23 March 2023 4:28:10.094 PM triangle_nco_rule_test(): FORTRAN90 version Test TRIANGLE_NCO_RULE(). 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 Sum of weights 1 1.000000000000000 2 1.000000000000000 3 1.000000000000000 4 1.000000000000000 5 1.000000000000000 6 1.000000000000000 7 1.000000000000002 8 0.9999999999999998 9 1.000000000000001 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 sum to 1. Rule Suborder Sum of coordinates 1 1 1.000000000000000 2 1 1.000000000000000 3 2 1.000000000000000 1.000000000000000 4 3 0.9999999999999999 0.9999999999999999 1.000000000000000 5 4 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999999 6 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 7 7 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999999 1.000000000000000 8 8 1.000000000000000 0.9999999999999999 0.9999999999999999 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 9 10 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 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 2.00000 * X ** 0 * Y ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 6.00000 * X ** 0 * Y ** 1 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 12.0000 * X ** 0 * Y ** 2 Rule QUAD ERROR 1 0.666667 0.33333333 2 0.750000 0.25000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 20.0000 * X ** 0 * Y ** 3 Rule QUAD ERROR 1 0.370370 0.62962963 2 0.520833 0.47916667 3 1.01333 0.01333333 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 30.0000 * X ** 0 * Y ** 4 Rule QUAD ERROR 1 0.185185 0.81481481 2 0.351562 0.64843750 3 0.964000 0.03600000 4 0.949074 0.05092593 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 42.0000 * X ** 0 * Y ** 5 Rule QUAD ERROR 1 0.864198E-01 0.91358025 2 0.232422 0.76757812 3 0.851200 0.14880000 4 0.853395 0.14660494 5 1.00416 0.00416493 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 56.0000 * X ** 0 * Y ** 6 Rule QUAD ERROR 1 0.384088E-01 0.96159122 2 0.150391 0.84960938 3 0.706347 0.29365333 4 0.735768 0.26423182 5 1.00177 0.00176514 6 0.990641 0.00935872 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 72.0000 * X ** 0 * Y ** 7 Rule QUAD ERROR 1 0.164609E-01 0.98353909 2 0.952148E-01 0.90478516 3 0.558797 0.44120320 4 0.614918 0.38508230 5 0.980173 0.01982677 6 0.963922 0.03607788 7 1.00094 0.00093820 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 90.0000 * X ** 0 * Y ** 8 Rule QUAD ERROR 1 0.685871E-02 0.99314129 2 0.590515E-01 0.94094849 3 0.426259 0.57374080 4 0.502025 0.49797454 5 0.933933 0.06606698 6 0.917833 0.08216667 7 1.00200 0.00200304 8 0.998382 0.00161800 9 1.00000 0.00000000 Integrate 110.000 * X ** 0 * Y ** 9 Rule QUAD ERROR 1 0.279429E-02 0.99720571 2 0.359472E-01 0.96405284 3 0.316143 0.68385707 4 0.402443 0.59755682 5 0.865185 0.13481489 6 0.855218 0.14478183 7 0.999980 0.00002000 8 0.992172 0.00782787 9 1.00018 0.00018377 Integrate 132.000 * X ** 0 * Y ** 10 Rule QUAD ERROR 1 0.111772E-02 0.99888228 2 0.215263E-01 0.97847366 3 0.229341 0.77065933 4 0.317879 0.68212119 5 0.780476 0.21952422 6 0.781209 0.21879140 7 0.990713 0.00928690 8 0.978375 0.02162480 9 1.00064 0.00064215 Integrate 6.00000 * X ** 1 * Y ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 24.0000 * X ** 1 * Y ** 1 Rule QUAD ERROR 1 1.33333 0.33333333 2 1.25000 0.25000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 60.0000 * X ** 1 * Y ** 2 Rule QUAD ERROR 1 1.11111 0.11111111 2 1.09375 0.09375000 3 0.980000 0.02000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 120.000 * X ** 1 * Y ** 3 Rule QUAD ERROR 1 0.740741 0.25925926 2 0.859375 0.14062500 3 1.11200 0.11200000 4 1.10185 0.10185185 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 210.000 * X ** 1 * Y ** 4 Rule QUAD ERROR 1 0.432099 0.56790123 2 0.649414 0.35058594 3 1.24600 0.24600000 4 1.18827 0.18827160 5 0.989588 0.01041233 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 336.000 * X ** 1 * Y ** 5 Rule QUAD ERROR 1 0.230453 0.76954733 2 0.478516 0.52148438 3 1.28576 0.28576000 4 1.20628 0.20627572 5 1.01136 0.01136431 6 1.02808 0.02807617 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 504.000 * X ** 1 * Y ** 6 Rule QUAD ERROR 1 0.115226 0.88477366 2 0.343506 0.65649414 3 1.22277 0.22277120 4 1.15874 0.15874486 5 1.07734 0.07733682 6 1.08416 0.08415833 7 0.996716 0.00328371 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 720.000 * X ** 1 * Y ** 7 Rule QUAD ERROR 1 0.548697E-01 0.94513032 2 0.239868 0.76013184 3 1.08895 0.08894720 4 1.06649 0.06648663 5 1.16513 0.16513406 6 1.14828 0.14827728 7 0.996679 0.00332116 8 1.00647 0.00647200 9 1.00000 0.00000000 Integrate 990.000 * X ** 1 * Y ** 8 Rule QUAD ERROR 1 0.251486E-01 0.97485139 2 0.163021 0.83697891 3 0.921782 0.07821760 4 0.950146 0.04985425 5 1.24330 0.24329860 6 1.19960 0.19960153 7 1.01111 0.01110675 8 1.02633 0.02632640 9 0.999173 0.00082696 Integrate 1320.00 * X ** 1 * Y ** 9 Rule QUAD ERROR 1 0.111772E-01 0.98882284 2 0.108051 0.89194870 3 0.750154 0.24984576 4 0.825265 0.17473498 5 1.28873 0.28873176 6 1.22527 0.22526601 7 1.04631 0.04631448 8 1.06116 0.06115680 9 0.997892 0.00210815 Integrate 12.0000 * X ** 2 * Y ** 0 Rule QUAD ERROR 1 0.666667 0.33333333 2 0.750000 0.25000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 60.0000 * X ** 2 * Y ** 1 Rule QUAD ERROR 1 1.11111 0.11111111 2 1.09375 0.09375000 3 0.980000 0.02000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 180.000 * X ** 2 * Y ** 2 Rule QUAD ERROR 1 1.11111 0.11111111 2 1.05469 0.05468750 3 0.732000 0.26800000 4 0.847222 0.15277778 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 420.000 * X ** 2 * Y ** 3 Rule QUAD ERROR 1 0.864198 0.13580247 2 0.888672 0.11132812 3 0.711200 0.28880000 4 0.853395 0.14660494 5 1.00416 0.00416493 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 840.000 * X ** 2 * Y ** 4 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.717773 0.28222656 3 0.862400 0.13760000 4 0.945216 0.05478395 5 0.913350 0.08665040 6 0.940348 0.05965169 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 1512.00 * X ** 2 * Y ** 5 Rule QUAD ERROR 1 0.345679 0.65432099 2 0.569092 0.43090820 3 1.03139 0.03138560 4 1.02948 0.02947531 5 0.786040 0.21396017 6 0.869266 0.13073425 7 1.00422 0.00422192 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 2520.00 * X ** 2 * Y ** 6 Rule QUAD ERROR 1 0.192044 0.80795610 2 0.442200 0.55780029 3 1.12923 0.12922880 4 1.06839 0.06839420 5 0.708599 0.29140069 6 0.835947 0.16405296 7 0.985277 0.01472318 8 0.982032 0.01796800 9 1.00000 0.00000000 Integrate 3960.00 * X ** 2 * Y ** 7 Rule QUAD ERROR 1 0.100594 0.89940558 2 0.334854 0.66514587 3 1.13600 0.13600256 4 1.05931 0.05930641 5 0.716042 0.28395828 6 0.851722 0.14827776 7 0.926271 0.07372868 8 0.940255 0.05974493 9 1.00170 0.00169539 Integrate 5940.00 * X ** 2 * Y ** 8 Rule QUAD ERROR 1 0.502972E-01 0.94970279 2 0.246420 0.75358009 3 1.06812 0.06812288 4 1.01228 0.01228049 5 0.794160 0.20583991 6 0.902320 0.09767985 7 0.839699 0.16030106 8 0.887061 0.11293888 9 1.00007 0.00006791 Integrate 20.0000 * X ** 3 * Y ** 0 Rule QUAD ERROR 1 0.370370 0.62962963 2 0.520833 0.47916667 3 1.01333 0.01333333 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 120.000 * X ** 3 * Y ** 1 Rule QUAD ERROR 1 0.740741 0.25925926 2 0.859375 0.14062500 3 1.11200 0.11200000 4 1.10185 0.10185185 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 420.000 * X ** 3 * Y ** 2 Rule QUAD ERROR 1 0.864198 0.13580247 2 0.888672 0.11132812 3 0.711200 0.28880000 4 0.853395 0.14660494 5 1.00416 0.00416493 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 1120.00 * X ** 3 * Y ** 3 Rule QUAD ERROR 1 0.768176 0.23182442 2 0.774740 0.22526042 3 0.433067 0.56693333 4 0.708162 0.29183813 5 1.11549 0.11548759 6 1.07251 0.07250977 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 2520.00 * X ** 3 * Y ** 4 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.640869 0.35913086 3 0.412608 0.58739200 4 0.700360 0.29963992 5 1.09934 0.09933786 6 1.05858 0.05857849 7 0.997654 0.00234551 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 5040.00 * X ** 3 * Y ** 5 Rule QUAD ERROR 1 0.384088 0.61591221 2 0.525513 0.47448730 3 0.542438 0.45756160 4 0.749871 0.25012860 5 0.914568 0.08543209 6 0.950529 0.04947090 7 1.04407 0.04406604 8 1.03125 0.03125200 9 1.00000 0.00000000 Integrate 9240.00 * X ** 3 * Y ** 6 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.428848 0.57115173 3 0.699185 0.30081536 4 0.799333 0.20066730 5 0.666056 0.33394370 6 0.816648 0.18335247 7 1.11272 0.11272057 8 1.07048 0.07048407 9 0.997925 0.00207472 Integrate 15840.0 * X ** 3 * Y ** 7 Rule QUAD ERROR 1 0.134126 0.86587410 2 0.344925 0.65507507 3 0.812698 0.18730240 4 0.826105 0.17389451 5 0.463522 0.53647772 6 0.712031 0.28796881 7 1.13519 0.13518605 8 1.07638 0.07637552 9 1.00932 0.00931829 Integrate 30.0000 * X ** 4 * Y ** 0 Rule QUAD ERROR 1 0.185185 0.81481481 2 0.351562 0.64843750 3 0.964000 0.03600000 4 0.949074 0.05092593 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 210.000 * X ** 4 * Y ** 1 Rule QUAD ERROR 1 0.432099 0.56790123 2 0.649414 0.35058594 3 1.24600 0.24600000 4 1.18827 0.18827160 5 0.989588 0.01041233 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 840.000 * X ** 4 * Y ** 2 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.717773 0.28222656 3 0.862400 0.13760000 4 0.945216 0.05478395 5 0.913350 0.08665040 6 0.940348 0.05965169 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 2520.00 * X ** 4 * Y ** 3 Rule QUAD ERROR 1 0.576132 0.42386831 2 0.640869 0.35913086 3 0.412608 0.58739200 4 0.700360 0.29963992 5 1.09934 0.09933786 6 1.05858 0.05857849 7 0.997654 0.00234551 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 6300.00 * X ** 4 * Y ** 4 Rule QUAD ERROR 1 0.480110 0.51989026 2 0.528717 0.47128296 3 0.186144 0.81385600 4 0.587009 0.41299083 5 1.26737 0.26737159 6 1.15230 0.15229607 7 0.936572 0.06342849 8 0.962106 0.03789400 9 1.00000 0.00000000 Integrate 13860.0 * X ** 4 * Y ** 5 Rule QUAD ERROR 1 0.352080 0.64791952 2 0.431786 0.56821442 3 0.175930 0.82407040 4 0.565254 0.43474580 5 1.21710 0.21710376 6 1.11733 0.11733174 7 0.935147 0.06485250 8 0.965777 0.03422273 9 1.00093 0.00093064 Integrate 27720.0 * X ** 4 * Y ** 6 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.356884 0.64311600 3 0.279713 0.72028672 4 0.578778 0.42122187 5 0.968331 0.03166892 6 0.983072 0.01692823 7 1.04951 0.04950562 8 1.03596 0.03595536 9 0.975146 0.02485380 Integrate 42.0000 * X ** 5 * Y ** 0 Rule QUAD ERROR 1 0.864198E-01 0.91358025 2 0.232422 0.76757812 3 0.851200 0.14880000 4 0.853395 0.14660494 5 1.00416 0.00416493 6 1.00000 0.00000000 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 336.000 * X ** 5 * Y ** 1 Rule QUAD ERROR 1 0.230453 0.76954733 2 0.478516 0.52148438 3 1.28576 0.28576000 4 1.20628 0.20627572 5 1.01136 0.01136431 6 1.02808 0.02807617 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 1512.00 * X ** 5 * Y ** 2 Rule QUAD ERROR 1 0.345679 0.65432099 2 0.569092 0.43090820 3 1.03139 0.03138560 4 1.02948 0.02947531 5 0.786040 0.21396017 6 0.869266 0.13073425 7 1.00422 0.00422192 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 5040.00 * X ** 5 * Y ** 3 Rule QUAD ERROR 1 0.384088 0.61591221 2 0.525513 0.47448730 3 0.542438 0.45756160 4 0.749871 0.25012860 5 0.914568 0.08543209 6 0.950529 0.04947090 7 1.04407 0.04406604 8 1.03125 0.03125200 9 1.00000 0.00000000 Integrate 13860.0 * X ** 5 * Y ** 4 Rule QUAD ERROR 1 0.352080 0.64791952 2 0.431786 0.56821442 3 0.175930 0.82407040 4 0.565254 0.43474580 5 1.21710 0.21710376 6 1.11733 0.11733174 7 0.935147 0.06485250 8 0.965777 0.03422273 9 1.00093 0.00093064 Integrate 33264.0 * X ** 5 * Y ** 5 Rule QUAD ERROR 1 0.281664 0.71833562 2 0.343666 0.65633392 3 0.205793E-01 0.97942067 4 0.480535 0.51946516 5 1.38440 0.38439922 6 1.19236 0.19236019 7 0.793913 0.20608716 8 0.887674 0.11232640 9 1.03230 0.03230412 Integrate 56.0000 * X ** 6 * Y ** 0 Rule QUAD ERROR 1 0.384088E-01 0.96159122 2 0.150391 0.84960938 3 0.706347 0.29365333 4 0.735768 0.26423182 5 1.00177 0.00176514 6 0.990641 0.00935872 7 1.00000 0.00000000 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 504.000 * X ** 6 * Y ** 1 Rule QUAD ERROR 1 0.115226 0.88477366 2 0.343506 0.65649414 3 1.22277 0.22277120 4 1.15874 0.15874486 5 1.07734 0.07733682 6 1.08416 0.08415833 7 0.996716 0.00328371 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 2520.00 * X ** 6 * Y ** 2 Rule QUAD ERROR 1 0.192044 0.80795610 2 0.442200 0.55780029 3 1.12923 0.12922880 4 1.06839 0.06839420 5 0.708599 0.29140069 6 0.835947 0.16405296 7 0.985277 0.01472318 8 0.982032 0.01796800 9 1.00000 0.00000000 Integrate 9240.00 * X ** 6 * Y ** 3 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.428848 0.57115173 3 0.699185 0.30081536 4 0.799333 0.20066730 5 0.666056 0.33394370 6 0.816648 0.18335247 7 1.11272 0.11272057 8 1.07048 0.07048407 9 0.997925 0.00207472 Integrate 27720.0 * X ** 6 * Y ** 4 Rule QUAD ERROR 1 0.234720 0.76527968 2 0.356884 0.64311600 3 0.279713 0.72028672 4 0.578778 0.42122187 5 0.968331 0.03166892 6 0.983072 0.01692823 7 1.04951 0.04950562 8 1.03596 0.03595536 9 0.975146 0.02485380 Integrate 72.0000 * X ** 7 * Y ** 0 Rule QUAD ERROR 1 0.164609E-01 0.98353909 2 0.952148E-01 0.90478516 3 0.558797 0.44120320 4 0.614918 0.38508230 5 0.980173 0.01982677 6 0.963922 0.03607788 7 1.00094 0.00093820 8 1.00000 0.00000000 9 1.00000 0.00000000 Integrate 720.000 * X ** 7 * Y ** 1 Rule QUAD ERROR 1 0.548697E-01 0.94513032 2 0.239868 0.76013184 3 1.08895 0.08894720 4 1.06649 0.06648663 5 1.16513 0.16513406 6 1.14828 0.14827728 7 0.996679 0.00332116 8 1.00647 0.00647200 9 1.00000 0.00000000 Integrate 3960.00 * X ** 7 * Y ** 2 Rule QUAD ERROR 1 0.100594 0.89940558 2 0.334854 0.66514587 3 1.13600 0.13600256 4 1.05931 0.05930641 5 0.716042 0.28395828 6 0.851722 0.14827776 7 0.926271 0.07372868 8 0.940255 0.05974493 9 1.00170 0.00169539 Integrate 15840.0 * X ** 7 * Y ** 3 Rule QUAD ERROR 1 0.134126 0.86587410 2 0.344925 0.65507507 3 0.812698 0.18730240 4 0.826105 0.17389451 5 0.463522 0.53647772 6 0.712031 0.28796881 7 1.13519 0.13518605 8 1.07638 0.07637552 9 1.00932 0.00931829 Integrate 90.0000 * X ** 8 * Y ** 0 Rule QUAD ERROR 1 0.685871E-02 0.99314129 2 0.590515E-01 0.94094849 3 0.426259 0.57374080 4 0.502025 0.49797454 5 0.933933 0.06606698 6 0.917833 0.08216667 7 1.00200 0.00200304 8 0.998382 0.00161800 9 1.00000 0.00000000 Integrate 990.000 * X ** 8 * Y ** 1 Rule QUAD ERROR 1 0.251486E-01 0.97485139 2 0.163021 0.83697891 3 0.921782 0.07821760 4 0.950146 0.04985425 5 1.24330 0.24329860 6 1.19960 0.19960153 7 1.01111 0.01110675 8 1.02633 0.02632640 9 0.999173 0.00082696 Integrate 5940.00 * X ** 8 * Y ** 2 Rule QUAD ERROR 1 0.502972E-01 0.94970279 2 0.246420 0.75358009 3 1.06812 0.06812288 4 1.01228 0.01228049 5 0.794160 0.20583991 6 0.902320 0.09767985 7 0.839699 0.16030106 8 0.887061 0.11293888 9 1.00007 0.00006791 Integrate 110.000 * X ** 9 * Y ** 0 Rule QUAD ERROR 1 0.279429E-02 0.99720571 2 0.359472E-01 0.96405284 3 0.316143 0.68385707 4 0.402443 0.59755682 5 0.865185 0.13481489 6 0.855218 0.14478183 7 0.999980 0.00002000 8 0.992172 0.00782787 9 1.00018 0.00018377 Integrate 1320.00 * X ** 9 * Y ** 1 Rule QUAD ERROR 1 0.111772E-01 0.98882284 2 0.108051 0.89194870 3 0.750154 0.24984576 4 0.825265 0.17473498 5 1.28873 0.28873176 6 1.22527 0.22526601 7 1.04631 0.04631448 8 1.06116 0.06115680 9 0.997892 0.00210815 Integrate 132.000 * X ** 10 * Y ** 0 Rule QUAD ERROR 1 0.111772E-02 0.99888228 2 0.215263E-01 0.97847366 3 0.229341 0.77065933 4 0.317879 0.68212119 5 0.780476 0.21952422 6 0.781209 0.21879140 7 0.990713 0.00928690 8 0.978375 0.02162480 9 1.00064 0.00064215 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 0.00000 0.00000 2 1.00000 0.00000 3 0.00000 1.00000 Rule 3 for reference triangle with area = 0.500000 X Y W 1 0.600000 0.200000 0.583333 2 0.200000 0.200000 0.583333 3 0.200000 0.600000 0.583333 4 0.400000 0.400000 -0.250000 5 0.400000 0.200000 -0.250000 6 0.200000 0.400000 -0.250000 The physical triangle: 1 1.00000 2.00000 2 1.00000 1.00000 3 3.00000 2.00000 Rule 3 for physical triangle with area = 1.00000 X Y W 1 1.40000 1.40000 0.583333 2 1.40000 1.80000 0.583333 3 2.20000 1.80000 0.583333 4 1.80000 1.60000 -0.250000 5 1.40000 1.60000 -0.250000 6 1.80000 1.80000 -0.250000 TRIANGLE_NCO_RULE_TEST(): Normal end of execution. 23 March 2023 4:28:10.096 PM