08-Jan-2022 10:38:30 triangle_fekete_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test triangle_fekete_rule(). TRIANGLE_FEKETE_RULE_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 TRIANGLE_FEKETE_RULE_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 1.000000 2 1.000000 3 1.000000 4 1.000000 5 1.000000 6 1.000000 7 1.000000 TRIANGLE_FEKETE_RULE_TEST025 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 sum to 1. Rule Suborder Sum of coordinates 1 3 1.000000e+00 1.000000e+00 1.000000e+00 2 7 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 3 12 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 4 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 5 21 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 1.000000e+00 1.000000e+00 6 28 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 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 7 38 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 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_FEKETE_RULE_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 sum to 1. Rule Suborder Sum of coordinates 1 3 1.000000e+00 1.000000e+00 1.000000e+00 2 7 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 3 12 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 4 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 5 21 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 1.000000e+00 1.000000e+00 6 28 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 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 7 38 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 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_FEKETE_RULE_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 2.000000 * 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 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 Integrate 12.000000 * X^0 * Y^2 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 Integrate 20.000000 * X^0 * Y^3 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 Integrate 30.000000 * X^0 * Y^4 Rule QUAD ERROR 1 1.033333 0.033333 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 Integrate 42.000000 * X^0 * Y^5 Rule QUAD ERROR 1 1.088889 0.088889 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 Integrate 56.000000 * X^0 * Y^6 Rule QUAD ERROR 1 1.155951 0.155951 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 Integrate 72.000000 * X^0 * Y^7 Rule QUAD ERROR 1 1.231407 0.231407 2 0.999814 0.000186 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 Integrate 90.000000 * X^0 * Y^8 Rule QUAD ERROR 1 1.317086 0.317086 2 0.999202 0.000798 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 Integrate 110.000000 * X^0 * Y^9 Rule QUAD ERROR 1 1.416591 0.416591 2 0.997929 0.002071 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 Integrate 132.000000 * X^0 * Y^10 Rule QUAD ERROR 1 1.533463 0.533463 2 0.995799 0.004201 3 1.000003 0.000003 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 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 Integrate 24.000000 * X^1 * 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 Integrate 60.000000 * X^1 * Y^2 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 Integrate 120.000000 * X^1 * Y^3 Rule QUAD ERROR 1 0.933333 0.066667 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 Integrate 210.000000 * X^1 * Y^4 Rule QUAD ERROR 1 0.894444 0.105556 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 Integrate 336.000000 * X^1 * Y^5 Rule QUAD ERROR 1 0.887704 0.112296 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 Integrate 504.000000 * X^1 * Y^6 Rule QUAD ERROR 1 0.891852 0.108148 2 1.000653 0.000653 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 Integrate 720.000000 * X^1 * Y^7 Rule QUAD ERROR 1 0.888691 0.111309 2 1.002261 0.002261 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 Integrate 990.000000 * X^1 * Y^8 Rule QUAD ERROR 1 0.869317 0.130683 2 1.004929 0.004929 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 Integrate 1320.000000 * X^1 * Y^9 Rule QUAD ERROR 1 0.832230 0.167770 2 1.008577 0.008577 3 0.999984 0.000016 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 12.000000 * X^2 * 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 Integrate 60.000000 * X^2 * 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 Integrate 180.000000 * X^2 * Y^2 Rule QUAD ERROR 1 1.100000 0.100000 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 Integrate 420.000000 * X^2 * Y^3 Rule QUAD ERROR 1 1.088889 0.088889 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 Integrate 840.000000 * X^2 * Y^4 Rule QUAD ERROR 1 1.099259 0.099259 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 Integrate 1512.000000 * X^2 * Y^5 Rule QUAD ERROR 1 1.163556 0.163556 2 0.999161 0.000839 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 Integrate 2520.000000 * X^2 * Y^6 Rule QUAD ERROR 1 1.262420 0.262420 2 0.998583 0.001417 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 Integrate 3960.000000 * X^2 * Y^7 Rule QUAD ERROR 1 1.365267 0.365267 2 0.999035 0.000965 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 Integrate 5940.000000 * X^2 * Y^8 Rule QUAD ERROR 1 1.448234 0.448234 2 1.001274 0.001274 3 1.000044 0.000044 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 20.000000 * X^3 * 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 Integrate 120.000000 * X^3 * Y^1 Rule QUAD ERROR 1 0.933333 0.066667 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 Integrate 420.000000 * X^3 * Y^2 Rule QUAD ERROR 1 1.088889 0.088889 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 Integrate 1120.000000 * X^3 * Y^3 Rule QUAD ERROR 1 1.092346 0.092346 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 Integrate 2520.000000 * X^3 * Y^4 Rule QUAD ERROR 1 1.099259 0.099259 2 1.000466 0.000466 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 Integrate 5040.000000 * X^3 * Y^5 Rule QUAD ERROR 1 1.180840 0.180840 2 0.998667 0.001333 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 Integrate 9240.000000 * X^3 * Y^6 Rule QUAD ERROR 1 1.337624 0.337624 2 0.995619 0.004381 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 Integrate 15840.000000 * X^3 * Y^7 Rule QUAD ERROR 1 1.538757 0.538757 2 0.991638 0.008362 3 0.999919 0.000081 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30.000000 * X^4 * Y^0 Rule QUAD ERROR 1 1.033333 0.033333 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 Integrate 210.000000 * X^4 * Y^1 Rule QUAD ERROR 1 0.894444 0.105556 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 Integrate 840.000000 * X^4 * Y^2 Rule QUAD ERROR 1 1.099259 0.099259 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 Integrate 2520.000000 * X^4 * Y^3 Rule QUAD ERROR 1 1.099259 0.099259 2 1.000466 0.000466 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 Integrate 6300.000000 * X^4 * Y^4 Rule QUAD ERROR 1 1.056049 0.056049 2 1.003640 0.003640 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 Integrate 13860.000000 * X^4 * Y^5 Rule QUAD ERROR 1 1.082436 0.082436 2 1.004261 0.004261 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 Integrate 27720.000000 * X^4 * Y^6 Rule QUAD ERROR 1 1.214424 0.214424 2 1.003877 0.003877 3 1.000114 0.000114 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 42.000000 * X^5 * Y^0 Rule QUAD ERROR 1 1.088889 0.088889 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 Integrate 336.000000 * X^5 * Y^1 Rule QUAD ERROR 1 0.887704 0.112296 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 Integrate 1512.000000 * X^5 * Y^2 Rule QUAD ERROR 1 1.163556 0.163556 2 0.999161 0.000839 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 Integrate 5040.000000 * X^5 * Y^3 Rule QUAD ERROR 1 1.180840 0.180840 2 0.998667 0.001333 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 Integrate 13860.000000 * X^5 * Y^4 Rule QUAD ERROR 1 1.082436 0.082436 2 1.004261 0.004261 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 Integrate 33264.000000 * X^5 * Y^5 Rule QUAD ERROR 1 1.013789 0.013789 2 1.006651 0.006651 3 0.999874 0.000126 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 56.000000 * X^6 * Y^0 Rule QUAD ERROR 1 1.155951 0.155951 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 Integrate 504.000000 * X^6 * Y^1 Rule QUAD ERROR 1 0.891852 0.108148 2 1.000653 0.000653 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 Integrate 2520.000000 * X^6 * Y^2 Rule QUAD ERROR 1 1.262420 0.262420 2 0.998583 0.001417 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 Integrate 9240.000000 * X^6 * Y^3 Rule QUAD ERROR 1 1.337624 0.337624 2 0.995619 0.004381 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 Integrate 27720.000000 * X^6 * Y^4 Rule QUAD ERROR 1 1.214424 0.214424 2 1.003877 0.003877 3 1.000114 0.000114 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 72.000000 * X^7 * Y^0 Rule QUAD ERROR 1 1.231407 0.231407 2 0.999814 0.000186 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 Integrate 720.000000 * X^7 * Y^1 Rule QUAD ERROR 1 0.888691 0.111309 2 1.002261 0.002261 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 Integrate 3960.000000 * X^7 * Y^2 Rule QUAD ERROR 1 1.365267 0.365267 2 0.999035 0.000965 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 Integrate 15840.000000 * X^7 * Y^3 Rule QUAD ERROR 1 1.538757 0.538757 2 0.991638 0.008362 3 0.999919 0.000081 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 90.000000 * X^8 * Y^0 Rule QUAD ERROR 1 1.317086 0.317086 2 0.999202 0.000798 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 Integrate 990.000000 * X^8 * Y^1 Rule QUAD ERROR 1 0.869317 0.130683 2 1.004929 0.004929 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 Integrate 5940.000000 * X^8 * Y^2 Rule QUAD ERROR 1 1.448234 0.448234 2 1.001274 0.001274 3 1.000044 0.000044 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 110.000000 * X^9 * Y^0 Rule QUAD ERROR 1 1.416591 0.416591 2 0.997929 0.002071 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 Integrate 1320.000000 * X^9 * Y^1 Rule QUAD ERROR 1 0.832230 0.167770 2 1.008577 0.008577 3 0.999984 0.000016 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 132.000000 * X^10 * Y^0 Rule QUAD ERROR 1 1.533463 0.533463 2 0.995799 0.004201 3 1.000003 0.000003 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 TRIANGLE_FEKETE_RULE_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". TRIANGLE_FEKETE_RULE_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 0.000000 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 0.333333 0.333333 0.108928 2 0.106335 0.106335 0.055210 3 0.106335 0.787329 0.055210 4 0.787329 0.106335 0.055210 5 0.500000 0.500000 0.017947 6 0.500000 0.000000 0.017947 7 0.000000 0.500000 0.017947 8 1.000000 0.000000 0.000201 9 0.000000 0.000000 0.000201 10 0.000000 1.000000 0.000201 11 0.117181 0.316270 0.088567 12 0.316270 0.566549 0.088567 13 0.566549 0.117181 0.088567 14 0.316270 0.117181 0.088567 15 0.566549 0.316270 0.088567 16 0.117181 0.566549 0.088567 17 0.000000 0.265565 0.013617 18 0.265565 0.734435 0.013617 19 0.734435 0.000000 0.013617 20 0.265565 0.000000 0.013617 21 0.734435 0.265565 0.013617 22 0.000000 0.734435 0.013617 23 0.000000 0.084885 0.009648 24 0.084885 0.915115 0.009648 25 0.915115 0.000000 0.009648 26 0.084885 0.000000 0.009648 27 0.915115 0.084885 0.009648 28 0.000000 0.915115 0.009648 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 1.666667 1.666667 0.108928 2 1.212671 1.893665 0.055210 3 2.574658 1.893665 0.055210 4 1.212671 1.212671 0.055210 5 2.000000 1.500000 0.017947 6 1.000000 1.500000 0.017947 7 2.000000 2.000000 0.017947 8 1.000000 1.000000 0.000201 9 1.000000 2.000000 0.000201 10 3.000000 2.000000 0.000201 11 1.632540 1.882819 0.088567 12 2.133099 1.683730 0.088567 13 1.234362 1.433451 0.088567 14 1.234362 1.683730 0.088567 15 1.632540 1.433451 0.088567 16 2.133099 1.882819 0.088567 17 1.531130 2.000000 0.013617 18 2.468870 1.734435 0.013617 19 1.000000 1.265565 0.013617 20 1.000000 1.734435 0.013617 21 1.531130 1.265565 0.013617 22 2.468870 2.000000 0.013617 23 1.169771 2.000000 0.009648 24 2.830229 1.915115 0.009648 25 1.000000 1.084885 0.009648 26 1.000000 1.915115 0.009648 27 1.169771 1.084885 0.009648 28 2.830229 2.000000 0.009648 triangle_fekete_rule_test(): Normal end of execution. 08-Jan-2022 10:38:30