03 March 2022 09:17:07 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 5.00002e-11 2 1 3.5e-10 3 1 5.50001e-10 4 1 2e-10 5 1 6.66134e-16 6 1 1.99998e-10 7 1 7e-10 Integrate 6 * X^0 * Y^1 Rule QUAD ERROR 1 1 5e-12 2 1 3.39107e-10 3 1 5.5548e-10 4 1 1.96868e-10 5 1 2.43028e-12 6 1 2.02298e-10 7 1 7.01631e-10 Integrate 12 * X^0 * Y^2 Rule QUAD ERROR 1 1 8.47025e-11 2 1 5.13482e-10 3 1 6.78407e-10 4 1 4.2786e-10 5 1 1.94267e-10 6 1 3.61277e-10 7 1 7.37832e-10 Integrate 20 * X^0 * Y^3 Rule QUAD ERROR 1 1 1.9509e-10 2 1 7.24666e-10 3 1 8.01958e-10 4 1 7.11683e-10 5 1 4.34796e-10 6 1 5.49096e-10 7 1 7.64732e-10 Integrate 30 * X^0 * Y^4 Rule QUAD ERROR 1 1.03333 0.0333333 2 1 9.49508e-10 3 1 9.13964e-10 4 1 1.00021e-09 5 1 7.08854e-10 6 1 7.62315e-10 7 1 8.19611e-10 Integrate 42 * X^0 * Y^5 Rule QUAD ERROR 1 1.08889 0.0888889 2 1 1.18225e-09 3 1 1.01495e-09 4 1 1.26844e-09 5 1 1.00283e-09 6 1 1.00264e-09 7 1 9.12948e-10 Integrate 56 * X^0 * Y^6 Rule QUAD ERROR 1 1.15595 0.155951 2 1 1.42647e-09 3 1 1.11113e-09 4 1 1.50361e-09 5 1 1.30302e-09 6 1 1.27113e-09 7 1 1.04328e-09 Integrate 72 * X^0 * Y^7 Rule QUAD ERROR 1 1.23141 0.231407 2 0.999814 0.000186456 3 1 1.20933e-09 4 1 1.69955e-09 5 1 1.59781e-09 6 1 1.56892e-09 7 1 1.20539e-09 Integrate 90 * X^0 * Y^8 Rule QUAD ERROR 1 1.31709 0.317086 2 0.999202 0.000798315 3 1 1.31471e-09 4 1 1.85378e-09 5 1 1.87861e-09 6 1 1.89714e-09 7 1 1.39375e-09 Integrate 110 * X^0 * Y^9 Rule QUAD ERROR 1 1.41659 0.416591 2 0.997929 0.00207095 3 1 1.43037e-09 4 1 1.96583e-09 5 1 2.13965e-09 6 1 2.25677e-09 7 1 1.60378e-09 Integrate 132 * X^0 * Y^10 Rule QUAD ERROR 1 1.53346 0.533463 2 0.995799 0.0042006 3 1 3.16194e-06 4 1 2.03622e-09 5 1 2.37736e-09 6 1 2.64858e-09 7 1 1.83203e-09 Integrate 6 * X^1 * Y^0 Rule QUAD ERROR 1 1 5e-12 2 1 3.39107e-10 3 1 5.5548e-10 4 1 1.96868e-10 5 1 2.43028e-12 6 1 2.02298e-10 7 1 7.01631e-10 Integrate 24 * X^1 * Y^1 Rule QUAD ERROR 1 1 4.70246e-12 2 1 1.42947e-10 3 1 4.43513e-10 4 1 4.03854e-11 5 1 1.84547e-10 6 1 4.79187e-11 7 1 6.68689e-10 Integrate 60 * X^1 * Y^2 Rule QUAD ERROR 1 1 5.87819e-12 2 1 1.78551e-10 3 1 5.02215e-10 4 1 4.83513e-12 5 1 1.62476e-10 6 1 8.00239e-11 7 1 6.98014e-10 Integrate 120 * X^1 * Y^3 Rule QUAD ERROR 1 0.933333 0.0666667 2 1 2.62878e-10 3 1 5.84035e-10 4 1 1.27664e-10 5 1 1.10621e-10 6 1 1.18509e-10 7 1 6.52412e-10 Integrate 210 * X^1 * Y^4 Rule QUAD ERROR 1 0.894444 0.105556 2 1 3.60591e-10 3 1 6.6506e-10 4 1 3.23446e-10 5 1 2.45117e-11 6 1 1.54459e-10 7 1 5.81862e-10 Integrate 336 * X^1 * Y^5 Rule QUAD ERROR 1 0.887704 0.112296 2 1 4.45838e-10 3 1 7.28278e-10 4 1 5.58047e-10 5 1 1.03094e-10 6 1 1.8919e-10 7 1 5.17048e-10 Integrate 504 * X^1 * Y^6 Rule QUAD ERROR 1 0.891852 0.108148 2 1.00065 0.000652602 3 1 7.68383e-10 4 1 8.14246e-10 5 1 2.71682e-10 6 1 2.21402e-10 7 1 4.71434e-10 Integrate 720 * X^1 * Y^7 Rule QUAD ERROR 1 0.888691 0.111309 2 1.00226 0.00226098 3 1 7.88285e-10 4 1 1.08019e-09 5 1 4.74828e-10 6 1 2.49777e-10 7 1 4.48293e-10 Integrate 990 * X^1 * Y^8 Rule QUAD ERROR 1 0.869317 0.130683 2 1.00493 0.00492854 3 1 7.94456e-10 4 1 1.34806e-09 5 1 7.04006e-10 6 1 2.7395e-10 7 1 4.45889e-10 Integrate 1320 * X^1 * Y^9 Rule QUAD ERROR 1 0.83223 0.16777 2 1.00858 0.00857732 3 0.999984 1.58183e-05 4 1 1.61294e-09 5 1 9.51131e-10 6 1 2.9419e-10 7 1 4.60581e-10 Integrate 12 * X^2 * Y^0 Rule QUAD ERROR 1 1 8.47025e-11 2 1 5.13482e-10 3 1 6.78407e-10 4 1 4.2786e-10 5 1 1.94267e-10 6 1 3.61277e-10 7 1 7.37833e-10 Integrate 60 * X^2 * Y^1 Rule QUAD ERROR 1 1 5.87819e-12 2 1 1.78552e-10 3 1 5.02215e-10 4 1 1.34948e-12 5 1 1.62477e-10 6 1 8.67291e-11 7 1 7.02386e-10 Integrate 180 * X^2 * Y^2 Rule QUAD ERROR 1 1.1 0.1 2 1 1.53177e-10 3 1 5.2015e-10 4 1 1.07745e-10 5 1 1.87781e-10 6 1 1.06711e-10 7 1 8.42288e-10 Integrate 420 * X^2 * Y^3 Rule QUAD ERROR 1 1.08889 0.0888889 2 1 1.93917e-10 3 1 5.73892e-10 4 1 9.62197e-11 5 1 1.81751e-10 6 1 1.3519e-10 7 1 8.78273e-10 Integrate 840 * X^2 * Y^4 Rule QUAD ERROR 1 1.09926 0.0992593 2 1 2.92667e-10 3 1 6.55397e-10 4 1 2.68663e-12 5 1 1.7216e-10 6 1 1.62149e-10 7 1 8.5173e-10 Integrate 1512 * X^2 * Y^5 Rule QUAD ERROR 1 1.16356 0.163556 2 0.999161 0.000839059 3 1 7.42247e-10 4 1 1.48536e-10 5 1 1.48924e-10 6 1 1.92799e-10 7 1 8.00853e-10 Integrate 2520 * X^2 * Y^6 Rule QUAD ERROR 1 1.26242 0.26242 2 0.998583 0.00141669 3 1 8.14301e-10 4 1 3.39608e-10 5 1 9.73386e-11 6 1 2.24171e-10 7 1 7.52705e-10 Integrate 3960 * X^2 * Y^7 Rule QUAD ERROR 1 1.36527 0.365267 2 0.999035 0.00096475 3 1 8.60816e-10 4 1 5.56788e-10 5 1 9.46354e-12 6 1 2.50733e-10 7 1 7.22931e-10 Integrate 5940 * X^2 * Y^8 Rule QUAD ERROR 1 1.44823 0.448234 2 1.00127 0.00127387 3 1.00004 4.38791e-05 4 1 7.89719e-10 5 1 1.15459e-10 6 1 2.6885e-10 7 1 7.18049e-10 Integrate 20 * X^3 * Y^0 Rule QUAD ERROR 1 1 1.9509e-10 2 1 7.24666e-10 3 1 8.01958e-10 4 1 7.11683e-10 5 1 4.34796e-10 6 1 5.49096e-10 7 1 7.64732e-10 Integrate 120 * X^3 * Y^1 Rule QUAD ERROR 1 0.933333 0.0666667 2 1 2.62878e-10 3 1 5.84035e-10 4 1 1.34635e-10 5 1 1.10621e-10 6 1 1.3192e-10 7 1 6.61158e-10 Integrate 420 * X^3 * Y^2 Rule QUAD ERROR 1 1.08889 0.0888889 2 1 1.93917e-10 3 1 5.73892e-10 4 1 8.84174e-11 5 1 1.81751e-10 6 1 1.47963e-10 7 1 8.87016e-10 Integrate 1120 * X^3 * Y^3 Rule QUAD ERROR 1 1.09235 0.0923457 2 1 1.56208e-10 3 1 5.86157e-10 4 1 1.75655e-10 5 1 1.71805e-10 6 1 1.69913e-10 7 1 1.00538e-09 Integrate 2520 * X^3 * Y^4 Rule QUAD ERROR 1 1.09926 0.0992593 2 1.00047 0.000466144 3 1 6.39692e-10 4 1 1.69326e-10 5 1 1.63437e-10 6 1 1.85874e-10 7 1 1.03893e-09 Integrate 5040 * X^3 * Y^5 Rule QUAD ERROR 1 1.18084 0.18084 2 0.998667 0.00133262 3 1 7.27932e-10 4 1 9.4723e-11 5 1 1.72292e-10 6 1 2.13252e-10 7 1 1.0149e-09 Integrate 9240 * X^3 * Y^6 Rule QUAD ERROR 1 1.33762 0.337624 2 0.995619 0.00438134 3 1 8.2921e-10 4 1 3.11309e-11 5 1 1.85253e-10 6 1 2.54685e-10 7 1 9.62413e-10 Integrate 15840 * X^3 * Y^7 Rule QUAD ERROR 1 1.53876 0.538757 2 0.991638 0.00836197 3 0.999919 8.06159e-05 4 1 1.94742e-10 5 1 1.84889e-10 6 1 3.01735e-10 7 1 9.07143e-10 Integrate 30 * X^4 * Y^0 Rule QUAD ERROR 1 1.03333 0.0333333 2 1 9.49508e-10 3 1 9.13964e-10 4 1 1.00021e-09 5 1 7.08854e-10 6 1 7.62315e-10 7 1 8.19611e-10 Integrate 210 * X^4 * Y^1 Rule QUAD ERROR 1 0.894444 0.105556 2 1 3.60591e-10 3 1 6.6506e-10 4 1 3.31744e-10 5 1 2.45119e-11 6 1 1.71541e-10 7 1 5.92796e-10 Integrate 840 * X^4 * Y^2 Rule QUAD ERROR 1 1.09926 0.0992593 2 1 2.92667e-10 3 1 6.55397e-10 4 1 1.13607e-11 5 1 1.7216e-10 6 1 1.86682e-10 7 1 8.68166e-10 Integrate 2520 * X^4 * Y^3 Rule QUAD ERROR 1 1.09926 0.0992593 2 1.00047 0.000466144 3 1 6.39692e-10 4 1 1.59028e-10 5 1 1.63437e-10 6 1 2.03686e-10 7 1 1.05076e-09 Integrate 6300 * X^4 * Y^4 Rule QUAD ERROR 1 1.05605 0.0560494 2 1.00364 0.00363957 3 1 6.50827e-10 4 1 2.27087e-10 5 1 1.24248e-10 6 1 1.97713e-10 7 1 1.15339e-09 Integrate 13860 * X^4 * Y^5 Rule QUAD ERROR 1 1.08244 0.0824362 2 1.00426 0.00426081 3 1 7.0804e-10 4 1 2.20471e-10 5 1 1.09378e-10 6 1 2.00211e-10 7 1 1.18248e-09 Integrate 27720 * X^4 * Y^6 Rule QUAD ERROR 1 1.21442 0.214424 2 1.00388 0.00387742 3 1.00011 0.000113777 4 1 1.55689e-10 5 1 1.25164e-10 6 1 2.29956e-10 7 1 1.15317e-09 Integrate 42 * X^5 * Y^0 Rule QUAD ERROR 1 1.08889 0.0888889 2 1 1.18225e-09 3 1 1.01495e-09 4 1 1.26844e-09 5 1 1.00283e-09 6 1 1.00264e-09 7 1 9.12948e-10 Integrate 336 * X^5 * Y^1 Rule QUAD ERROR 1 0.887704 0.112296 2 1 4.45838e-10 3 1 7.28278e-10 4 1 5.65705e-10 5 1 1.03094e-10 6 1 2.06707e-10 7 1 5.27967e-10 Integrate 1512 * X^5 * Y^2 Rule QUAD ERROR 1 1.16356 0.163556 2 0.999161 0.000839059 3 1 7.42247e-10 4 1 1.64839e-10 5 1 1.48924e-10 6 1 2.24442e-10 7 1 8.2145e-10 Integrate 5040 * X^5 * Y^3 Rule QUAD ERROR 1 1.18084 0.18084 2 0.998667 0.00133262 3 1 7.27932e-10 4 1 7.71142e-11 5 1 1.72292e-10 6 1 2.47217e-10 7 1 1.03678e-09 Integrate 13860 * X^5 * Y^4 Rule QUAD ERROR 1 1.08244 0.0824362 2 1.00426 0.00426081 3 1 7.0804e-10 4 1 2.09755e-10 5 1 1.09378e-10 6 1 2.22493e-10 7 1 1.19643e-09 Integrate 33264 * X^5 * Y^5 Rule QUAD ERROR 1 1.01379 0.013789 2 1.00665 0.0066505 3 0.999874 0.000125614 4 1 2.63395e-10 5 1 4.99922e-11 6 1 1.86069e-10 7 1 1.2919e-09 Integrate 56 * X^6 * Y^0 Rule QUAD ERROR 1 1.15595 0.155951 2 1 1.42647e-09 3 1 1.11113e-09 4 1 1.50361e-09 5 1 1.30302e-09 6 1 1.27113e-09 7 1 1.04328e-09 Integrate 504 * X^6 * Y^1 Rule QUAD ERROR 1 0.891852 0.108148 2 1.00065 0.000652602 3 1 7.68383e-10 4 1 8.20299e-10 5 1 2.71682e-10 6 1 2.37131e-10 7 1 4.80946e-10 Integrate 2520 * X^6 * Y^2 Rule QUAD ERROR 1 1.26242 0.26242 2 0.998583 0.00141669 3 1 8.14301e-10 4 1 3.54798e-10 5 1 9.73386e-11 6 1 2.5771e-10 7 1 7.73849e-10 Integrate 9240 * X^6 * Y^3 Rule QUAD ERROR 1 1.33762 0.337624 2 0.995619 0.00438134 3 1 8.2921e-10 4 1 5.13389e-11 5 1 1.85253e-10 6 1 2.99182e-10 7 1 9.90129e-10 Integrate 27720 * X^6 * Y^4 Rule QUAD ERROR 1 1.21442 0.214424 2 1.00388 0.00387742 3 1.00011 0.000113777 4 1 1.37871e-10 5 1 1.25164e-10 6 1 2.72403e-10 7 1 1.17885e-09 Integrate 72 * X^7 * Y^0 Rule QUAD ERROR 1 1.23141 0.231407 2 0.999814 0.000186456 3 1 1.20933e-09 4 1 1.69955e-09 5 1 1.59781e-09 6 1 1.56892e-09 7 1 1.20539e-09 Integrate 720 * X^7 * Y^1 Rule QUAD ERROR 1 0.888691 0.111309 2 1.00226 0.00226098 3 1 7.88285e-10 4 1 1.0845e-09 5 1 4.74828e-10 6 1 2.62664e-10 7 1 4.55841e-10 Integrate 3960 * X^7 * Y^2 Rule QUAD ERROR 1 1.36527 0.365267 2 0.999035 0.00096475 3 1 8.60817e-10 4 1 5.69117e-10 5 1 9.46332e-12 6 1 2.82132e-10 7 1 7.42075e-10 Integrate 15840 * X^7 * Y^3 Rule QUAD ERROR 1 1.53876 0.538757 2 0.991638 0.00836197 3 0.999919 8.06159e-05 4 1 2.13753e-10 5 1 1.84889e-10 6 1 3.50174e-10 7 1 9.36291e-10 Integrate 90 * X^8 * Y^0 Rule QUAD ERROR 1 1.31709 0.317086 2 0.999202 0.000798315 3 1 1.31471e-09 4 1 1.85378e-09 5 1 1.87861e-09 6 1 1.89714e-09 7 1 1.39375e-09 Integrate 990 * X^8 * Y^1 Rule QUAD ERROR 1 0.869317 0.130683 2 1.00493 0.00492854 3 1 7.94456e-10 4 1 1.3509e-09 5 1 7.04006e-10 6 1 2.83821e-10 7 1 4.51483e-10 Integrate 5940 * X^8 * Y^2 Rule QUAD ERROR 1 1.44823 0.448234 2 1.00127 0.00127387 3 1.00004 4.38791e-05 4 1 7.98807e-10 5 1 1.15459e-10 6 1 2.9578e-10 7 1 7.33916e-10 Integrate 110 * X^9 * Y^0 Rule QUAD ERROR 1 1.41659 0.416591 2 0.997929 0.00207095 3 1 1.43037e-09 4 1 1.96583e-09 5 1 2.13965e-09 6 1 2.25677e-09 7 1 1.60378e-09 Integrate 1320 * X^9 * Y^1 Rule QUAD ERROR 1 0.83223 0.16777 2 1.00858 0.00857732 3 0.999984 1.58183e-05 4 1 1.61471e-09 5 1 9.51131e-10 6 1 3.01366e-10 7 1 4.64513e-10 Integrate 132 * X^10 * Y^0 Rule QUAD ERROR 1 1.53346 0.533463 2 0.995799 0.0042006 3 1 3.16194e-06 4 1 2.03622e-09 5 1 2.37736e-09 6 1 2.64858e-09 7 1 1.83203e-09 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 2 for reference triangle with area = 0.5 X Y W 0 0.333333 0.333333 0.108928 1 0.106335 0.106335 0.0552097 2 0.106335 0.787329 0.0552097 3 0.787329 0.106335 0.0552097 4 0.5 0.5 0.017947 5 0.5 0 0.017947 6 0 0.5 0.017947 7 1 0 0.000201064 8 0 0 0.000201064 9 0 1 0.000201064 10 0.117181 0.31627 0.0885674 11 0.31627 0.566549 0.0885674 12 0.566549 0.117181 0.0885674 13 0.31627 0.117181 0.0885674 14 0.566549 0.31627 0.0885674 15 0.117181 0.566549 0.0885674 16 0 0.265565 0.0136172 17 0.265565 0.734435 0.0136172 18 0.734435 0 0.0136172 19 0.265565 0 0.0136172 20 0.734435 0.265565 0.0136172 21 0 0.734435 0.0136172 22 0 0.0848854 0.00964847 23 0.0848854 0.915115 0.00964847 24 0.915115 0 0.00964847 25 0.0848854 0 0.00964847 26 0.915115 0.0848854 0.00964847 27 0 0.915115 0.00964847 The physical triangle: 1 1 2 2 1 1 3 3 2 Rule 2 for physical triangle with area = 1 X Y W 0 1.66667 1.66667 0.108928 1 1.21267 1.89366 0.0552097 2 2.57466 1.89366 0.0552097 3 1.21267 1.21267 0.0552097 4 2 1.5 0.017947 5 1 1.5 0.017947 6 2 2 0.017947 7 1 1 0.000201064 8 1 2 0.000201064 9 3 2 0.000201064 10 1.63254 1.88282 0.0885674 11 2.1331 1.68373 0.0885674 12 1.23436 1.43345 0.0885674 13 1.23436 1.68373 0.0885674 14 1.63254 1.43345 0.0885674 15 2.1331 1.88282 0.0885674 16 1.53113 2 0.0136172 17 2.46887 1.73443 0.0136172 18 1 1.26557 0.0136172 19 1 1.73443 0.0136172 20 1.53113 1.26557 0.0136172 21 2.46887 2 0.0136172 22 1.16977 2 0.00964847 23 2.83023 1.91511 0.00964847 24 1 1.08489 0.00964847 25 1 1.91511 0.00964847 26 1.16977 1.08489 0.00964847 27 2.83023 2 0.00964847 TRIANGLE_FEKETE_RULE_TEST: Normal end of execution. 03 March 2022 09:17:07 AM