Tue Oct 19 11:26:24 2021 CUBE_MONTE_CARLO_TEST Python version: 3.6.9 Test CUBE_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. CUBE01_MONOMIAL_INTEGRAL_TEST Python version: 3.6.9 CUBE01_MONOMIAL_INTEGRAL computes the integral of a monomial within the interior of the unit cube in 3D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 Ex Ey Ez MC-Estimate Exact Error 4 4 6 0.00549041 0.00571429 0.00022 7 0 3 0.030393 0.03125 0.00086 6 2 4 0.0093874 0.00952381 0.00014 7 4 1 0.0124744 0.0125 2.6e-05 6 5 0 0.0235845 0.0238095 0.00023 6 3 5 0.00581679 0.00595238 0.00014 0 3 7 0.031032 0.03125 0.00022 4 7 7 0.00289018 0.003125 0.00023 3 3 3 0.0152203 0.015625 0.0004 2 0 1 0.162318 0.166667 0.0043 4 3 4 0.00972164 0.01 0.00028 4 0 2 0.064587 0.0666667 0.0021 7 5 3 0.00499595 0.00520833 0.00021 7 2 6 0.00589797 0.00595238 5.4e-05 3 6 2 0.0116117 0.0119048 0.00029 0 5 5 0.0279063 0.0277778 0.00013 5 5 0 0.027539 0.0277778 0.00024 7 4 7 0.00302466 0.003125 0.0001 7 5 7 0.00247141 0.00260417 0.00013 1 3 1 0.062407 0.0625 9.3e-05 CUBE01_MONOMIAL_INTEGRAL_TEST: Normal end of execution. CUBE01_MONTE_CARLO_TEST Use CUBE01_SAMPLE to estimate integrals along the interior of the unit cube in 3D. N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 1 0.446564 0.371847 0.514643 0.19942 0.166054 0.229821 0.13827 0.191368 0.264857 2 1 0.774314 0.602218 0.430402 0.61665 0.443449 0.383851 0.393239 0.191534 0.334989 4 1 0.280645 0.563922 0.778081 0.223342 0.257445 0.224145 0.437796 0.398628 0.643253 8 1 0.325049 0.658958 0.361897 0.19292 0.195618 0.121692 0.465624 0.252432 0.16905 16 1 0.482921 0.55891 0.536149 0.347711 0.204904 0.290525 0.393552 0.264709 0.349408 32 1 0.39478 0.538871 0.529615 0.239229 0.255427 0.209065 0.355643 0.295522 0.350611 64 1 0.459575 0.50425 0.484078 0.284205 0.226422 0.220884 0.354468 0.237385 0.311905 128 1 0.493706 0.534846 0.522386 0.342816 0.268773 0.244836 0.372178 0.264482 0.352771 256 1 0.481752 0.506181 0.471337 0.309863 0.253515 0.225211 0.338508 0.236343 0.313608 512 1 0.531956 0.504175 0.492707 0.360674 0.270414 0.262855 0.335775 0.243394 0.322274 1024 1 0.511623 0.497263 0.497489 0.348702 0.258505 0.253808 0.331502 0.244968 0.334038 2048 1 0.492591 0.498956 0.497492 0.32298 0.247677 0.244962 0.330808 0.251258 0.333672 4096 1 0.501492 0.50925 0.500852 0.334518 0.255592 0.249785 0.343262 0.255799 0.333505 8192 1 0.49711 0.500803 0.496322 0.329954 0.246827 0.245724 0.334006 0.248876 0.329524 16384 1 0.502292 0.498901 0.501023 0.335754 0.24979 0.251537 0.333196 0.249325 0.335327 32768 1 0.497331 0.500561 0.497789 0.331693 0.248697 0.24766 0.33375 0.249673 0.331345 65536 1 0.499144 0.497194 0.501095 0.332457 0.247529 0.25017 0.330329 0.249413 0.334603 Exact 1 0.5 0.5 0.5 0.333333 0.25 0.25 0.333333 0.25 0.333333 CUBE01_SAMPLE_TEST Python version: 3.6.9 CUBE01_SAMPLE samples the unit cube. Sample points in the unit cube. Row: 0 1 2 Col 0 : 0.147771 0.177444 0.326701 1 : 0.754663 0.111055 0.818925 2 : 0.273329 0.903667 0.44325 3 : 0.230721 0.92304 0.495041 4 : 0.2807 0.854913 0.509342 5 : 0.0570367 0.517794 0.184577 6 : 0.0709948 0.768341 0.651757 7 : 0.712458 0.736978 0.592429 8 : 0.198642 0.153764 0.976236 9 : 0.768739 0.947843 0.571851 CUBE01_SAMPLE_TEST Normal end of execution. CUBE01_VOLUME_TEST Python version: 3.6.9 CUBE01_VOLUME returns the volume of the unit cube. CUBE01_VOLUME() = 1 CUBE01_VOLUME_TEST Normal end of execution. cube_monte_carlo_test(): Normal end of execution. Tue Oct 19 11:26:26 2021