03-Mar-2019 15:38:54 random_data_test MATLAB version Test random_data. BAD_IN_SIMPLEX01_TEST: BAD_IN_SIMPLEX01 is a "bad" sampling technique for the unit simplex. Spatial dimension DIM_NUM = 2 Number of points N = 10000 Initial random number SEED = 123456789 Data written to "bad_in_triangle.txt" Spatial dimension DIM_NUM = 3 Number of points N = 10000 Initial random number SEED = 123456789 Data written to "bad_in_tetrahedron.txt" RANDOM_DATA_TEST01: BROWNIAN generates Brownian motion points. Spatial dimension DIM_NUM = 2 Number of points N = 100 Initial random number SEED = 123456789 Final random number SEED = 1621315646 Data written to "brownian.txt". R8_NORMAL_01_TEST R8_NORMAL_01 generates normally distributed random values. Using initial random number seed = 123456789 1.679040 -0.472769 -0.566060 -0.231124 1.212934 0.535037 1.269381 1.049543 -1.666087 -1.865228 -2.242464 0.735809 0.039675 -1.350736 0.673068 0.007775 -0.275127 0.374940 2.164005 0.185600 R8_UNIFORM_01_TEST R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 RANDOM_DATA_TEST04 GRID_IN_CUBE01 generates grid points in the unit hypercube. Spatial dimension DIM_NUM = 2 Number of points N = 85 CENTER option = 1 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to "grid_in_cube01.txt". RANDOM_DATA_TEST05 HALTON_IN_CIRCLE01_ACCEPT generates Halton points in a unit circle by acceptance/rejection. Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 123457299 Data written to "halton_in_circle01_accept.txt". RANDOM_DATA_TEST06 HALTON_IN_CIRCLE01_MAP maps Halton points into a unit circle. Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 123457189 Data written to "halton_in_circle01_map.txt". RANDOM_DATA_TEST07 HALTON_IN_CUBE01 generates Halton points in the unit hypercube. Spatial dimension DIM_NUM = 2 Number of points N = 510 Initial random number SEED = 123456789 Final random number SEED = 123457299 Data written to "halton_in_cube01.txt". RANDOM_DATA_TEST08 HAMMERSLEY_IN_CUBE01 generates Hammersley points in the unit hypercube. Spatial dimension DIM_NUM = 2 Number of points N = 100 Initial random number SEED = 123456789 Final random number SEED = 123456889 Data written to "hammersley_in_cube01.txt". RANDOM_DATA_TEST09 NORMAL generates normal points in M dimensions, using a nonzero mean, and with user-specified variance-covariance matrix. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Mean vector MU: 1 6.000000 2 100.000000 Variance-covariance matrix V: Col: 1 2 Row 1 5 2 2 2 1 Cholesky factor R: Col: 1 2 Row 1 2.23607 0.894427 2 0 0.447214 Final random number SEED = 1328042058 Data written to "normal.txt". RANDOM_DATA_TEST10 NORMAL_CIRCULAR generates points in 2D distributed according to a circular normal. Spatial dimension DIM_NUM = 2 Number of points N = 2000 Initial random number SEED = 123456789 Final random number SEED = 1539989115 Data written to "normal_circular.txt". RANDOM_DATA_TEST11 NORMAL_SIMPLE generates normal points in M dimensions, using a zero mean, and with the identity as the variance-covariance matrix. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Final random number SEED = 1328042058 Data written to "normal_simple.txt". RANDOM_DATA_TEST115 UNIFORM_IN_ANNULUS generates uniform points in an annulus by mapping. Spatial dimension DIM_NUM = 2 Number of points N = 400 Center PC(1:2) = 10.000000 5.000000 Inner radius is R1 = 1.000000 Outer radius is R2 = 3.000000 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to "uniform_in_annulus.txt". RANDOM_DATA_TEST12 UNIFORM_IN_ANNULUS_ACCEPT generates uniform points in an annulus by acceptance/rejection. Spatial dimension DIM_NUM = 2 Number of points N = 400 Center PC(1:2) = 10.000000 5.000000 Inner radius is R1 = 1.000000 Outer radius is R2 = 3.000000 Initial random number SEED = 123456789 Final random number SEED = 1747129609 Data written to "uniform_in_annulus_accept.txt". RANDOM_DATA_TEST125 UNIFORM_IN_ANNULUS_SECTOR generates uniform points in an annular sector by mapping. Spatial dimension DIM_NUM = 2 Number of points N = 400 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 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to "uniform_in_annulus_sector.txt". RANDOM_DATA_TEST13 UNIFORM_IN_CIRCLE01_MAP maps uniform points into a unit circle. Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to "uniform_in_circle01_map.txt". RANDOM_DATA_TEST14 UNIFORM_IN_CUBE01 generates uniform points in the unit hypercube. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Final random number SEED = 1328042058 Data written to "uniform_in_cube01.txt". RANDOM_DATA_TEST15 UNIFORM_IN_ELLIPSOID_MAP maps uniform points into an ellipsoid. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Final random number SEED = 70876380 Data written to "uniform_in_ellipsoid_map.txt". 0 points failed the ellipsoid test. 1000 points satisfy the ellipsoid test. RANDOM_DATA_TEST16 UNIFORM_IN_PARALLELOGRAM_MAP maps uniform points into an arbitrary parallelogram. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.750000 0.900000 V2 = 0.000000 0.200000 V3 = 1.100000 0.650000 V4 = 0.350000 -0.050000 Final random number SEED = 1328042058 Data written to "uniform_in_parallelogram_map.txt". RANDOM_DATA_TEST17 UNIFORM_IN_POLYGON_MAP maps uniform points into a polygon. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Polygonal vertices: Col: 1 2 3 4 5 Row 1 0 0.5 1 0.7 1 2 0 0.3 0 0.4 0.6 Col: 6 7 8 9 10 Row 1 0.6 0.5 0.4 0 0.3 2 0.6 1 0.6 0.6 0.4 Final random number SEED = 70876380 Data written to "uniform_in_polygon_map.txt". RANDOM_DATA_TEST18 UNIFORM_IN_SECTOR_MAP maps uniform points into a circular sector. R1 = 1.000000 R2 = 2.000000 T1 = 0.780000 T2 = 2.350000 Spatial dimension DIM_NUM = 2 Number of points N = 300 Initial random number SEED = 123456789 Final random number SEED = 379008056 Data written to "uniform_in_sector_map.txt". RANDOM_DATA_TEST19 UNIFORM_IN_SIMPLEX01_MAP maps uniform points into the unit simplex. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Final random number SEED = 70876380 Data written to "uniform_in_simplex01_map.txt". RANDOM_DATA_TEST20 UNIFORM_IN_SPHERE01_MAP maps uniform points into the unit sphere. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 Final random number SEED = 70876380 Data written to "uniform_in_sphere01_map.txt". RANDOM_DATA_TEST205 UNIFORM_IN_TETRAHEDRON returns uniform points in a tetrahedron. Spatial dimension DIM_NUM = 3 Number of points N = 1000 Initial random number SEED = 123456789 Tetrahedron vertices: Col: 1 2 3 4 Row 1 1 4 2 3 2 2 1 4 2 3 3 2 4 5 Final random number SEED = 70876380 Data written to "uniform_in_tetrahedron.txt". UNIFORM_IN_TRIANGLE_MAP1_TEST UNIFORM_IN_TRIANGLE_MAP1 maps uniform points into a triangle. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.750000 0.900000 V2 = 0.000000 0.200000 V3 = 0.950000 0.650000 Final random number SEED = 1328042058 Data written to "uniform_in_triangle_map1.txt". RANDOM_DATA_TEST22 UNIFORM_IN_TRIANGLE_MAP maps uniform points into a triangle. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.750000 0.900000 V2 = 0.000000 0.200000 V3 = 0.950000 0.650000 Final random number SEED = 1328042058 Data written to "uniform_in_triangle_map2.txt". RANDOM_DATA_TEST23 UNIFORM_IN_TRIANGLE01_MAP maps uniform points into the unit triangle. Spatial dimension DIM_NUM = 2 Number of points N = 2000 Initial random number SEED = 123456789 Final random number SEED = 1539989115 Data written to "uniform_in_triangle01_map.txt". RANDOM_DATA_TEST235 UNIFORM_ON_CUBE01 samples N uniform points on the surface of the unit M-dimensional cube. Spatial dimension M = 3 Number of points N = 200 Data written to "uniform_on_cube01.txt". RANDOM_DATA_TEST24 UNIFORM_ON_ELLIPSOID_MAP maps uniform points onto an ellipsoid. Spatial dimension M = 2 Number of points N = 200 Initial random number SEED = 123456789 Final random number SEED = 123456789 Data written to "uniform_on_ellipsoid_map.txt". Image written to "uniform_on_ellipsoid_map.png". RANDOM_DATA_TEST245 UNIFORM_ON_HEMISPHERE01_PHONG maps uniform points onto the unit hemisphere with Phong density. Spatial dimension DIM_NUM = 3 Number of points N = 50 Phong exponent M = 2 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to "uniform_on_hemisphere01_phong.txt". RANDOM_DATA_TEST25 UNIFORM_ON_SIMPLEX01_MAP maps uniform points onto the unit simplex. Spatial dimension DIM_NUM = 2 Number of points N = 50 Initial random number SEED = 123456789 Final random number SEED = 882857018 Data written to "uniform_on_simplex01_map.txt". RANDOM_DATA_TEST26 UNIFORM_ON_SPHERE01_MAP maps uniform points onto the unit sphere. Spatial dimension DIM_NUM = 2 Number of points N = 50 Initial random number SEED = 123456789 Final random number SEED = 123456789 Data written to "uniform_on_sphere01_map.txt". RANDOM_DATA_TEST264 UNIFORM_ON_SPHERE01_PATCH_TP maps uniform points onto a TP (THETA,PHI) patch of the unit sphere. Spatial dimension = 3 Data dimension = 2 Number of points N = 50 Latitudinal angle PHI1 = 1.308997 Latitudinal angle PHI2 = 1.570796 Longitudinal angle THETA1 = 0.000000 Longitudinal angle THETA2 = 0.261799 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to "uniform_on_sphere01_patch_tp.txt". RANDOM_DATA_TEST265 UNIFORM_ON_SPHERE01_PATCH_XYZ maps uniform points onto an XYZ patch of the unit sphere. Spatial dimension DIM_NUM = 3 Number of points N = 50 Latitudinal angle PHI1 = 1.308997 Latitudinal angle PHI2 = 1.570796 Longitudinal angle THETA1 = 0.000000 Longitudinal angle THETA2 = 0.261799 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to "uniform_on_sphere01_patch_xyz.txt". RANDOM_DATA_TEST267 UNIFORM_ON_SPHERE01_TRIANGLE_XYZ maps uniform points onto a spherical triangle using XYZ coordinates. Spatial dimension DIM_NUM = 3 Number of points N = 500 Initial random number SEED = 123456789 Vertices of spherical triangle: V1: -0.440789 0.886569 -0.140357 V2: 0.956006 0.030386 -0.291771 V3: 0.053397 0.615235 -0.786534 Final random number SEED = 1760444247 Data written to "uniform_on_sphere01_triangle_xyz.txt". RANDOM_DATA_TEST27: UNIFORM_WALK generates points on a uniform random walk Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 1252896212 Data written to "uniform_walk.txt". random_data_test Normal end of execution. 03-Mar-2019 15:39:05