0.945130 2 1.170910 0.170910 3 1.020816 0.020816 4 1.035863 0.035863 5 1.082131 0.082131 6 0.999233 0.000767 7 1.001712 0.001712 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 3960.000000 * X^7 * Y^2 Rule QUAD ERROR 1 0.100594 0.899406 2 1.074121 0.074121 3 1.103432 0.103432 4 0.769683 0.230317 5 0.846090 0.153910 6 0.981678 0.018322 7 0.979223 0.020777 8 0.999209 0.000791 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 15840.000000 * X^7 * Y^3 Rule QUAD ERROR 1 0.134126 0.865874 2 0.718176 0.281824 3 0.860170 0.139830 4 0.720497 0.279503 5 0.797080 0.202920 6 1.042706 0.042706 7 1.039343 0.039343 8 1.006134 0.006134 9 1.001881 0.001881 10 1.000000 0.000000 Integrate 90.000000 * X^8 * Y^0 Rule QUAD ERROR 1 0.006859 0.993141 2 0.585294 0.414706 3 0.389922 0.610078 4 1.012161 0.012161 5 0.956602 0.043398 6 1.000439 0.000439 7 0.999572 0.000428 8 1.000000 0.000000 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 990.000000 * X^8 * Y^1 Rule QUAD ERROR 1 0.025149 0.974851 2 1.073089 0.073089 3 0.852434 0.147566 4 1.083738 0.083738 5 1.120935 0.120935 6 1.002030 0.002030 7 1.007157 0.007157 8 1.000260 0.000260 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 5940.000000 * X^8 * Y^2 Rule QUAD ERROR 1 0.050297 0.949703 2 1.073286 0.073286 3 1.012554 0.012554 4 0.761318 0.238682 5 0.849523 0.150477 6 0.957945 0.042055 7 0.956754 0.043246 8 0.996306 0.003694 9 0.999303 0.000697 10 1.000000 0.000000 Integrate 110.000000 * X^9 * Y^0 Rule QUAD ERROR 1 0.002794 0.997206 2 0.476896 0.523104 3 0.287142 0.712858 4 0.996255 0.003745 5 0.920084 0.079916 6 1.000086 0.000086 7 0.997886 0.002114 8 0.999942 0.000058 9 1.000000 0.000000 10 1.000000 0.000000 Integrate 1320.000000 * X^9 * Y^1 Rule QUAD ERROR 1 0.011177 0.988823 2 0.953802 0.046198 3 0.686695 0.313305 4 1.132942 0.132942 5 1.152148 0.152148 6 1.009418 0.009418 7 1.017444 0.017444 8 1.001344 0.001344 9 1.000151 0.000151 10 1.000000 0.000000 Integrate 132.000000 * X^10 * Y^0 Rule QUAD ERROR 1 0.001118 0.998882 2 0.381514 0.618486 3 0.207231 0.792769 4 0.968918 0.031082 5 0.873671 0.126329 6 0.998219 0.001781 7 0.993975 0.006025 8 0.999662 0.000338 9 0.999970 0.000030 10 1.000000 0.000000 TRIANGLE_DUNAVANT_RULE_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 0.000000 0.000000 2 1.000000 0.000000 3 0.000000 1.000000 Rule 2 for reference triangle with area = 0.500000 X Y W 1 0.666667 0.166667 0.333333 2 0.166667 0.166667 0.333333 3 0.166667 0.666667 0.333333 The physical triangle: 1 1.000000 2.000000 2 1.000000 1.000000 3 3.000000 2.000000 Rule 2 for physical triangle with area = 1.000000 X Y W 1 1.333333 1.333333 0.333333 2 1.333333 1.833333 0.333333 3 2.333333 1.833333 0.333333 triangle_dunavant_rule_test(): Normal end of execution. 08-Jan-2022 10:38:21