15 June 2014 11:21:21 AM
TRIANGLE_NCO_RULE_PRB:
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 0.6296296296296297
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 1.000000000000001 1.110223024625157e-15
8 1 0
9 1.000000000000001 8.881784197001252e-16
Integrate 30 * X^0 * Y^4
Rule QUAD ERROR
1 0.1851851851851852 0.8148148148148149
2 0.3515625 0.6484375
3 0.964 0.03600000000000003
4 0.9490740740740743 0.05092592592592571
5 1 0
6 0.9999999999999999 1.110223024625157e-16
7 1.000000000000002 2.220446049250313e-15
8 1 4.440892098500626e-16
9 1 0
Integrate 42 * X^0 * Y^5
Rule QUAD ERROR
1 0.08641975308641975 0.9135802469135803
2 0.232421875 0.767578125
3 0.8512 0.1488
4 0.8533950617283951 0.1466049382716049
5 1.004164931278634 0.004164931278634487
6 0.9999999999999998 2.220446049250313e-16
7 1.000000000000002 2.220446049250313e-15
8 1 0
9 1.000000000000005 4.884981308350689e-15
Integrate 56 * X^0 * Y^6
Rule QUAD ERROR
1 0.03840877914951989 0.9615912208504801
2 0.150390625 0.849609375
3 0.7063466666666667 0.2936533333333333
4 0.7357681755829903 0.2642318244170097
5 1.001765137541897 0.001765137541897444
6 0.9906412760416662 0.009358723958333814
7 1.000000000000002 1.77635683940025e-15
8 1.000000000000002 1.554312234475219e-15
9 1.000000000000003 3.108624468950438e-15
Integrate 72 * X^0 * Y^7
Rule QUAD ERROR
1 0.01646090534979424 0.9835390946502057
2 0.09521484375 0.90478515625
3 0.5587968 0.4412032
4 0.6149176954732509 0.3850823045267491
5 0.9801732271417528 0.01982677285824719
6 0.963922119140625 0.03607788085937502
7 1.000938203864588 0.0009382038645884272
8 1.000000000000002 1.554312234475219e-15
9 0.9999999999999997 3.33066907387547e-16
Integrate 90 * X^0 * Y^8
Rule QUAD ERROR
1 0.006858710562414265 0.9931412894375857
2 0.059051513671875 0.940948486328125
3 0.4262591999999999 0.5737408000000001
4 0.5020254629629629 0.4979745370370371
5 0.9339330186766209 0.06606698132337907
6 0.9178333282470701 0.08216667175292991
7 1.002003044552453 0.002003044552453259
8 0.998382000000002 0.00161799999999801
9 1.000000000000003 3.108624468950438e-15
Integrate 110 * X^0 * Y^9
Rule QUAD ERROR
1 0.002794289488390997 0.997205710511609
2 0.03594716389973958 0.9640528361002604
3 0.3161429333333333 0.6838570666666667
4 0.4024431774881876 0.5975568225118124
5 0.8651851122007511 0.1348148877992489
6 0.8552181720733643 0.1447818279266357
7 0.9999799984765407 2.000152345926764e-05
8 0.9921721333333346 0.007827866666665351
9 1.00018376814224 0.0001837681422396376
Integrate 132 * X^0 * Y^10
Rule QUAD ERROR
1 0.001117715795356399 0.9988822842046436
2 0.02152633666992188 0.9784736633300781
3 0.229340672 0.770659328
4 0.3178788088070924 0.6821211911929077
5 0.7804757824994433 0.2195242175005567
6 0.7812086045742037 0.2187913954257963
7 0.9907131021663657 0.009286897833634344
8 0.9783752000000018 0.02162479999999822
9 1.000642152285983 0.0006421522859831885
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 0.7407407407407407 0.2592592592592593
2 0.859375 0.140625
3 1.112 0.1120000000000001
4 1.101851851851852 0.1018518518518519
5 0.9999999999999997 3.33066907387547e-16
6 0.9999999999999999 1.110223024625157e-16
7 1.000000000000002 1.77635683940025e-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 0.246
4 1.188271604938271 0.1882716049382713
5 0.9895876718034158 0.01041232819658422
6 0.9999999999999999 1.110223024625157e-16
7 1.000000000000004 4.218847493575595e-15
8 0.9999999999999991 8.881784197001252e-16
9 1.000000000000003 2.664535259100376e-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 0.206275720164609
5 1.011364312488844 0.01136431248884362
6 1.028076171875 0.028076171875
7 1.000000000000004 4.440892098500626e-15
8 1.000000000000001 6.661338147750939e-16
9 1.000000000000002 1.77635683940025e-15
Integrate 504 * X^1 * Y^6
Rule QUAD ERROR
1 0.1152263374485597 0.8847736625514403
2 0.343505859375 0.656494140625
3 1.2227712 0.2227711999999999
4 1.158744855967078 0.1587448559670783
5 1.077336823942405 0.07733682394240504
6 1.084158325195313 0.08415832519531263
7 0.9967162864739487 0.00328371352605128
8 1 2.220446049250313e-16
9 1 4.440892098500626e-16
Integrate 720 * X^1 * Y^7
Rule QUAD ERROR
1 0.05486968449931412 0.9451303155006858
2 0.2398681640625 0.7601318359375
3 1.0889472 0.0889472
4 1.066486625514403 0.06648662551440299
5 1.16513406100228 0.1651340610022798
6 1.148277282714844 0.1482772827148438
7 0.9966788411131281 0.0033211588868719
8 1.006472000000001 0.006472000000001144
9 1.000000000000001 6.661338147750939e-16
Integrate 990 * X^1 * Y^8
Rule QUAD ERROR
1 0.02514860539551897 0.974851394604481
2 0.1630210876464844 0.8369789123535156
3 0.9217823999999999 0.07821760000000011
4 0.9501457475994513 0.04985425240054875
5 1.243298597818034 0.2432985978180344
6 1.199601531028748 0.1996015310287476
7 1.011106751894067 0.01110675189406662
8 1.026326400000002 0.02632640000000208
9 0.999173043359938 0.0008269566400620487
Integrate 1320 * X^1 * Y^9
Rule QUAD ERROR
1 0.01117715795356399 0.988822842046436
2 0.1080513000488281 0.8919486999511719
3 0.7501542400000001 0.2498457599999999
4 0.8252650208936644 0.1747349791063356
5 1.28873176070729 0.2887317607072901
6 1.225266009569168 0.2252660095691683
7 1.046314480027414 0.04631448002741378
8 1.061156800000002 0.06115680000000201
9 0.997891847423519 0.002108152576481004
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 0.8641975308641975 0.1358024691358025
2 0.888671875 0.111328125
3 0.7111999999999999 0.2888000000000001
4 0.8533950617283952 0.1466049382716048
5 1.004164931278634 0.004164931278633599
6 1 2.220446049250313e-16
7 1.000000000000003 3.108624468950438e-15
8 0.999999999999997 2.997602166487923e-15
9 0.9999999999999958 4.218847493575595e-15
Integrate 840 * X^2 * Y^4
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
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 1.000000000000004 3.552713678800501e-15
8 0.9999999999999973 2.664535259100376e-15
9 0.999999999999996 3.996802888650564e-15
Integrate 1512 * X^2 * Y^5
Rule QUAD ERROR
1 0.345679012345679 0.654320987654321
2 0.569091796875 0.430908203125
3 1.0313856 0.03138560000000012
4 1.029475308641975 0.02947530864197523
5 0.7860398303427989 0.2139601696572011
6 0.8692657470703125 0.1307342529296875
7 1.004221917390647 0.00422191739064659
8 0.9999999999999979 2.109423746787797e-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 0.1292288000000001
4 1.068394204389575 0.06839420438957489
5 0.7085993081114168 0.2914006918885832
6 0.8359470367431641 0.1640529632568359
7 0.9852768228269977 0.01472317717300231
8 0.9820319999999984 0.01796800000000165
9 1.000000000000004 3.996802888650564e-15
Integrate 3960 * X^2 * Y^7
Rule QUAD ERROR
1 0.1005944215820759 0.8994055784179241
2 0.3348541259765625 0.6651458740234375
3 1.13600256 0.1360025600000001
4 1.059306412894376 0.05930641289437588
5 0.7160417159239331 0.2839582840760669
6 0.8517222404479983 0.1482777595520017
7 0.926271318087159 0.07372868191284099
8 0.940255066666667 0.05974493333333297
9 1.001695386563747 0.001695386563747237
Integrate 5940 * X^2 * Y^8
Rule QUAD ERROR
1 0.05029721079103795 0.949702789208962
2 0.2464199066162109 0.7535800933837891
3 1.06812288 0.06812288
4 1.012280485539552 0.01228048553955152
5 0.7941600858629574 0.2058399141370426
6 0.9023201465606693 0.09767985343933072
7 0.8396989401353052 0.1603010598646948
8 0.8870611200000005 0.1129388799999995
9 1.000067908419098 6.790841909798395e-05
Integrate 20 * X^3 * Y^0
Rule QUAD ERROR
1 0.3703703703703703 0.6296296296296297
2 0.5208333333333333 0.4791666666666667
3 1.013333333333333 0.0133333333333332
4 1 0
5 1 0
6 1 2.220446049250313e-16
7 1.000000000000001 1.332267629550188e-15
8 1.000000000000001 8.881784197001252e-16
9 1 4.440892098500626e-16
Integrate 120 * X^3 * Y^1
Rule QUAD ERROR
1 0.7407407407407407 0.2592592592592593
2 0.859375 0.140625
3 1.112 0.1120000000000001
4 1.101851851851852 0.1018518518518519
5 1 0
6 1 2.220446049250313e-16
7 1.000000000000002 2.220446049250313e-15
8 0.999999999999999 9.992007221626409e-16
9 0.9999999999999997 3.33066907387547e-16
Integrate 420 * X^3 * Y^2
Rule QUAD ERROR
1 0.8641975308641975 0.1358024691358025
2 0.888671875 0.111328125
3 0.7112000000000003 0.2887999999999997
4 0.8533950617283952 0.1466049382716048
5 1.004164931278634 0.004164931278634265
6 1 2.220446049250313e-16
7 1.000000000000004 3.996802888650564e-15
8 0.9999999999999988 1.221245327087672e-15
9 0.9999999999999991 8.881784197001252e-16
Integrate 1120 * X^3 * Y^3
Rule QUAD ERROR
1 0.7681755829903978 0.2318244170096022
2 0.7747395833333333 0.2252604166666667
3 0.4330666666666667 0.5669333333333333
4 0.7081618655692727 0.2918381344307273
5 1.115487594454691 0.1154875944546914
6 1.072509765625 0.07250976562499978
7 1.000000000000006 5.551115123125783e-15
8 0.9999999999999983 1.665334536937735e-15
9 0.9999999999999941 5.88418203051333e-15
Integrate 2520 * X^3 * Y^4
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0.640869140625 0.359130859375
3 0.412608 0.587392
4 0.700360082304527 0.299639917695473
5 1.099337860925295 0.09933786092529462
6 1.058578491210938 0.0585784912109375
7 0.9976544903385381 0.002345509661461853
8 0.9999999999999989 1.110223024625157e-15
9 1.000000000000006 5.551115123125783e-15
Integrate 5040 * X^3 * Y^5
Rule QUAD ERROR
1 0.3840877914951988 0.6159122085048012
2 0.5255126953125 0.4744873046875
3 0.5424384000000001 0.4575615999999999
4 0.7498713991769546 0.2501286008230454
5 0.9145679096294909 0.08543209037050914
6 0.9505290985107422 0.04947090148925781
7 1.044066039315753 0.04406603931575326
8 1.031251999999998 0.03125199999999828
9 1.000000000000002 2.220446049250313e-15
Integrate 9240 * X^3 * Y^6
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0.4288482666015625 0.5711517333984375
3 0.6991846399999999 0.3008153600000001
4 0.7993327046181983 0.2006672953818017
5 0.6660562957854057 0.3339437042145943
6 0.8166475296020509 0.1833524703979491
7 1.112720571678392 0.1127205716783921
8 1.070484066666665 0.07048406666666529
9 0.9979252780138695 0.002074721986130457
Integrate 15840 * X^3 * Y^7
Rule QUAD ERROR
1 0.1341258954427678 0.8658741045572321
2 0.3449249267578125 0.6550750732421875
3 0.8126976 0.1873024
4 0.8261054907788445 0.1738945092211555
5 0.4635222819115034 0.5364777180884966
6 0.712031185626984 0.287968814373016
7 1.135186045877924 0.1351860458779237
8 1.076375519999999 0.07637551999999936
9 1.009318294923954 0.009318294923953863
Integrate 30 * X^4 * Y^0
Rule QUAD ERROR
1 0.1851851851851852 0.8148148148148149
2 0.3515625 0.6484375
3 0.964 0.03600000000000003
4 0.9490740740740741 0.05092592592592593
5 1 2.220446049250313e-16
6 0.9999999999999999 1.110223024625157e-16
7 1.000000000000001 1.332267629550188e-15
8 1 4.440892098500626e-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 1.188271604938272 0.1882716049382718
5 0.9895876718034151 0.01041232819658489
6 1 0
7 1.000000000000003 3.108624468950438e-15
8 0.9999999999999998 2.220446049250313e-16
9 0.9999999999999993 6.661338147750939e-16
Integrate 840 * X^4 * Y^2
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
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 1.000000000000005 4.662936703425657e-15
8 0.9999999999999981 1.887379141862766e-15
9 0.9999999999999996 4.440892098500626e-16
Integrate 2520 * X^4 * Y^3
Rule QUAD ERROR
1 0.5761316872427983 0.4238683127572017
2 0.640869140625 0.359130859375
3 0.4126079999999998 0.5873920000000001
4 0.7003600823045268 0.2996399176954732
5 1.099337860925295 0.09933786092529506
6 1.058578491210938 0.0585784912109375
7 0.997654490338538 0.002345509661461964
8 0.999999999999998 1.998401444325282e-15
9 0.9999999999999912 8.770761894538737e-15
Integrate 6300 * X^4 * Y^4
Rule QUAD ERROR
1 0.4801097393689986 0.5198902606310014
2 0.528717041015625 0.471282958984375
3 0.1861439999999997 0.8138560000000004
4 0.5870091735253773 0.4129908264746227
5 1.267371588368792 0.2673715883687919
6 1.15229606628418 0.1522960662841797
7 0.936571510289953 0.063428489710047
8 0.9621059999999964 0.03789400000000365
9 0.9999999999999947 5.329070518200751e-15
Integrate 13860 * X^4 * Y^5
Rule QUAD ERROR
1 0.3520804755372656 0.6479195244627344
2 0.4317855834960938 0.5682144165039062
3 0.1759295999999999 0.8240704000000001
4 0.5652542009602194 0.4347457990397806
5 1.217103764726656 0.2171037647266565
6 1.117331743240356 0.1173317432403564
7 0.9351474993879398 0.06485250061206016
8 0.9657772666666634 0.03422273333333659
9 1.000930639849091 0.0009306398490906975
Integrate 27720 * X^4 * Y^6
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0.3568840026855469 0.6431159973144531
3 0.2797132799999998 0.7202867200000002
4 0.5787781254762994 0.4212218745237006
5 0.9683310837616075 0.03166891623839252
6 0.9830717742443085 0.01692822575569153
7 1.04950561739651 0.04950561739651027
8 1.035955359999997 0.03595535999999711
9 0.975146202469334 0.02485379753066597
Integrate 42 * X^5 * Y^0
Rule QUAD ERROR
1 0.08641975308641975 0.9135802469135803
2 0.232421875 0.767578125
3 0.8512000000000001 0.1487999999999999
4 0.8533950617283952 0.1466049382716048
5 1.004164931278634 0.004164931278634265
6 1 0
7 1.000000000000002 1.998401444325282e-15
8 1 2.220446049250313e-16
9 1.000000000000004 4.218847493575595e-15
Integrate 336 * X^5 * Y^1
Rule QUAD ERROR
1 0.2304526748971193 0.7695473251028807
2 0.478515625 0.521484375
3 1.28576 0.2857599999999998
4 1.206275720164609 0.206275720164609
5 1.011364312488844 0.01136431248884406
6 1.028076171875 0.02807617187499978
7 1.000000000000004 3.552713678800501e-15
8 1.000000000000001 6.661338147750939e-16
9 1.000000000000004 4.440892098500626e-15
Integrate 1512 * X^5 * Y^2
Rule QUAD ERROR
1 0.3456790123456789 0.654320987654321
2 0.569091796875 0.430908203125
3 1.0313856 0.03138560000000012
4 1.029475308641975 0.02947530864197523
5 0.7860398303427996 0.2139601696572004
6 0.8692657470703125 0.1307342529296875
7 1.004221917390645 0.004221917390645258
8 0.9999999999999984 1.554312234475219e-15
9 1.000000000000002 1.554312234475219e-15
Integrate 5040 * X^5 * Y^3
Rule QUAD ERROR
1 0.3840877914951988 0.6159122085048012
2 0.5255126953125 0.4744873046875
3 0.5424383999999999 0.4575616000000001
4 0.7498713991769548 0.2501286008230452
5 0.9145679096294912 0.08543209037050881
6 0.9505290985107422 0.04947090148925781
7 1.044066039315753 0.04406603931575326
8 1.031251999999997 0.03125199999999739
9 0.9999999999999916 8.43769498715119e-15
Integrate 13860 * X^5 * Y^4
Rule QUAD ERROR
1 0.3520804755372656 0.6479195244627344
2 0.4317855834960938 0.5682144165039062
3 0.1759296 0.8240704000000001
4 0.5652542009602195 0.4347457990397805
5 1.217103764726657 0.2171037647266567
6 1.117331743240356 0.1173317432403564
7 0.9351474993879382 0.06485250061206183
8 0.9657772666666639 0.03422273333333614
9 1.000930639849098 0.000930639849097803
Integrate 33264 * X^5 * Y^5
Rule QUAD ERROR
1 0.2816643804298125 0.7183356195701875
2 0.3436660766601562 0.6563339233398438
3 0.02057932799999972 0.9794206720000003
4 0.4805348365340649 0.5194651634659351
5 1.384399218637381 0.384399218637381
6 1.192360192537308 0.1923601925373077
7 0.7939128394936346 0.2060871605063654
8 0.8876735999999964 0.1123264000000036
9 1.032304123535361 0.03230412353536138
Integrate 56 * X^6 * Y^0
Rule QUAD ERROR
1 0.03840877914951989 0.9615912208504801
2 0.150390625 0.849609375
3 0.7063466666666667 0.2936533333333333
4 0.7357681755829903 0.2642318244170097
5 1.001765137541897 0.001765137541897444
6 0.9906412760416666 0.00935872395833337
7 1.000000000000001 1.110223024625157e-15
8 1.000000000000001 1.110223024625157e-15
9 1.000000000000001 1.110223024625157e-15
Integrate 504 * X^6 * Y^1
Rule QUAD ERROR
1 0.1152263374485597 0.8847736625514403
2 0.343505859375 0.656494140625
3 1.2227712 0.2227711999999997
4 1.158744855967078 0.1587448559670783
5 1.077336823942405 0.07733682394240482
6 1.084158325195312 0.08415832519531219
7 0.9967162864739483 0.003283713526051724
8 1.000000000000001 6.661338147750939e-16
9 0.9999999999999978 2.220446049250313e-15
Integrate 2520 * X^6 * Y^2
Rule QUAD ERROR
1 0.1920438957475994 0.8079561042524006
2 0.44219970703125 0.55780029296875
3 1.1292288 0.1292288000000001
4 1.068394204389575 0.06839420438957466
5 0.7085993081114164 0.2914006918885836
6 0.8359470367431641 0.1640529632568359
7 0.985276822826995 0.01472317717300498
8 0.9820319999999985 0.01796800000000154
9 0.999999999999997 2.997602166487923e-15
Integrate 9240 * X^6 * Y^3
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0.4288482666015625 0.5711517333984375
3 0.6991846400000001 0.3008153599999999
4 0.7993327046181983 0.2006672953818017
5 0.6660562957854057 0.3339437042145943
6 0.8166475296020508 0.1833524703979492
7 1.112720571678389 0.1127205716783894
8 1.070484066666666 0.07048406666666573
9 0.9979252780138679 0.002074721986132122
Integrate 27720 * X^6 * Y^4
Rule QUAD ERROR
1 0.2347203170248437 0.7652796829751563
2 0.3568840026855469 0.6431159973144531
3 0.2797132799999998 0.7202867200000002
4 0.5787781254762993 0.4212218745237007
5 0.9683310837616076 0.03166891623839241
6 0.9830717742443085 0.01692822575569153
7 1.049505617396507 0.04950561739650672
8 1.035955359999998 0.03595535999999799
9 0.9751462024693343 0.02485379753066574
Integrate 72 * X^7 * Y^0
Rule QUAD ERROR
1 0.01646090534979424 0.9835390946502057
2 0.09521484375 0.90478515625
3 0.5587967999999999 0.4412032000000001
4 0.6149176954732508 0.3850823045267492
5 0.9801732271417527 0.0198267728582473
6 0.963922119140625 0.03607788085937502
7 1.000938203864589 0.0009382038645886492
8 1.000000000000002 1.77635683940025e-15
9 0.9999999999999993 6.661338147750939e-16
Integrate 720 * X^7 * Y^1
Rule QUAD ERROR
1 0.05486968449931412 0.9451303155006858
2 0.2398681640625 0.7601318359375
3 1.0889472 0.0889472
4 1.066486625514403 0.06648662551440299
5 1.16513406100228 0.1651340610022798
6 1.148277282714844 0.1482772827148438
7 0.9966788411131282 0.003321158886871789
8 1.006472000000001 0.006472000000000921
9 0.9999999999999992 7.771561172376096e-16
Integrate 3960 * X^7 * Y^2
Rule QUAD ERROR
1 0.1005944215820759 0.8994055784179241
2 0.3348541259765625 0.6651458740234375
3 1.13600256 0.1360025600000001
4 1.059306412894376 0.05930641289437566
5 0.7160417159239328 0.2839582840760672
6 0.851722240447998 0.148277759552002
7 0.9262713180871595 0.07372868191284054
8 0.940255066666667 0.05974493333333297
9 1.001695386563741 0.001695386563740575
Integrate 15840 * X^7 * Y^3
Rule QUAD ERROR
1 0.1341258954427678 0.8658741045572321
2 0.3449249267578125 0.6550750732421875
3 0.8126975999999998 0.1873024000000002
4 0.8261054907788445 0.1738945092211555
5 0.4635222819115036 0.5364777180884963
6 0.7120311856269838 0.2879688143730162
7 1.135186045877925 0.135186045877925
8 1.076375519999999 0.0763755199999987
9 1.009318294923952 0.009318294923952086
Integrate 90 * X^8 * Y^0
Rule QUAD ERROR
1 0.006858710562414265 0.9931412894375857
2 0.059051513671875 0.940948486328125
3 0.4262591999999999 0.5737408000000001
4 0.5020254629629629 0.4979745370370371
5 0.9339330186766209 0.06606698132337907
6 0.91783332824707 0.08216667175293002
7 1.002003044552454 0.002003044552454147
8 0.9983820000000014 0.001617999999998565
9 1.000000000000004 3.774758283725532e-15
Integrate 990 * X^8 * Y^1
Rule QUAD ERROR
1 0.02514860539551897 0.974851394604481
2 0.1630210876464844 0.8369789123535156
3 0.9217824 0.0782176
4 0.9501457475994513 0.04985425240054875
5 1.243298597818035 0.2432985978180349
6 1.199601531028748 0.1996015310287478
7 1.011106751894067 0.01110675189406662
8 1.026326400000001 0.02632640000000142
9 0.9991730433599397 0.0008269566400602724
Integrate 5940 * X^8 * Y^2
Rule QUAD ERROR
1 0.05029721079103794 0.949702789208962
2 0.2464199066162109 0.7535800933837891
3 1.06812288 0.06812288
4 1.012280485539552 0.01228048553955174
5 0.7941600858629565 0.2058399141370435
6 0.9023201465606694 0.09767985343933061
7 0.8396989401353055 0.1603010598646945
8 0.8870611200000007 0.1129388799999993
9 1.000067908419095 6.790841909531942e-05
Integrate 110 * X^9 * Y^0
Rule QUAD ERROR
1 0.002794289488390997 0.997205710511609
2 0.03594716389973959 0.9640528361002604
3 0.3161429333333333 0.6838570666666667
4 0.4024431774881876 0.5975568225118124
5 0.8651851122007509 0.1348148877992491
6 0.8552181720733644 0.1447818279266356
7 0.9999799984765405 2.000152345948969e-05
8 0.9921721333333346 0.007827866666665351
9 1.00018376814224 0.0001837681422396376
Integrate 1320 * X^9 * Y^1
Rule QUAD ERROR
1 0.01117715795356399 0.988822842046436
2 0.1080513000488281 0.8919486999511719
3 0.7501542400000001 0.2498457599999999
4 0.8252650208936644 0.1747349791063356
5 1.28873176070729 0.2887317607072903
6 1.225266009569168 0.2252660095691683
7 1.046314480027413 0.04631448002741334
8 1.061156800000002 0.06115680000000179
9 0.9978918474235202 0.002108152576479783
Integrate 132 * X^10 * Y^0
Rule QUAD ERROR
1 0.001117715795356399 0.9988822842046436
2 0.02152633666992188 0.9784736633300781
3 0.229340672 0.770659328
4 0.3178788088070924 0.6821211911929077
5 0.7804757824994432 0.2195242175005568
6 0.7812086045742036 0.2187913954257964
7 0.9907131021663652 0.009286897833634788
8 0.9783752000000018 0.02162479999999822
9 1.000642152285983 0.0006421522859829665
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_PRB:
Normal end of execution.
15 June 2014 11:21:21 AM