Tue Oct 19 17:25:05 2021 tetrahedron01_monte_carlo_tests(): Python version: 3.6.9 Test tetrahedron01_monte_carlo(). i4vec_print_test Python version: 3.6.9 i4vec_print prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 i4vec_print_test: Normal end of execution. i4vec_transpose_print_test Python version: 3.6.9 i4vec_transpose_print prints an I4VEC with 5 entries to a row, and an optional title. My array: 1 2 3 4 5 6 7 8 9 10 11 12 i4vec_transpose_print_test: Normal end of execution. r8mat_print_test Python version: 3.6.9 r8mat_print prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 r8mat_print_test: Normal end of execution. r8mat_print_some_test Python version: 3.6.9 r8mat_print_some prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 r8mat_print_some_test: Normal end of execution. r8mat_transpose_print_test Python version: 3.6.9 r8mat_transpose_print prints an R8MAT. Here is an R8MAT, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 r8mat_transpose_print_test: Normal end of execution. r8mat_transpose_print_some_test Python version: 3.6.9 r8mat_transpose_print_some prints some of an R8MAT, transposed. R8MAT, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 r8mat_transpose_print_some_test: Normal end of execution. r8vec_print_test Python version: 3.6.9 r8vec_print prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 r8vec_print_test: Normal end of execution. tetrahedron01_monte_carlo_test Python version: 3.6.9 tetrahedron01_sample can be used to estimate integrals over the unit tetrahedron using the Monte Carlo method. Compare with exact values returned by tetrahedron_monomial_integral. Number of sample points used is 4192 Ex Ey Ez MC-Estimate Exact Error 0 0 0 0.166667 0.166667 0 0 0 1 0.0418702 0.0416667 0.0002 0 0 2 0.0165704 0.0166667 9.6e-05 0 0 3 0.00816781 0.00833333 0.00017 0 1 0 0.0410755 0.0416667 0.00059 0 1 1 0.0084118 0.00833333 7.8e-05 0 1 2 0.00280106 0.00277778 2.3e-05 0 1 3 0.0011888 0.00119048 1.7e-06 0 2 0 0.0162309 0.0166667 0.00044 0 2 1 0.00280631 0.00277778 2.9e-05 0 2 2 0.000807828 0.000793651 1.4e-05 0 2 3 0.000301202 0.000297619 3.6e-06 0 3 0 0.00798735 0.00833333 0.00035 0 3 1 0.00119861 0.00119048 8.1e-06 0 3 2 0.000304658 0.000297619 7e-06 0 3 3 0.000101593 9.92063e-05 2.4e-06 1 0 0 0.0417504 0.0416667 8.4e-05 1 0 1 0.0084961 0.00833333 0.00016 1 0 2 0.00283884 0.00277778 6.1e-05 1 0 3 0.00121034 0.00119048 2e-05 1 1 0 0.00818104 0.00833333 0.00015 1 1 1 0.0014004 0.00138889 1.2e-05 1 1 2 0.00040396 0.000396825 7.1e-06 1 1 3 0.000151444 0.00014881 2.6e-06 1 2 0 0.00270517 0.00277778 7.3e-05 1 2 1 0.000396109 0.000396825 7.2e-07 1 2 2 0.000100315 9.92063e-05 1.1e-06 1 2 3 3.35839e-05 3.30688e-05 5.2e-07 1 3 0 0.00115532 0.00119048 3.5e-05 1 3 1 0.000147282 0.00014881 1.5e-06 1 3 2 3.3171e-05 3.30688e-05 1e-07 1 3 3 1.00309e-05 9.92063e-06 1.1e-07 2 0 0 0.0166877 0.0166667 2.1e-05 2 0 1 0.00284644 0.00277778 6.9e-05 2 0 2 0.000819587 0.000793651 2.6e-05 2 0 3 0.000306627 0.000297619 9e-06 2 1 0 0.00271555 0.00277778 6.2e-05 2 1 1 0.000400196 0.000396825 3.4e-06 2 1 2 0.000101587 9.92063e-05 2.4e-06 2 1 3 3.39729e-05 3.30688e-05 9e-07 2 2 0 0.000768593 0.000793651 2.5e-05 2 2 1 9.84152e-05 9.92063e-05 7.9e-07 2 2 2 2.22479e-05 2.20459e-05 2e-07 2 2 3 6.72489e-06 6.61376e-06 1.1e-07 2 3 0 0.000288276 0.000297619 9.3e-06 2 3 1 3.24605e-05 3.30688e-05 6.1e-07 2 3 2 6.58618e-06 6.61376e-06 2.8e-08 2 3 3 1.81336e-06 1.80375e-06 9.6e-09 3 0 0 0.00833501 0.00833333 1.7e-06 3 0 1 0.00122492 0.00119048 3.4e-05 3 0 2 0.000310226 0.000297619 1.3e-05 3 0 3 0.000103475 9.92063e-05 4.3e-06 3 1 0 0.00116189 0.00119048 2.9e-05 3 1 1 0.000150632 0.00014881 1.8e-06 3 1 2 3.4158e-05 3.30688e-05 1.1e-06 3 1 3 1.03114e-05 9.92063e-06 3.9e-07 3 2 0 0.000287021 0.000297619 1.1e-05 3 2 1 3.27604e-05 3.30688e-05 3.1e-07 3 2 2 6.70005e-06 6.61376e-06 8.6e-08 3 2 3 1.84766e-06 1.80375e-06 4.4e-08 3 3 0 9.55913e-05 9.92063e-05 3.6e-06 3 3 1 9.69179e-06 9.92063e-06 2.3e-07 3 3 2 1.79507e-06 1.80375e-06 8.7e-09 3 3 3 4.54381e-07 4.50938e-07 3.4e-09 tetrahedron01_monte_carlo_test: Normal end of execution. tetrahedron01_sample_test Python version: 3.6.9 tetrahedron01_sample samples the unit tetrahedron. Sample points in the unit tetrahedron. Row: 0 1 2 Col 0 : 0.0785586 0.550751 0.273567 1 : 0.741575 0.0269153 0.119918 2 : 0.0965051 0.00966696 0.488978 3 : 0.0395575 0.0567979 0.480613 4 : 0.455474 0.408094 0.097147 5 : 0.0462674 0.649223 0.175284 6 : 0.501416 0.276604 0.0844702 7 : 0.0733172 0.281085 0.216431 8 : 0.147448 0.137813 0.294182 9 : 0.127959 0.058924 0.509037 tetrahedron01_sample_test Normal end of execution. tetrahedron01_volume_test Python version: 3.6.9 tetrahedron01_volume returns the volume of the unit tetrahedron. tetrahedron01_volume() = 0.166667 tetrahedron01_volume_test Normal end of execution. tetrahedron01_monte_carlo_tests(): Normal end of execution. Tue Oct 19 17:25:06 2021