13-Apr-2022 20:40:29 random_data_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test random_data() brownian_test(): brownian() generates Brownian motion points. Spatial dimension D = 2 Number of points N = 100 Graphics saved as "brownian.png". normal_circular_test(): normal_circular() generates points distributed according to a circular normal. Number of points N = 2000 Spatial dimension D = 2 Graphics saved as "normal_circular.png". normal_square_test(): normal_square() generates normal points in D dimensions, using a zero mean, and with the identity as the variance-covariance matrix. Number of points N = 1000 Spatial dimension D = 2 Graphics saved as "normal_square.png". uniform_in_annulus_test(): uniform_in_annulus() generates uniform points in an annulus by mapping. Number of points N = 1000 Center PC(1:2) = 10.000000 5.000000 Inner radius is R1 = 1.000000 Outer radius is R2 = 3.000000 Graphics saved as "uniform_in_annulus.png". uniform_in_annulus_sector_test(): uniform_in_annulus_sector() generates uniform points in an annular sector by mapping. Number of points N = 1000 Center PC(1:2) = 10.000000 5.000000 Inner radius is R1 = 1.000000 Outer radius is R2 = 3.000000 THETA1 = 0.000000 THETA2 = 1.570796 Graphics saved as "uniform_in_annulus_sector.png". uniform_in_circle_test(): uniform_in_circle() maps uniform points into a unit circle. Number of points N = 1000 Graphics saved as "uniform_in_circle.png". uniform_in_ellipse_test(): uniform_in_ellipse() returns uniform random points from inside an ellipse x'Ax=r^2. Number of points N = 400 R = 1 Matrix A: 4.0000 1.0000 1.0000 0.5000 Graphics saved as "uniform_in_ellipse.png". uniform_in_ellipsoid_test() uniform_in_ellipsoid() maps uniform points into an ellipsoid x'Ax=r^2. Number of points N = 1000 Spatial dimension D = 2 Ellipsoid matrix A: 3 1 1 2 Ellipsoid right hand side r = 1 p = 0.4059 -0.3177 0.3087 -0.0382 0.0158 -0.0049 -0.1498 -0.1729 -0.2728 0.1939 -0.1925 -0.0102 0.1235 -0.5188 0.0942 -0.2350 0.1153 0.1196 -0.2294 0.0306 -0.1826 0.5905 -0.0797 -0.3586 0.1187 0.2177 0.0734 -0.0869 -0.0173 0.3783 -0.2829 0.0162 0.1046 -0.3207 -0.2584 0.3717 -0.0741 0.0493 0.3734 -0.4865 -0.2940 0.1142 -0.3512 0.1723 -0.4072 0.3892 0.1242 -0.3607 0.3933 -0.3759 0.0153 -0.3446 -0.2022 0.3768 -0.1292 0.0090 0.2325 0.0464 0.2084 -0.0911 -0.2495 0.2772 0.3401 -0.2137 0.0549 -0.4226 0.3995 -0.5052 0.2590 0.0298 -0.4013 0.4929 0.1212 0.1617 0.0149 0.0531 0.3305 -0.2354 0.2565 0.1035 -0.0979 -0.1338 -0.2317 0.2896 0.3161 -0.0769 -0.0143 -0.0903 0.1031 0.1507 -0.1527 -0.1267 -0.0268 0.4582 0.2559 -0.1976 -0.1963 0.1414 -0.3022 0.2915 0.2128 -0.4191 -0.1690 0.5612 -0.0935 -0.0147 0.4135 -0.3653 -0.1306 -0.0083 -0.3561 0.5393 -0.1782 0.4838 -0.0786 -0.0620 -0.3928 0.4102 -0.1818 0.1790 0.1654 -0.3921 0.3540 -0.1007 -0.1918 0.2272 -0.2773 0.5276 -0.3187 0.1350 0.0038 -0.3388 0.0676 0.3722 0.2680 0.0514 0.0820 0.0802 -0.1227 0.0630 0.0329 -0.3063 0.1950 0.1943 0.0956 -0.4921 0.1404 0.0121 0.1541 -0.4040 -0.2039 -0.1781 0.2692 -0.2147 0.0121 0.0347 -0.0505 -0.3217 0.3663 -0.2999 -0.2182 -0.1275 -0.0493 0.4595 -0.2392 0.2893 0.1465 0.2324 0.0157 0.2686 -0.2826 -0.0062 -0.3977 0.3169 0.1079 -0.0604 0.1385 -0.3399 0.3752 -0.4963 -0.1051 0.0102 -0.1114 0.1534 0.2867 -0.2104 0.0322 -0.4117 -0.3649 0.5104 0.3754 -0.2288 -0.1186 -0.1509 -0.0185 0.0157 -0.1442 -0.0178 0.3091 -0.2571 -0.3189 0.2712 0.2476 -0.4001 -0.3632 0.2431 0.2921 -0.5157 -0.2768 0.0147 -0.1690 -0.0744 0.2866 -0.3570 -0.2397 0.5122 -0.0839 0.0791 0.2786 -0.5171 -0.1549 0.0505 0.1967 -0.3917 0.4044 -0.4311 -0.2554 -0.0981 0.1522 0.2519 -0.2790 0.0244 -0.0463 0.2512 -0.0119 -0.0620 0.0772 -0.0914 0.0409 -0.1534 0.2460 -0.5749 -0.1577 0.0704 -0.2734 0.5112 0.2847 -0.2486 -0.1142 0.4618 -0.1476 -0.0326 -0.2444 0.2908 0.2500 -0.0021 0.3402 -0.2425 0.3212 -0.4371 -0.4126 0.4818 0.2459 -0.6026 -0.0877 -0.1718 0.1167 -0.5348 -0.3423 0.4466 -0.1209 -0.2992 0.2426 -0.3831 -0.2495 0.5855 0.1163 0.2169 0.4240 -0.4240 -0.0081 0.2983 -0.3464 0.3968 0.2905 0.0478 -0.1824 0.1911 -0.3289 0.2825 0.0683 -0.1366 -0.0598 0.2428 0.0261 0.3208 -0.0591 -0.1205 -0.1361 0.5423 -0.4100 0.4475 0.0431 -0.1583 -0.2873 0.4757 0.3735 -0.2361 -0.0596 0.1643 -0.0377 0.2883 -0.1188 0.4233 0.3030 -0.0123 0.1434 -0.5500 -0.3513 0.2296 -0.3178 0.0778 -0.1420 -0.0441 -0.1727 0.2619 -0.2499 0.5715 -0.1469 0.5493 -0.1594 0.5510 -0.1625 -0.1984 0.0144 -0.3987 0.1382 0.0321 -0.2522 0.4841 0.0294 -0.2396 -0.0420 0.1516 -0.3005 0.1665 0.0876 -0.2408 -0.2421 0.5544 0.2234 0.1575 0.1112 -0.2751 -0.2798 0.0925 0.2371 -0.2344 0.1177 -0.2611 -0.0200 0.0109 0.0242 0.0949 -0.2450 0.4784 -0.2721 0.2054 -0.3895 0.3554 0.0548 0.2840 0.3562 -0.5333 -0.0196 0.1849 -0.4020 0.3781 0.1680 -0.3588 0.0826 0.2787 -0.1244 0.1037 0.3646 -0.3737 0.0994 -0.3798 0.1284 -0.4481 -0.3877 0.5691 0.0058 -0.1416 0.0467 0.3026 -0.3142 0.3830 -0.0776 0.3230 0.1122 -0.2899 0.1069 -0.1098 0.1097 0.2331 0.3567 -0.4349 -0.2058 0.3418 0.4191 -0.5024 -0.2606 0.5480 -0.3026 0.5607 0.1427 -0.1597 0.0794 0.3001 0.2603 -0.1050 -0.3677 0.2227 0.3821 -0.4059 0.0378 0.2467 -0.1687 -0.0169 0.0603 -0.1842 -0.3751 0.5570 0.2113 -0.3093 -0.2184 0.2613 0.2896 -0.4403 -0.2913 0.6043 -0.0938 0.2164 -0.4314 0.4254 0.2216 -0.5784 0.2525 -0.0841 -0.3028 0.0654 0.3836 -0.2462 -0.1003 -0.0351 -0.3278 0.0607 -0.1270 0.2277 0.1137 -0.4581 0.2233 -0.2919 -0.2314 -0.0825 0.2532 -0.0547 0.2955 -0.5967 0.1989 -0.4458 0.0465 0.3903 0.1479 0.2591 -0.1350 0.0945 -0.0253 0.1016 0.2071 -0.5058 0.2784 -0.5958 0.1114 -0.1594 0.3803 -0.2958 0.2286 0.1461 -0.3402 0.5941 0.0088 0.0747 0.2600 -0.0433 0.3702 -0.1806 -0.3324 0.2426 0.2323 -0.6075 0.1088 -0.0074 0.0774 -0.1648 -0.3079 0.5580 -0.3302 0.1053 -0.0802 0.1104 0.0480 0.3230 -0.1804 0.0247 -0.3010 0.4631 -0.1127 0.4884 -0.0771 0.3993 -0.3547 0.1447 0.0881 -0.4052 -0.3191 0.5471 -0.1400 0.3671 0.0318 -0.2800 0.1613 -0.0363 -0.1807 -0.2018 -0.1520 0.5191 0.1563 -0.5307 -0.0196 -0.2285 0.2325 -0.1287 -0.2527 0.4784 0.2174 -0.2860 0.2531 -0.2271 -0.1066 -0.1654 0.3323 -0.5742 0.1339 0.1737 -0.2390 0.4495 -0.0264 0.1532 0.2157 -0.2052 0.0399 -0.2602 -0.2346 0.2598 -0.0990 0.0772 0.1638 -0.3269 -0.3253 0.4644 0.4336 -0.5396 -0.1460 0.0743 0.1140 -0.1346 -0.1187 0.2870 -0.3199 0.1656 -0.1366 0.2223 0.0268 -0.3586 0.2640 -0.0726 0.2279 -0.2097 -0.0415 0.4290 -0.0526 0.0104 0.0769 -0.4291 -0.0122 0.4326 0.2892 -0.4359 -0.2505 0.2649 -0.0622 -0.0947 -0.2742 0.5459 0.0742 -0.1397 -0.3536 0.3705 0.1926 -0.4042 -0.3288 0.5370 0.3667 -0.2484 -0.3171 0.5092 -0.2623 0.4264 0.3096 -0.4375 -0.0016 -0.2164 -0.0759 0.1211 0.3616 -0.5630 0.1472 -0.2413 -0.3484 0.0809 0.2130 -0.5840 -0.1331 0.3348 0.1161 -0.2868 0.1869 0.1961 0.2691 0.0106 0.0625 0.3465 0.0945 -0.0691 -0.0591 -0.2109 0.4146 -0.4546 -0.2277 0.0495 -0.1817 0.3062 0.1952 -0.2010 -0.0649 0.4846 0.2226 0.1292 0.3440 -0.2605 -0.3185 0.0838 0.2875 -0.5423 0.1064 0.3214 -0.3682 0.4980 0.2603 -0.1652 -0.1460 0.0559 -0.2603 -0.0820 -0.2655 0.1739 -0.0607 -0.3351 -0.2980 0.4693 -0.3676 0.5759 -0.0998 0.4177 0.3537 -0.5648 -0.2825 0.0260 -0.3942 0.5285 -0.3189 0.4637 -0.0778 0.2534 -0.3834 0.4127 -0.0688 0.1168 -0.0883 0.0965 -0.3045 0.0231 0.2212 -0.2382 -0.0390 0.4798 -0.0186 0.2914 -0.3166 0.2079 -0.3597 0.5590 -0.0412 0.2685 -0.1227 -0.2216 -0.3550 0.5254 0.0288 0.0768 -0.2745 -0.0487 0.2195 -0.5522 0.0631 -0.0290 0.4200 -0.4815 0.0387 -0.1742 -0.2626 0.1785 -0.1800 0.2183 0.3513 -0.4608 -0.1782 0.1939 -0.3881 0.5560 -0.1238 0.1241 -0.3648 0.4260 0.0799 -0.2704 -0.2059 0.3978 0.1160 -0.0318 -0.3493 0.3798 0.4064 -0.2292 0.0970 -0.2153 -0.1576 0.2107 -0.2076 0.0523 0.0724 -0.2423 0.1278 -0.3399 0.1369 0.1133 -0.1863 -0.2062 -0.2545 0.4493 0.1355 -0.1538 -0.1440 -0.1963 -0.1565 0.3969 0.0362 0.3964 0.0080 -0.3279 0.3356 -0.6168 0.3787 -0.3533 0.1742 -0.2059 -0.3244 0.3648 -0.1701 0.2918 -0.3021 0.2755 0.0763 -0.4085 0.1151 -0.2436 -0.1190 0.3391 -0.0221 -0.0857 -0.0677 0.3225 -0.0601 -0.2132 0.1359 -0.2616 0.3025 -0.3455 0.0616 0.2508 0.2897 -0.0235 0.0824 -0.4459 0.2617 -0.2902 -0.1853 -0.0122 -0.2309 0.5115 -0.3413 0.4008 0.1708 0.1677 -0.0182 0.4587 0.1671 -0.4587 -0.1204 0.0477 -0.1914 0.3111 -0.0282 0.0841 0.4176 -0.2708 -0.0496 0.2637 -0.0795 0.0048 -0.3762 0.4886 0.0918 -0.1663 0.3453 -0.1496 0.0820 -0.3826 -0.0952 0.2463 0.0376 -0.4736 0.3050 -0.5053 -0.3299 0.0484 0.2465 -0.5017 -0.0245 -0.1809 -0.0938 0.3819 -0.2294 -0.1246 -0.2033 -0.1681 -0.2558 0.2621 -0.2968 0.4449 0.1060 0.2223 -0.0606 -0.2879 -0.1260 0.2540 -0.0795 0.3744 0.4401 -0.4536 -0.0706 0.3500 -0.3650 0.1738 0.3105 -0.2556 -0.1990 0.2358 0.2350 -0.4877 0.3172 -0.1270 0.1099 -0.5383 0.2931 -0.0501 0.2078 -0.4576 0.3415 -0.5622 -0.2048 0.0705 -0.0552 0.1098 0.3428 -0.3334 -0.2953 0.5848 0.1554 -0.4428 0.1754 -0.0610 0.1140 -0.3625 -0.1223 -0.1598 -0.1018 -0.2893 -0.1885 -0.1608 -0.2580 0.4667 -0.0767 -0.0057 0.0324 0.3512 0.0362 -0.0619 -0.2908 0.5439 0.0079 -0.1882 -0.1725 0.0157 -0.0518 -0.2507 0.1717 -0.2133 -0.2592 0.2016 -0.3143 0.5632 0.2568 -0.1368 0.4298 -0.4095 0.0750 0.2220 0.0429 0.0252 0.0106 0.2886 -0.1119 0.4496 0.2790 -0.2861 -0.2943 0.4950 0.1791 0.1226 0.0068 0.3805 -0.0879 -0.0367 0.2890 -0.2037 -0.2812 -0.0551 -0.1849 0.2996 -0.1288 0.1119 -0.0196 0.0143 -0.1769 -0.0013 0.2673 -0.0897 0.1393 -0.3652 0.1382 -0.3262 0.0382 -0.1067 0.0810 -0.3148 -0.1655 -0.1335 -0.1002 0.3542 0.1481 0.1494 0.3105 -0.1745 -0.0534 0.1885 -0.2147 -0.0055 0.0217 -0.2336 -0.1139 -0.2654 -0.3072 0.2061 0.2979 -0.5490 -0.1183 0.3602 0.1835 0.0934 0.1653 -0.4727 0.0326 0.2733 0.0648 -0.0731 -0.3496 0.5423 -0.2907 0.0657 -0.1825 0.4314 -0.0143 -0.2449 0.1754 -0.5819 -0.2166 0.5581 -0.2271 0.2239 -0.0813 -0.0020 -0.1943 0.1268 -0.3724 0.4736 0.1911 0.0493 0.0507 0.1927 0.1493 -0.1833 -0.1393 -0.2113 0.3774 -0.5014 0.3007 -0.5339 0.2605 -0.3393 -0.0068 0.1925 -0.2435 0.3954 -0.0269 -0.1649 0.2743 -0.0524 0.2692 -0.4988 0.3195 -0.4839 0.0120 0.2998 0.2781 -0.5437 0.3241 -0.5497 -0.1342 -0.2033 0.0197 -0.1220 -0.3366 0.6250 0.1306 -0.4226 0.2834 0.0525 0.1358 -0.1032 0.0206 -0.4085 -0.1299 -0.0217 0.3465 -0.5298 -0.2582 0.2082 0.1808 -0.2398 -0.2360 0.0774 -0.3681 0.6046 -0.2403 0.5595 0.2560 -0.2723 0.2054 0.1820 0.0775 0.1814 -0.2984 0.4252 -0.0446 0.1199 -0.3391 0.3791 -0.0617 -0.0107 0.1596 0.1263 0.2553 -0.3880 -0.1474 0.4794 -0.1522 0.4226 -0.3802 0.6024 -0.0242 -0.1948 -0.3647 0.5305 0.2502 -0.5108 0.0806 0.0376 -0.1842 0.3649 0.3110 -0.0115 -0.0297 -0.3910 -0.2694 -0.0759 0.3922 -0.5009 0.0289 0.3285 0.3304 -0.6036 0.3957 -0.5792 -0.0061 -0.1265 -0.1160 0.3748 -0.0155 0.1370 -0.0574 -0.1563 -0.0812 -0.1352 -0.1491 0.2716 0.2182 -0.5877 0.4157 -0.3768 -0.3690 0.5679 0.0059 -0.1552 0.2372 0.0786 0.0094 -0.0536 -0.1227 -0.0896 0.2118 -0.5894 -0.1601 0.2594 0.2613 -0.1008 -0.0502 -0.2220 -0.2426 0.5133 0.0657 -0.1944 0.2793 -0.1665 -0.2363 0.2440 0.2571 -0.4960 -0.0291 0.2865 -0.2870 -0.0353 0.3747 -0.4590 0.1766 -0.4088 -0.4422 0.4672 0.0568 0.2844 -0.3721 0.3898 -0.0480 -0.1189 0.1847 -0.5249 0.1067 0.2619 0.0242 0.2882 -0.1056 0.2232 -0.1871 -0.1687 -0.3043 0.1397 -0.3302 0.5799 0.0914 -0.0977 0.2832 -0.1921 -0.3193 0.5209 0.0510 -0.0091 0.4142 -0.3707 0.2566 -0.0966 0.2184 -0.2149 -0.2886 0.1087 0.2350 0.0575 -0.2249 0.5420 -0.2064 0.1652 -0.2506 0.2328 -0.1559 0.3711 0.1340 -0.4913 0.1514 -0.2934 0.0510 -0.2452 -0.2778 0.3189 -0.2918 0.0518 0.1541 -0.5584 -0.1327 0.5581 0.1472 -0.0896 -0.2423 0.0123 0.0751 0.3241 -0.3480 0.1000 0.1726 -0.3379 0.3682 -0.5915 0.0341 0.2792 0.0688 0.0655 0.1817 -0.0131 0.1658 0.1642 0.2365 -0.6124 0.0686 0.2948 -0.1675 0.3324 0.2758 -0.4419 0.0443 0.2363 0.0494 -0.1863 0.2867 -0.0758 -0.0911 0.0021 -0.0549 -0.0995 -0.0330 -0.0503 0.0182 0.1915 0.1861 -0.1955 -0.0152 -0.4158 -0.0909 0.2603 -0.2827 0.4203 0.4345 -0.4694 -0.1719 -0.0341 -0.1333 0.2696 0.2723 -0.1714 0.0220 -0.0220 0.2232 -0.4850 -0.3925 0.4382 0.2161 -0.4292 0.2529 0.0817 0.0162 0.0372 0.2969 -0.1707 -0.3740 0.4347 -0.0600 0.4259 0.1561 -0.3820 -0.2096 0.4021 0.1431 0.1079 0.3354 -0.1114 -0.1527 0.2947 0.0472 -0.2166 0.1351 0.0101 0.1328 -0.2045 -0.2210 0.4682 -0.4329 0.3812 0.0675 -0.4130 -0.4404 0.3929 -0.3329 0.2004 0.0021 0.2760 -0.1291 0.0503 -0.1315 0.3406 0.0645 0.3401 0.1942 -0.4877 0.1854 0.1488 0.0857 -0.3427 0.0349 0.2261 -0.1808 -0.1897 0.1706 0.2345 -0.2163 0.5055 -0.0082 0.0785 -0.0369 0.2071 -0.0838 0.0528 0.1380 -0.4139 0.2020 -0.5637 -0.3003 0.1949 -0.0591 0.2418 -0.1081 -0.2827 0.1029 0.0432 -0.3198 0.4505 -0.2112 0.3894 -0.1106 0.5065 -0.2626 0.5634 -0.4060 0.5445 0.0693 0.2403 -0.0595 -0.3327 -0.0786 0.2774 -0.0879 -0.2568 -0.4436 0.4994 -0.2155 0.4830 0.1020 -0.0634 0.1178 -0.5279 0.0519 0.1638 -0.2767 0.2321 0.2255 -0.1785 -0.1683 0.3838 0.1267 -0.4270 -0.0784 -0.2382 0.3980 -0.2435 0.0364 0.3631 -0.0081 -0.1075 -0.2210 0.0156 0.0929 0.0254 -0.1255 0.2902 -0.2616 0.0258 -0.0644 -0.1656 0.0682 0.0591 0.0252 -0.4531 0.0156 -0.3545 -0.1709 -0.1491 0.0602 -0.2491 -0.0724 0.3940 0.2292 -0.4718 0.3343 -0.5468 -0.2491 0.1159 0.4183 -0.2999 0.0414 -0.4571 0.1269 -0.4341 -0.0281 -0.1747 -0.1617 0.5417 -0.0360 0.4770 0.0345 0.2274 0.2545 -0.3306 -0.2243 -0.1580 0.0063 -0.4019 -0.3411 0.4583 -0.2885 -0.0410 -0.1335 0.5453 0.3162 -0.0615 -0.1371 0.1797 -0.2165 -0.0020 -0.3077 0.3018 -0.0295 -0.0730 -0.2482 0.0733 -0.2108 0.0644 -0.1299 0.4859 -0.2738 0.2402 -0.1759 -0.1671 -0.4096 0.3569 -0.0598 -0.3721 0.3629 -0.5525 0.2430 -0.3592 0.0149 -0.4606 -0.2982 0.1914 -0.3178 0.1110 0.3634 -0.1289 0.2483 -0.1428 -0.2869 0.3077 0.2687 -0.1169 -0.0446 -0.0718 0.3632 -0.4170 -0.1463 0.1070 -0.3095 0.0919 0.0498 0.1599 -0.1709 0.3471 -0.2359 0.2665 0.0154 -0.3131 -0.3270 0.2839 -0.1280 -0.0525 0.2277 -0.4896 -0.2593 0.2962 -0.3309 0.2023 0.3184 -0.0798 -0.0507 0.3952 0.1341 0.2123 0.0507 0.2007 -0.3486 0.4711 -0.3758 0.1598 -0.1936 0.1571 0.0146 0.2821 0.3917 -0.2618 0.3439 -0.2679 -0.1100 0.5420 0.0869 -0.0396 -0.4152 0.5190 0.4282 -0.3337 -0.0468 0.0136 0.2960 -0.1218 0.1044 -0.5343 -0.4077 0.3271 0.2603 -0.4027 -0.2804 0.6288 -0.0979 0.1171 -0.2982 0.1942 0.0953 -0.2199 -0.1803 0.4898 0.0274 -0.1932 0.0997 0.1757 0.1845 0.1580 0.2483 -0.3407 0.1040 -0.3497 0.1306 -0.1691 -0.2297 0.1858 0.3904 -0.4171 -0.1525 0.2083 0.2530 -0.1660 -0.2688 0.1340 -0.4261 0.4243 0.3658 -0.2065 0.0009 0.1177 -0.2847 0.0100 0.0807 -0.0651 -0.3293 0.4278 0.2150 -0.5947 -0.3200 0.0675 0.3300 -0.2038 0.1734 -0.0210 0.3660 -0.1197 -0.2127 0.1053 -0.0682 -0.0339 0.3266 -0.1004 -0.1203 0.5361 0.0250 -0.4051 0.1941 -0.1196 0.0672 -0.1319 0.3918 -0.3325 -0.3896 0.5535 -0.0214 0.4672 -0.1084 -0.3045 -0.0565 -0.3175 0.0225 -0.3312 0.2231 0.0680 -0.1924 -0.1953 0.1363 0.1785 -0.3094 0.0776 0.2431 -0.0203 0.3622 -0.5432 -0.0026 0.2980 0.3656 -0.6215 -0.0515 0.0994 0.3524 -0.3085 -0.1781 0.2919 0.0043 -0.0912 -0.0316 0.3731 -0.0083 -0.1441 0.1139 -0.0481 -0.1250 -0.0925 0.1591 -0.0745 -0.0699 -0.3376 0.1250 0.1324 0.2779 -0.1488 -0.1937 0.0366 0.0021 -0.0190 0.0537 -0.0417 0.2828 -0.5232 -0.0274 -0.1328 -0.2951 0.5964 0.2301 -0.4233 0.1421 0.0354 -0.0591 0.3370 -0.1045 -0.2529 0.0890 -0.1167 0.2468 -0.4553 0.1819 -0.0362 0.2248 -0.1883 0.3051 -0.5736 -0.3383 0.1426 0.1603 -0.0049 0.2438 -0.2774 -0.0931 -0.3268 0.3643 -0.4514 0.1273 -0.2822 0.1845 0.0192 -0.3451 0.2675 -0.3218 0.3242 0.2841 -0.6135 0.2739 -0.3634 -0.4317 0.4884 0.0705 0.2807 -0.1763 0.1975 0.3643 -0.6109 0.0047 0.1923 0.2019 -0.2645 -0.3334 0.5715 -0.1473 -0.2170 -0.2886 0.5191 0.2079 -0.2066 -0.2712 0.2695 0.2590 -0.4664 -0.0427 0.0762 0.3598 -0.2429 0.3255 -0.1604 -0.2526 0.5115 0.1756 -0.5015 -0.1366 -0.2574 0.1119 0.1562 0.0619 -0.1836 0.2405 -0.4594 -0.1560 0.0128 0.3072 -0.1471 -0.0206 -0.0452 0.1864 0.0894 -0.0696 -0.3378 0.3353 -0.6077 -0.3816 0.2714 0.2064 -0.4946 -0.1867 0.2441 0.1348 -0.1779 0.1186 0.2845 -0.1810 0.1454 0.1138 0.2633 0.3422 -0.4122 0.2817 -0.1337 -0.2918 0.4681 0.1886 -0.2351 -0.0645 0.3174 0.4056 -0.4801 -0.0574 0.2766 -0.0674 -0.3485 -0.0245 0.3206 -0.1022 -0.0953 -0.1742 0.1415 0.1188 0.0365 0.1329 -0.0200 -0.1616 0.3352 -0.0690 0.3986 0.0245 0.3989 -0.0450 0.2203 -0.1563 0.5245 0.1060 -0.4103 -0.2252 -0.0725 -0.0953 0.1266 0.1142 0.0481 -0.0136 0.1046 0.0341 -0.3739 0.2465 -0.0463 0.1365 -0.2784 0.3830 -0.4386 0.3310 -0.4311 0.1623 -0.0184 -0.0451 0.3633 -0.0302 0.2277 -0.0640 0.0455 -0.1159 -0.2718 -0.0144 -0.2566 -0.1994 0.3614 -0.3369 0.3958 0.1884 -0.2265 0.2802 -0.2041 -0.3313 0.3916 -0.0003 -0.0430 0.1523 0.0948 0.1598 0.0631 -0.1211 -0.0948 0.3311 -0.0943 -0.3288 0.2563 0.0601 -0.4609 0.2456 0.0482 -0.4013 0.4026 0.1839 -0.0491 0.1953 -0.3246 -0.0586 0.0153 0.3932 -0.2611 -0.0704 0.0064 0.2260 0.1382 0.2019 0.1970 0.0702 -0.0805 0.2631 -0.1665 0.2288 -0.3855 -0.1973 -0.1199 0.2172 -0.1789 0.3127 -0.0276 0.1008 0.3341 -0.3321 0.5651 0.0282 0.2834 -0.0374 0.1192 0.1931 0.1000 0.2016 -0.2264 0.0071 0.3940 0.1033 -0.4751 -0.0239 0.4520 -0.3188 0.4671 -0.1924 0.0189 -0.0771 -0.0307 0.0262 0.1234 -0.2652 0.5921 -0.2211 0.2316 -0.0011 -0.2066 Graphics saved as "uniform_in_ellipsoid.png" uniform_in_hexagon_test(): uniform_in_hexagon() maps uniform points into the unit hexagon. Number of points N = 1000 Graphics saved as "uniform_in_hexagon.png". d = 3 uniform_in_hypercube_test(): uniform_in_hypercube() generates uniform points in the unit hypercube. Number of points N = 1000 Spatial dimension D = 3 Graphics saved as "uniform_in_hypercube.png". uniform_in_hypersphere_test(): uniform_in_hypersphere() maps uniform points into the unit hypersphere. Number of points N = 1000 Spatial dimension D = 3 Graphics saved as "uniform_in_hypersphere.png". uniform_in_parallelogram_test(): uniform_in_parallelogram() maps uniform points into an arbitrary parallelogram. Number of points N = 1000 V1 = 0.750000 0.900000 V2 = 0.000000 0.200000 V3 = 1.500000 0.650000 V4 = 0.750000 -0.050000 Graphics saved as "uniform_in_parallelogram.png". uniform_in_polygon_test(): uniform_in_polygon() maps uniform points into a polygon. Number of points N = 1000 Number of vertices NV = 10 Polygonal vertices: 0 0 0.5000 0.3000 1.0000 0 0.7000 0.4000 1.0000 0.6000 0.6000 0.6000 0.5000 1.0000 0.4000 0.6000 0 0.6000 0.3000 0.4000 im1 = 10 Graphics saved as "uniform_in_polygon.png" uniform_in_sector_test(): uniform_in_sector() maps uniform points into a circular sector. Number of points N = 300 R = 2.000000 T1 = 0.780000 T2 = 2.350000 Graphics saved as "uniform_in_sector.png". uniform_in_simplex_test(): uniform_in_simplex() maps uniform points into the unit simplex. Number of points N = 1000 Spatial dimension D = 2 Graphics saved as "uniform_in_simplex.png" uniform_in_tetrahedron_test(): uniform_in_tetrahedron() returns uniform points in a tetrahedron. Number of points N = 1000 Vertices: 1 2 3 4 1 2 2 4 4 3 2 5 Graphics saved as "uniform_in_tetrahedron.png". uniform_in_triangle_test(): uniform_in_triangle() maps uniform points into a triangle. Number of points N = 1000 V1 = 0.750000 0.900000 V2 = 0.000000 0.200000 V3 = 0.950000 0.650000 Graphics saved as "uniform_in_triangle.png" uniform_on_circle_test(): uniform_on_circle() returns uniform random points on a circle x^2 + y^2 = 1. N = 100 Graphics saved as "uniform_on_circle.png". uniform_on_ellipse_test(): uniform_on_ellipse() returns uniform random points on an ellipse (x/a)^2+(y/b)^2=1. N = 100 A = 2 B = 3 Graphics saved as "uniform_on_ellipse.png". uniform_on_ellipsoid_test(): uniform_on_ellipsoid() maps uniform points onto an ellipsoid x'Ax=r^2. Number of points N = 200 Spatial dimension D = 2 Ellipsoid matrix: 3 1 1 2 Right hand side R = 1 Graphics saved as "uniform_on_ellipsoid.png". uniform_on_hemisphere_phong_test(): uniform_on_hemisphere_phong() maps uniform points onto the unit hemisphere with Phong density. Spatial dimension D = 3 Number of points N = 500 Phong exponent M = 2 Graphics saved as "uniform_on_hemisphere_phong.png". uniform_on_hypercube_test(): uniform_on_hypercube() samples N uniform points on the surface of the unit M-dimensional hypercube. Number of points N = 1000 Spatial dimension D = 3 Graphics saved as "uniform_on_hypercube.png". uniform_on_hypersphere_test(): uniform_on_hypersphere() returns uniform random points on the surface of the unit hypersphere. Number of points N = 2000 Spatial dimension D = 3 Graphics saved as "uniform_on_hypersphere.png". uniform_on_simplex_test(): uniform_on_simplex() returns uniform random points on the surface of the unit simplex. Number of points N = 500 Spatial dimension D = 3 Graphics saved as "uniform_on_simplex.png". uniform_on_sphere_patch_tp_test(): uniform_on_sphere_patch_tp() maps uniform points onto a TP (THETA,PHI) patch of the unit sphere. The points are returned as (X,Y,Z) coordinates. Number of points N = 500 Latitudinal angle PHI1 = 1.396263 Latitudinal angle PHI2 = 1.745329 Longitudinal angle THETA1 = 0.000000 Longitudinal angle THETA2 = 6.283185 Graphics saved as "uniform_on_sphere_patch_tp.png". uniform_on_sphere_patch_xyz_test(): uniform_on_sphere_patch_xyz(): maps uniform points onto an XYZ patch of the unit sphere. Number of points N = 500 Latitudinal angle PHI1 = 1.396263 Latitudinal angle PHI2 = 1.745329 Longitudinal angle THETA1 = 0.000000 Longitudinal angle THETA2 = 6.283185 Graphics saved as "uniform_on_sphere_patch_xyz.png". uniform_on_sphere_triangle_xyz_test(): uniform_on_sphere_triangle_xyz() maps uniform points onto a spherical triangle using XYZ coordinates. Number of points N = 500 Vertices of the spherical triangle: V1: 1.000000 0.000000 0.000000 V2: 0.000000 1.000000 0.000000 V3: 0.000000 0.000000 1.000000 Graphics saved as "uniform_on_sphere_triangle_xyz.png". uniform_on_triangle_test(): uniform_on_triangle() maps uniform points onto the surface of the unit triangle. Number of points N = 100 Graphics saved as "uniform_on_triangle.png". uniform_walk_test(): uniform_walk() generates points on a uniform random walk of fixed steps in coordinate directions. Number of points N = 400 Spatial dimension D = 2 Graphics saved as "uniform_walk.png". random_data_test(): Normal end of execution. 13-Apr-2022 20:40:41