03 March 2022 09:16:49 AM TRIANGLE_FEKETE_RULE_TEST: C++ version Test the TRIANGLE_FEKETE_RULE library. TEST01 FEKETE_RULE_NUM returns the number of rules; FEKETE_DEGREE returns the degree of a rule; FEKETE_ORDER_NUM returns the order of a rule. Number of available rules = 7 Rule Degree Order 1 3 10 2 6 28 3 9 55 4 12 91 5 12 91 6 15 136 7 18 190 TEST02 FEKETE_RULE returns the points and weights of a Fekete rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 7 Rule Sum of weights 1 1 2 1 3 1 4 1 5 1 6 1 7 1 TEST03 FEKETE_RULE returns the points and weights of a Fekete 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 3 1 1 1 2 7 1 1 1 1 1 1 1 3 12 1 1 1 1 1 1 1 1 1 1 1 1 4 19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 TEST04 FEKETE_RULE returns the points and weights of a Fekete 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 1.00000000005 5.000022618162347e-11 2 1.00000000035 3.500004730483397e-10 3 0.999999999449999 5.500010447079262e-10 4 1.0000000002 2.00000460637284e-10 5 1.000000000000001 6.661338147750939e-16 6 0.9999999998000024 1.9999757405742e-10 7 0.9999999993000003 6.999997248513523e-10 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 1.000000000005 5.000000413701855e-12 2 1.000000000339107 3.391071867753226e-10 3 0.9999999994445201 5.554798843121489e-10 4 1.000000000196868 1.968680773956066e-10 5 0.9999999999975697 2.430278200904468e-12 6 0.9999999997977025 2.022975120752335e-10 7 0.9999999992983694 7.016306424745267e-10 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 0.9999999999152975 8.470246726233199e-11 2 1.000000000513482 5.134819236474186e-10 3 0.9999999993215931 6.784068862231152e-10 4 1.00000000042786 4.278604137653019e-10 5 0.9999999998057331 1.942669358712124e-10 6 0.9999999996387232 3.612767862648525e-10 7 0.9999999992621675 7.378324617945964e-10 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 0.9999999998049101 1.95089944199367e-10 2 1.000000000724666 7.246656608117519e-10 3 0.9999999991980418 8.019581665408282e-10 4 1.000000000711683 7.116831568509951e-10 5 0.9999999995652045 4.347955329109254e-10 6 0.9999999994509036 5.490964349874616e-10 7 0.9999999992352679 7.647320554582393e-10 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 1.03333333301119 0.03333333301118979 2 1.000000000949508 9.495078057142337e-10 3 0.999999999086036 9.139640155808593e-10 4 1.000000001000211 1.000210803070445e-09 5 0.9999999992911462 7.088537534727379e-10 6 0.9999999992376855 7.62314544822118e-10 7 0.9999999991803886 8.19611378766183e-10 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 1.088888888424756 0.08888888842475606 2 1.00000000118225 1.182250297659948e-09 3 0.9999999989850538 1.014946238164782e-09 4 1.000000001268445 1.268444904667376e-09 5 0.9999999989971702 1.002829819185536e-09 6 0.9999999989973642 1.002635752200831e-09 7 0.9999999990870521 9.129479394687223e-10 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 1.155950616665946 0.1559506166659459 2 1.000000001426466 1.426465612297534e-09 3 0.9999999988888659 1.111134073639164e-09 4 1.000000001503607 1.503607016672959e-09 5 0.9999999986969788 1.303021246457092e-09 6 0.99999999872887 1.271129979052432e-09 7 0.9999999989567177 1.043282349399988e-09 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 1.231407406626621 0.2314074066266212 2 0.9998135441340021 0.0001864558659978588 3 0.9999999987906669 1.209333078122654e-09 4 1.000000001699548 1.699548279887608e-09 5 0.9999999984021902 1.597809773379311e-09 6 0.9999999984310814 1.568918550631793e-09 7 0.9999999987946117 1.205388344693858e-09 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 1.317086418802287 0.3170864188022875 2 0.9992016850633901 0.0007983149366098674 3 0.999999998685292 1.314708009125809e-09 4 1.000000001853784 1.853784459271424e-09 5 0.9999999981213941 1.878605937477573e-09 6 0.9999999981028593 1.89714066678448e-09 7 0.9999999986062461 1.393753890077676e-09 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 1.416590762475256 0.4165907624752556 2 0.9979290498636655 0.002070950136334515 3 0.9999999985696346 1.430365381693832e-09 4 1.000000001965827 1.96582661260436e-09 5 0.9999999978603521 2.13964790329868e-09 6 0.9999999977432281 2.256771880482233e-09 7 0.9999999983962182 1.603781774051072e-09 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 1.533462970795029 0.5334629707950289 2 0.9957993960340967 0.004200603965903271 3 1.000003161939595 3.161939595264229e-06 4 1.000000002036216 2.036216084633224e-09 5 0.9999999976226406 2.37735942043571e-09 6 0.9999999973514213 2.648578689701253e-09 7 0.9999999981679656 1.8320344130629e-09 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 1.000000000005 5.000000413701855e-12 2 1.000000000339107 3.391071867753226e-10 3 0.9999999994445201 5.554798843121489e-10 4 1.000000000196868 1.968680773956066e-10 5 0.9999999999975697 2.430278200904468e-12 6 0.9999999997977025 2.022975120752335e-10 7 0.9999999992983695 7.016305314522242e-10 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1.000000000004702 4.702460643102313e-12 2 1.000000000142947 1.42946765535612e-10 3 0.9999999995564874 4.435125600110723e-10 4 0.9999999999596146 4.038536172146223e-11 5 1.000000000184547 1.845470443129216e-10 6 0.9999999999520813 4.791866903275377e-11 7 0.9999999993313107 6.686893261331761e-10 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1.000000000005878 5.878186826180354e-12 2 1.000000000178551 1.785513958907359e-10 3 0.9999999994977853 5.022147142597078e-10 4 0.9999999999951649 4.835132294545019e-12 5 1.000000000162476 1.624764767171882e-10 6 0.9999999999199761 8.002387641425912e-11 7 0.9999999993019865 6.980135358602979e-10 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 0.9333333333423512 0.06666666665764875 2 1.000000000262878 2.628781636815347e-10 3 0.9999999994159653 5.840347094832055e-10 4 1.000000000127664 1.276636574232271e-10 5 1.000000000110621 1.106206237722063e-10 6 0.9999999998814907 1.185093134736803e-10 7 0.9999999993475878 6.524122353468442e-10 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 0.8944444444481074 0.1055555555518926 2 1.000000000360591 3.60591112524844e-10 3 0.9999999993349398 6.650602291102814e-10 4 1.000000000323446 3.234459367007503e-10 5 1.000000000024512 2.451172598227913e-11 6 0.9999999998455406 1.544594452340675e-10 7 0.9999999994181379 5.818621140463165e-10 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 0.8877037036856311 0.1122962963143689 2 1.000000000445838 4.458378111138472e-10 3 0.9999999992717225 7.282775493777649e-10 4 1.000000000558047 5.580467199450823e-10 5 0.999999999896906 1.030939777990625e-10 6 0.9999999998108101 1.891898859796015e-10 7 0.9999999994829517 5.17048293069422e-10 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 0.8918518517958048 0.1081481482041952 2 1.000652601948206 0.0006526019482064882 3 0.9999999992316166 7.683833569416265e-10 4 1.000000000814246 8.14245781910472e-10 5 0.9999999997283181 2.716818991999048e-10 6 0.9999999997785975 2.214024519275881e-10 7 0.9999999995285663 4.714336698796728e-10 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 0.8886913579202516 0.1113086420797484 2 1.002260980415554 0.00226098041555356 3 0.9999999992117152 7.882847707918472e-10 4 1.00000000108019 1.080190159541417e-09 5 0.9999999995251722 4.748278437105569e-10 6 0.999999999750223 2.497769768794456e-10 7 0.9999999995517074 4.482926252435959e-10 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 0.869316872272234 0.130683127727766 2 1.00492854346174 0.004928543461739654 3 0.9999999992055436 7.94456389563436e-10 4 1.000000001348059 1.348059219807851e-09 5 0.9999999992959937 7.040062977026196e-10 6 0.9999999997260496 2.739504179061214e-10 7 0.9999999995541107 4.458893254621898e-10 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 0.8322297208756354 0.1677702791243646 2 1.008577319011327 0.008577319011326745 3 0.9999841817197399 1.581828026009369e-05 4 1.000000001612938 1.612937783335155e-09 5 0.9999999990488686 9.511313958654455e-10 6 0.9999999997058102 2.94189783645038e-10 7 0.9999999995394189 4.605811287916595e-10 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 0.9999999999152975 8.470246726233199e-11 2 1.000000000513482 5.134819236474186e-10 3 0.9999999993215931 6.784068862231152e-10 4 1.00000000042786 4.278604137653019e-10 5 0.9999999998057331 1.942669358712124e-10 6 0.9999999996387234 3.612765642202476e-10 7 0.9999999992621674 7.378325728168988e-10 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1.000000000005878 5.878186826180354e-12 2 1.000000000178552 1.785516179353408e-10 3 0.9999999994977853 5.022147142597078e-10 4 0.9999999999986505 1.349476086431878e-12 5 1.000000000162477 1.624766987617932e-10 6 0.9999999999132709 8.672906837148275e-11 7 0.9999999992976135 7.023864823096915e-10 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.100000000054107 0.1000000000541075 2 1.000000000153177 1.53177026618323e-10 3 0.9999999994798504 5.201495900664099e-10 4 0.9999999998922552 1.077448130715197e-10 5 1.000000000187781 1.877811239836547e-10 6 0.9999999998932895 1.067105293017789e-10 7 0.9999999991577123 8.422876840441518e-10 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 1.088888888990903 0.08888888899090319 2 1.000000000193917 1.939166605069431e-10 3 0.9999999994261083 5.7389171193023e-10 4 0.9999999999037803 9.621969887518844e-11 5 1.000000000181751 1.817508366031007e-10 6 0.9999999998648105 1.351895262402536e-10 7 0.9999999991217267 8.78273342941327e-10 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 1.099259259396871 0.09925925939687064 2 1.000000000292667 2.92667445833672e-10 3 0.9999999993446034 6.553966258593391e-10 4 0.9999999999973134 2.686628697290416e-12 5 1.00000000017216 1.721602860271787e-10 6 0.9999999998378506 1.621494050141337e-10 7 0.9999999991482701 8.517299088239838e-10 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 1.163555555704592 0.1635555557045918 2 0.9991609414233338 0.0008390585766662184 3 0.9999999992577531 7.422469305851109e-10 4 1.000000000148536 1.485356282415751e-10 5 1.000000000148924 1.489244283447988e-10 6 0.9999999998072014 1.927985548988431e-10 7 0.9999999991991474 8.008526064529065e-10 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 1.262419753214934 0.2624197532149337 2 0.9985833051697768 0.00141669483022322 3 0.9999999991856986 8.143014040840058e-10 4 1.000000000339608 3.396083414486384e-10 5 1.000000000097339 9.733858163940567e-11 6 0.9999999997758289 2.241711261063983e-10 7 0.9999999992472948 7.527052314770799e-10 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 1.365267489787675 0.3652674897876749 2 0.999035250101947 0.0009647498980529523 3 0.9999999991391836 8.608164181467259e-10 4 1.000000000556788 5.567879490797623e-10 5 1.000000000009464 9.463541061904834e-12 6 0.9999999997492672 2.507327678813454e-10 7 0.9999999992770694 7.229306042688677e-10 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 1.44823374485292 0.4482337448529203 2 1.001273865832612 0.001273865832612131 3 1.000043879102872 4.387910287162455e-05 4 1.000000000789719 7.897194009842678e-10 5 0.9999999998845414 1.154586426466153e-10 6 0.9999999997311498 2.688501643532959e-10 7 0.9999999992819512 7.180488426072884e-10 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 0.9999999998049101 1.95089944199367e-10 2 1.000000000724666 7.246656608117519e-10 3 0.9999999991980418 8.019581665408282e-10 4 1.000000000711683 7.116831568509951e-10 5 0.9999999995652044 4.347956439332279e-10 6 0.9999999994509037 5.490963239651592e-10 7 0.9999999992352679 7.647320554582393e-10 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 0.9333333333423512 0.06666666665764875 2 1.000000000262878 2.628781636815347e-10 3 0.9999999994159653 5.840347094832055e-10 4 1.000000000134635 1.346345257502435e-10 5 1.000000000110621 1.106206237722063e-10 6 0.9999999998680803 1.319196973881276e-10 7 0.9999999993388422 6.61157795178724e-10 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 1.088888888990903 0.08888888899090297 2 1.000000000193917 1.939166605069431e-10 3 0.9999999994261083 5.7389171193023e-10 4 0.9999999999115826 8.841738452503023e-11 5 1.000000000181751 1.817508366031007e-10 6 0.999999999852037 1.479629752054734e-10 7 0.9999999991129843 8.870156831264353e-10 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 1.092345679204606 0.09234567920460557 2 1.000000000156208 1.562083795647595e-10 3 0.9999999994138432 5.86156789772474e-10 4 0.9999999998243454 1.756546019748839e-10 5 1.000000000171805 1.718054587485085e-10 6 0.9999999998300872 1.699127505361275e-10 7 0.9999999989946209 1.00537911329468e-09 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 1.099259259527404 0.09925925952740355 2 1.000466144077805 0.0004661440778046533 3 0.9999999993603083 6.39691744019899e-10 4 0.9999999998306736 1.69326441756823e-10 5 1.000000000163437 1.634370416780939e-10 6 0.9999999998141257 1.858743159388609e-10 7 0.9999999989610743 1.038925723229056e-09 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 1.180839506499019 0.1808395064990189 2 0.9986673762974549 0.001332623702545055 3 0.9999999992720681 7.279319369501991e-10 4 0.999999999905277 9.472300721569127e-11 5 1.000000000172292 1.722924025671091e-10 6 0.9999999997867485 2.132515275476976e-10 7 0.9999999989850967 1.014903272533729e-09 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 1.337624143019043 0.3376241430190434 2 0.995618664400385 0.004381335599614955 3 0.99999999917079 8.292100339701847e-10 4 1.000000000031131 3.113087565509431e-11 5 1.000000000185253 1.852533682011881e-10 6 0.9999999997453147 2.546852728713134e-10 7 0.9999999990375874 9.624125940632666e-10 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 1.538756653302583 0.5387566533025832 2 0.9916380340322138 0.008361965967786156 3 0.9999193840661035 8.061593389652177e-05 4 1.000000000194742 1.947415562142396e-10 5 1.000000000184889 1.848889930045061e-10 6 0.9999999996982651 3.017348593203906e-10 7 0.9999999990928571 9.071429163398648e-10 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 1.03333333301119 0.03333333301118979 2 1.000000000949508 9.495078057142337e-10 3 0.999999999086036 9.139640155808593e-10 4 1.000000001000211 1.000210803070445e-09 5 0.9999999992911462 7.088537534727379e-10 6 0.9999999992376855 7.62314544822118e-10 7 0.9999999991803886 8.19611378766183e-10 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 0.8944444444481074 0.1055555555518926 2 1.000000000360591 3.60591112524844e-10 3 0.9999999993349397 6.650603401325839e-10 4 1.000000000331744 3.317444097206135e-10 5 1.000000000024512 2.451194802688406e-11 6 0.999999999828459 1.715410036240428e-10 7 0.9999999994072042 5.9279581243743e-10 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 1.099259259396871 0.09925925939687064 2 1.000000000292667 2.92667445833672e-10 3 0.9999999993446034 6.553966258593391e-10 4 1.000000000011361 1.13606901663843e-11 5 1.00000000017216 1.721602860271787e-10 6 0.9999999998133182 1.866817811446708e-10 7 0.9999999991318338 8.681662055920469e-10 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 1.099259259527403 0.09925925952740333 2 1.000466144077805 0.0004661440778046533 3 0.9999999993603083 6.39691744019899e-10 4 0.9999999998409718 1.59028235025005e-10 5 1.000000000163437 1.63436819633489e-10 6 0.9999999997963136 2.036864010790396e-10 7 0.9999999989492367 1.050763254184517e-09 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 1.056049383086711 0.05604938308671081 2 1.003639571591667 0.003639571591666613 3 0.9999999993491727 6.508272809568894e-10 4 0.9999999997729127 2.270873489251812e-10 5 1.000000000124248 1.242477232210604e-10 6 0.9999999998022866 1.977134012065562e-10 7 0.9999999988466084 1.153391604447052e-09 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 1.082436214447029 0.08243621444702853 2 1.004260812222665 0.004260812222665278 3 0.9999999992919604 7.080396269287803e-10 4 0.9999999997795295 2.204705307207178e-10 5 1.000000000109378 1.093776180738359e-10 6 0.9999999997997894 2.002106258558456e-10 7 0.9999999988175202 1.182479780759138e-09 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 1.214424143190367 0.2144241431903668 2 1.003877422679327 0.003877422679327447 3 1.000113776760087 0.0001137767600867257 4 0.9999999998443113 1.556886841669325e-10 5 1.000000000125164 1.25164101305586e-10 6 0.9999999997700436 2.299563872654176e-10 7 0.9999999988468253 1.15317466686804e-09 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 1.088888888424756 0.08888888842475606 2 1.000000001182251 1.182250519704553e-09 3 0.9999999989850537 1.014946349187085e-09 4 1.000000001268445 1.268444904667376e-09 5 0.9999999989971702 1.002829819185536e-09 6 0.9999999989973641 1.002635863223134e-09 7 0.9999999990870521 9.129479394687223e-10 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 0.887703703685631 0.112296296314369 2 1.000000000445838 4.458380331584522e-10 3 0.9999999992717225 7.282775493777649e-10 4 1.000000000565705 5.657052604135515e-10 5 0.9999999998969058 1.030941998436674e-10 6 0.9999999997932926 2.067074289513471e-10 7 0.9999999994720328 5.27967225494308e-10 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 1.163555555704592 0.1635555557045918 2 0.9991609414233338 0.0008390585766662184 3 0.9999999992577528 7.422471526297159e-10 4 1.000000000164839 1.648388092689856e-10 5 1.000000000148924 1.489244283447988e-10 6 0.9999999997755584 2.24441576435197e-10 7 0.9999999991785501 8.214499080949622e-10 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 1.180839506499018 0.1808395064990185 2 0.9986673762974549 0.001332623702545055 3 0.9999999992720682 7.279318259278966e-10 4 0.9999999999228858 7.711420391132151e-11 5 1.000000000172292 1.722921805225042e-10 6 0.9999999997527826 2.472173576961723e-10 7 0.9999999989632169 1.036783103813832e-09 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 1.082436214447028 0.08243621444702809 2 1.004260812222665 0.004260812222665278 3 0.9999999992919603 7.080397379510828e-10 4 0.9999999997902455 2.097545470647333e-10 5 1.000000000109378 1.093776180738359e-10 6 0.9999999997775065 2.224934680938873e-10 7 0.9999999988035667 1.196433285777232e-09 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 1.013788971739736 0.01378897173973614 2 1.006650502845561 0.006650502845560569 3 0.9998743856837484 0.0001256143162515766 4 0.9999999997366055 2.633945284102879e-10 5 1.000000000049992 4.999223257584617e-11 6 0.999999999813931 1.860690490573802e-10 7 0.9999999987080969 1.291903140021589e-09 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 1.155950616665946 0.1559506166659459 2 1.000000001426466 1.426465834342139e-09 3 0.999999998888866 1.111133962616861e-09 4 1.000000001503607 1.503607016672959e-09 5 0.9999999986969788 1.303021246457092e-09 6 0.9999999987288701 1.27112986803013e-09 7 0.9999999989567177 1.043282349399988e-09 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 0.8918518517958048 0.1081481482041952 2 1.000652601948206 0.0006526019482062662 3 0.9999999992316165 7.68383467963929e-10 4 1.000000000820299 8.202989398853333e-10 5 0.999999999728318 2.716820102222073e-10 6 0.9999999997628687 2.371313145843601e-10 7 0.9999999995190537 4.809462827992661e-10 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 1.262419753214934 0.2624197532149337 2 0.9985833051697768 0.00141669483022322 3 0.9999999991856987 8.143012930617033e-10 4 1.000000000354798 3.547981908269549e-10 5 1.000000000097339 9.733858163940567e-11 6 0.9999999997422905 2.577095203903923e-10 7 0.9999999992261515 7.738485408026463e-10 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 1.337624143019043 0.3376241430190434 2 0.9956186644003853 0.004381335599614733 3 0.9999999991707901 8.292099229478822e-10 4 1.000000000051339 5.133893310471649e-11 5 1.000000000185253 1.852533682011881e-10 6 0.9999999997008179 2.991821235198699e-10 7 0.999999999009871 9.901289788061263e-10 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 1.214424143190367 0.2144241431903668 2 1.003877422679327 0.003877422679327447 3 1.000113776760087 0.0001137767600869477 4 0.9999999998621287 1.378712699562357e-10 5 1.000000000125164 1.25163879260981e-10 6 0.999999999727597 2.724029890543989e-10 7 0.9999999988211469 1.178853126226898e-09 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 1.231407406626621 0.2314074066266212 2 0.9998135441340021 0.0001864558659978588 3 0.999999998790667 1.209332967100352e-09 4 1.000000001699548 1.699548279887608e-09 5 0.9999999984021903 1.597809662357008e-09 6 0.9999999984310813 1.568918661654095e-09 7 0.9999999987946117 1.205388344693858e-09 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 0.8886913579202516 0.1113086420797484 2 1.002260980415553 0.002260980415553338 3 0.9999999992117151 7.882848818141497e-10 4 1.000000001084498 1.084498046921567e-09 5 0.999999999525172 4.748279547328593e-10 6 0.9999999997373357 2.626643347269919e-10 7 0.9999999995441589 4.558411426103248e-10 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 1.365267489787675 0.3652674897876751 2 0.999035250101947 0.0009647498980529523 3 0.9999999991391834 8.608166401913309e-10 4 1.000000000569117 5.691167537236197e-10 5 1.000000000009463 9.463319017299909e-12 6 0.9999999997178676 2.821324285307014e-10 7 0.9999999992579252 7.42074846016294e-10 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 1.538756653302583 0.5387566533025832 2 0.9916380340322138 0.008361965967786156 3 0.9999193840661035 8.061593389652177e-05 4 1.000000000213753 2.137525711987109e-10 5 1.000000000184889 1.848887709599012e-10 6 0.9999999996498258 3.501742229516935e-10 7 0.9999999990637093 9.362907116283736e-10 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 1.317086418802287 0.3170864188022875 2 0.9992016850633901 0.0007983149366098674 3 0.999999998685292 1.314708009125809e-09 4 1.000000001853784 1.853784459271424e-09 5 0.9999999981213942 1.878605826455271e-09 6 0.9999999981028593 1.89714066678448e-09 7 0.9999999986062461 1.393753890077676e-09 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 0.8693168722722338 0.1306831277277662 2 1.00492854346174 0.004928543461739876 3 0.9999999992055437 7.944562785411335e-10 4 1.0000000013509 1.350900058483262e-09 5 0.9999999992959936 7.04006408724922e-10 6 0.9999999997161793 2.838207446842489e-10 7 0.9999999995485175 4.514825180379489e-10 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 1.44823374485292 0.4482337448529203 2 1.001273865832612 0.001273865832612131 3 1.000043879102871 4.387910287140251e-05 4 1.000000000798807 7.988070205300346e-10 5 0.9999999998845414 1.154586426466153e-10 6 0.99999999970422 2.957799560832086e-10 7 0.9999999992660835 7.339164831421385e-10 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 1.416590762475256 0.4165907624752556 2 0.9979290498636655 0.002070950136334515 3 0.9999999985696346 1.430365381693832e-09 4 1.000000001965827 1.96582661260436e-09 5 0.9999999978603521 2.13964790329868e-09 6 0.9999999977432281 2.256771880482233e-09 7 0.9999999983962183 1.603781663028769e-09 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 0.8322297208756354 0.1677702791243646 2 1.008577319011327 0.008577319011326523 3 0.9999841817197398 1.581828026020471e-05 4 1.000000001614706 1.614705924524173e-09 5 0.9999999990488686 9.511313958654455e-10 6 0.9999999996986342 3.013658211870052e-10 7 0.9999999995354875 4.645125395441596e-10 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 1.533462970795029 0.5334629707950289 2 0.9957993960340967 0.004200603965903271 3 1.000003161939595 3.161939595264229e-06 4 1.000000002036216 2.036216306677829e-09 5 0.9999999976226406 2.37735942043571e-09 6 0.9999999973514213 2.648578689701253e-09 7 0.9999999981679656 1.8320344130629e-09 TEST05 This routine creates an EPS plot of each set of Fekete points. Rule 1 plotted in "fekete_rule_1.eps". Rule 2 plotted in "fekete_rule_2.eps". Rule 3 plotted in "fekete_rule_3.eps". Rule 4 plotted in "fekete_rule_4.eps". Rule 5 plotted in "fekete_rule_5.eps". Rule 6 plotted in "fekete_rule_6.eps". Rule 7 plotted in "fekete_rule_7.eps". TEST06 REFERENCE_TO_PHYSICAL_T3 transforms a rule on the unit (reference) triangle to a rule on an arbitrary (physical) triangle. The reference triangle: 1 0 0 2 1 0 3 0 1 Rule 2 for reference triangle with area = 0.5 X Y W 0 0.3333333333 0.3333333333 0.10892817855 1 0.1063354684 0.1063354684 0.0552096687 2 0.1063354684 0.7873290632 0.0552096687 3 0.7873290632 0.1063354684 0.0552096687 4 0.5 0.5 0.0179469881 5 0.5 0 0.0179469881 6 0 0.5 0.0179469881 7 1 0 0.0002010639 8 0 0 0.0002010639 9 0 1 0.0002010639 10 0.1171809171 0.3162697959 0.088567433 11 0.3162697959 0.566549287 0.088567433 12 0.566549287 0.1171809171 0.088567433 13 0.3162697959 0.1171809171 0.088567433 14 0.566549287 0.3162697959 0.088567433 15 0.1171809171 0.566549287 0.088567433 16 0 0.2655651402 0.01361720395 17 0.2655651402 0.7344348598 0.01361720395 18 0.7344348598 0 0.01361720395 19 0.2655651402 0 0.01361720395 20 0.7344348598 0.2655651402 0.01361720395 21 0 0.7344348598 0.01361720395 22 0 0.0848854223 0.009648472999999999 23 0.0848854223 0.9151145777 0.009648472999999999 24 0.9151145777 0 0.009648472999999999 25 0.0848854223 0 0.009648472999999999 26 0.9151145777 0.0848854223 0.009648472999999999 27 0 0.9151145777 0.009648472999999999 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 2 for physical triangle with area = 1 X Y W 0 1.6666666666 1.6666666667 0.10892817855 1 1.2126709368 1.8936645316 0.0552096687 2 2.5746581264 1.8936645316 0.0552096687 3 1.2126709368 1.2126709368 0.0552096687 4 2 1.5 0.0179469881 5 1 1.5 0.0179469881 6 2 2 0.0179469881 7 1 1 0.0002010639 8 1 2 0.0002010639 9 3 2 0.0002010639 10 1.6325395918 1.8828190829 0.088567433 11 2.133098574 1.6837302041 0.088567433 12 1.2343618342 1.433450713 0.088567433 13 1.2343618342 1.6837302041 0.088567433 14 1.6325395918 1.433450713 0.088567433 15 2.133098574 1.8828190829 0.088567433 16 1.5311302804 2 0.01361720395 17 2.4688697196 1.7344348598 0.01361720395 18 1 1.2655651402 0.01361720395 19 1 1.7344348598 0.01361720395 20 1.5311302804 1.2655651402 0.01361720395 21 2.4688697196 2 0.01361720395 22 1.1697708446 2 0.009648472999999999 23 2.830229155400001 1.9151145777 0.009648472999999999 24 1 1.0848854223 0.009648472999999999 25 1 1.9151145777 0.009648472999999999 26 1.1697708446 1.0848854223 0.009648472999999999 27 2.830229155400001 2 0.009648472999999999 TRIANGLE_FEKETE_RULE_TEST: Normal end of execution. 03 March 2022 09:16:49 AM