03-Apr-2019 12:35:05 tetrahedron_integrals_test MATLAB version Test tetrahedron_integrals. TETRAHEDRON_INTEGRALS_TEST01 Estimate monomial integrals using Monte Carlo over the interior of the unit tetrahedron in 3D. Number of sample points used is 4192 Ex Ey Ez MC-Estimate Exact Error 0 0 0 0.166667 0.166667 0.00e+00 0 0 1 0.0413718 0.0416667 2.95e-04 0 0 2 0.0165098 0.0166667 1.57e-04 0 0 3 0.00828332 0.00833333 5.00e-05 0 1 0 0.0416317 0.0416667 3.49e-05 0 1 1 0.00827531 0.00833333 5.80e-05 0 1 2 0.00273194 0.00277778 4.58e-05 0 1 3 0.00116758 0.00119048 2.29e-05 0 2 0 0.0165018 0.0166667 1.65e-04 0 2 1 0.00276951 0.00277778 8.27e-06 0 2 2 0.000784884 0.000793651 8.77e-06 0 2 3 0.000292169 0.000297619 5.45e-06 0 3 0 0.00811291 0.00833333 2.20e-04 0 3 1 0.00118868 0.00119048 1.80e-06 0 3 2 0.000297023 0.000297619 5.96e-07 0 3 3 9.81799e-05 9.92063e-05 1.03e-06 1 0 0 0.0416734 0.0416667 6.70e-06 1 0 1 0.00817139 0.00833333 1.62e-04 1 0 2 0.00268252 0.00277778 9.53e-05 1 0 3 0.00114358 0.00119048 4.69e-05 1 1 0 0.00838004 0.00833333 4.67e-05 1 1 1 0.00137025 0.00138889 1.86e-05 1 1 2 0.00038193 0.000396825 1.49e-05 1 1 3 0.000140955 0.00014881 7.85e-06 1 2 0 0.00278426 0.00277778 6.48e-06 1 2 1 0.000393528 0.000396825 3.30e-06 1 2 2 9.62722e-05 9.92063e-05 2.93e-06 1 2 3 3.15096e-05 3.30688e-05 1.56e-06 1 3 0 0.00118823 0.00119048 2.24e-06 1 3 1 0.000148482 0.00014881 3.28e-07 1 3 2 3.25608e-05 3.30688e-05 5.08e-07 1 3 3 9.60372e-06 9.92063e-06 3.17e-07 2 0 0 0.0168692 0.0166667 2.03e-04 2 0 1 0.00272847 0.00277778 4.93e-05 2 0 2 0.00075755 0.000793651 3.61e-05 2 0 3 0.000280062 0.000297619 1.76e-05 2 1 0 0.00283389 0.00277778 5.61e-05 2 1 1 0.000395751 0.000396825 1.07e-06 2 1 2 9.54467e-05 9.92063e-05 3.76e-06 2 1 3 3.09608e-05 3.30688e-05 2.11e-06 2 2 0 0.000803078 0.000793651 9.43e-06 2 2 1 9.8966e-05 9.92063e-05 2.40e-07 2 2 2 2.12827e-05 2.20459e-05 7.63e-07 2 2 3 6.19862e-06 6.61376e-06 4.15e-07 2 3 0 0.000299022 0.000297619 1.40e-06 2 3 1 3.30027e-05 3.30688e-05 6.60e-08 2 3 2 6.43774e-06 6.61376e-06 1.76e-07 2 3 3 1.70702e-06 1.80375e-06 9.67e-08 3 0 0 0.00855041 0.00833333 2.17e-04 3 0 1 0.0011797 0.00119048 1.08e-05 3 0 2 0.000283257 0.000297619 1.44e-05 3 0 3 9.21137e-05 9.92063e-05 7.09e-06 3 1 0 0.00123659 0.00119048 4.61e-05 3 1 1 0.00015128 0.00014881 2.47e-06 3 1 2 3.22126e-05 3.30688e-05 8.56e-07 3 1 3 9.32737e-06 9.92063e-06 5.93e-07 3 2 0 0.000305507 0.000297619 7.89e-06 3 2 1 3.36147e-05 3.30688e-05 5.46e-07 3 2 2 6.46534e-06 6.61376e-06 1.48e-07 3 2 3 1.69869e-06 1.80375e-06 1.05e-07 3 3 0 0.000100207 9.92063e-05 1.00e-06 3 3 1 1.00213e-05 9.92063e-06 1.01e-07 3 3 2 1.76656e-06 1.80375e-06 3.72e-08 3 3 3 4.26312e-07 4.50938e-07 2.46e-08 tetrahedron_integrals_test Normal end of execution. 03-Apr-2019 12:35:05