03 March 2022 09:38:51 PM RANDOM_DATA_TEST C version Test the RANDOM_DATA library. 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 file "bad_in_triangle.txt". Spatial dimension DIM_NUM = 3 Number of points N = 10000 Initial random number SEED = 123456789 Data written to file "bad_in_tetrahedron.txt". BROWNIAN_TEST: BROWNIAN generates Brownian motion points. Spatial dimension DIM_NUM = 2 Number of points N = 100 Initial random number SEED = 123456789 Final random number SEED = 490201319 Data written to file "brownian.txt". R8_NORMAL_01_TEST: R8_NORMAL_01 generates a single normal pseudorandom value. Seed Seed R8_NORMAL_01 (Input) (Output) 123456789 2053676357 1.67904 2053676357 1206231778 -0.56606 1206231778 141988902 1.21293 141988902 236130416 1.26938 236130416 1361431000 -1.66609 1361431000 965377566 -2.24246 965377566 1620648971 0.0396749 1620648971 3947872 0.673068 3947872 753234910 -0.275127 753234910 29242052 2.164 R8_UNIFORM_01_TEST: R8_UNIFORM_01 generates a single uniform pseudorandom value. Seed Seed R8_UNIFORM_01 (Input) (Output) 123456789 469049721 0.218418 469049721 2053676357 0.956318 2053676357 1781357515 0.829509 1781357515 1206231778 0.561695 1206231778 891865166 0.415307 891865166 141988902 0.0661187 141988902 553144097 0.257578 553144097 236130416 0.109957 236130416 94122056 0.043829 94122056 1361431000 0.633966 GRID_IN_CUBE01_TEST 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 file "grid_in_cube01.txt". HALTON_IN_CIRCLE01_ACCEPT_TEST HALTON_IN_CIRCLE01_ACCEPT accepts Halton points in the unit circle. Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 123457299 Data written to file "halton_in_circle01_accept.txt". HALTON_IN_CIRCLE01_MAP_TEST HALTON_IN_CIRCLE01_MAP maps Halton points into the 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 file "halton_in_circle01_map.txt". HALTON_IN_CUBE01_TEST HALTON_IN_CUBE01 generates Halton 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 file "halton_in_cube01.txt". HAMMERSLEY_IN_CUBE01_TEST 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 file "hammersley_in_cube01.txt". NORMAL_TEST 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: 0: 6 1: 100 Variance-covariance matrix V: Col: 0 1 Row 0: 5 2 1: 2 1 Cholesky factor R: Col: 0 1 Row 0: 2.23607 0.894427 1: 2 0.447214 Final random number SEED = 1328042058 Data written to file "normal.txt". NORMAL_CIRCULAR_TEST 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 file "normal_circular.txt". NORMAL_SIMPLE_TEST 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 file "normal_simple.txt". UNIFORM_IN_ANNULUS_TEST 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 5 Inner radius is R1 = 1 Outer radius is R2 = 3 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to file "uniform_in_annulus.txt". UNIFORM_IN_ANNULUS_ACCEPT_TEST 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 5 Inner radius is R1 = 1 Outer radius is R2 = 3 Initial random number SEED = 123456789 Final random number SEED = 1747129609 Data written to file "uniform_in_annulus_accept.txt". UNIFORM_IN_ANNULUS_SECTOR_TEST 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 5 Inner radius is R1 = 1 Outer radius is R2 = 3 THETA1 = 0 THETA2 = 1.5708 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to file "uniform_in_annulus_sector.txt". UNIFORM_IN_CIRCLE01_TEST UNIFORM_IN_CIRCLE01_MAP maps uniform points into the 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 file "uniform_in_circle01_map.txt". UNIFORM_IN_CUBE01_TEST 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 file "uniform_in_cube01.txt". UNIFORM_IN_ELLIPSOID_MAP_TEST 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 file "uniform_in_ellipsoid_map.txt". 0 points failed the ellipsoid test. 1000 points satisfy the ellipsoid test. UNIFORM_IN_PARALLELOGRAM_MAP_TEST UNIFORM_IN_PARALLELOGRAM_MAP maps uniform points into a parallelogram. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.75, 0.9 V2 = 0, 0.2 V3 = 1.1, 0.65 V4 = 0.35, -0.05 Final random number SEED = 1328042058 Data written to file "uniform_in_parallelogram_map.txt". UNIFORM_IN_POLYGON_MAP_TEST 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: 0 1 2 3 4 Row 0: 0 0.5 1 0.7 1 1: 0 0.3 0 0.4 0.6 Col: 5 6 7 8 9 Row 0: 0.6 0.5 0.4 0 0.3 1: 0.6 1 0.6 0.6 0.4 Final random number SEED = 70876380 Data written to file "uniform_in_polygon_map.txt". UNIFORM_IN_SECTOR_MAP_TEST UNIFORM_IN_SECTOR_MAP maps uniform points into a circular sector. R1 = 1 R2 = 2 T1 = 0.78 T2 = 2.35 Spatial dimension DIM_NUM = 2 Number of points N = 300 Initial random number SEED = 123456789 Final random number SEED = 379008056 Data written to file "uniform_in_sector_map.txt". UNIFORM_IN_SIMPLEX01_MAP_TEST 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 file "uniform_in_simplex01_map.txt". UNIFORM_IN_SPHERE01_MAP_TEST 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 file "uniform_in_sphere01_map.txt". UNIFORM_IN_TETRAHEDRON_TEST UNIFORM_IN_TETRAHEDRON returns uniform points from a tetrahedron. Spatial dimension DIM_NUM = 3 Number of points N = 1000 Initial random number SEED = 123456789 Tetrahedron vertices: Col: 0 1 2 3 Row 0: 1 4 2 3 1: 2 1 4 2 2: 3 2 4 5 Final random number SEED = 70876380 Data written to file "uniform_in_tetrahedron.txt". UNIFORM_IN_TRIANGLE_MAP1_TEST UNIFORM_IN_TRIANGLE_MAP1 maps uniform points into a triangle, by Turk 1 mapping. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.75, 0.9 V2 = 0, 0.2 V3 = 0.95, 0.65 Final random number SEED = 1328042058 Data written to file "uniform_in_triangle_map1.txt". UNIFORM_IN_TRIANGLE_MAP2_TEST UNIFORM_IN_TRIANGLE_MAP2 maps uniform points into a triangle, by Turk 2 mapping. Spatial dimension DIM_NUM = 2 Number of points N = 1000 Initial random number SEED = 123456789 V1 = 0.75, 0.9 V2 = 0, 0.2 V3 = 0.95, 0.65 Final random number SEED = 1328042058 Data written to file "uniform_in_triangle_map2.txt". UNIFORM_IN_TRIANGLE01_MAP_TEST 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 file "uniform_in_triangle01_map.txt". UNIFORM_ON_CUBE01_TEST UNIFORM_ON_CUBE01 samples N uniform points on the surface of the unit M-dimensional cube. Spatial dimension M = 2 Number of points N = 200 Initial random number SEED = 123456789 Final random number SEED = 818450921 Data written to file "uniform_on_cube01.txt". UNIFORM_ON_ELLIPSOID_MAP_TEST UNIFORM_ON_ELLIPSOID_MAP maps uniform points onto an ellipsoid. Spatial dimension DIM_NUM = 2 Number of points N = 200 Initial random number SEED = 123456789 Final random number SEED = 1349476249 Data written to file "uniform_on_ellipsoid_map.txt". UNIFORM_ON_HEMISPHERE01_PHONG_TEST 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 file "uniform_on_hemisphere01_phong.txt". UNIFORM_ON_SIMPLEX01_MAP_TEST 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 file "uniform_on_simplex01_map.txt". UNIFORM_ON_SPHERE01_MAP_TEST 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 = 873654221 Data written to file "uniform_on_sphere01_map.txt". UNIFORM_ON_SPHERE01_PATCH_TP_TEST UNIFORM_ON_SPHERE01_PATCH_TP maps uniform points onto a TP (THETA,PHI) patch of the unit sphere. Spatial dimension DIM_NUM = 3 Data dimension = 2 Number of points N = 50 Latitudinal angle PHI1 = 1.309 Latitudinal angle PHI2 = 1.5708 Longitudinal angle THETA1 = 0 Longitudinal angle THETA2 = 0.261799 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to file "uniform_on_sphere01_patch_tp.txt". UNIFORM_ON_SPHERE01_PATCH_XYZ_TEST 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 = 1.309 Latitudinal angle PHI2 = 1.5708 Longitudinal angle THETA1 = 0 Longitudinal angle THETA2 = 0.261799 Initial random number SEED = 123456789 Final random number SEED = 873654221 Data written to file "uniform_on_sphere01_patch_xyz.txt". UNIFORM_ON_SPHERE01_TRIANGLE_XYZ_TEST 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: (0.915568,-0.257797,-0.308668) V2: (0.660845,0.291505,0.691599) V3: (-0.495992,-0.555276,-0.667578) Final random number SEED = 9968847 Data written to file "uniform_on_sphere01_triangle_xyz.txt". UNIFORM_WALK_TEST: UNIFORM_WALK generates uniform random walk points. Spatial dimension DIM_NUM = 2 Number of points N = 400 Initial random number SEED = 123456789 Final random number SEED = 1252896212 Data written to file "uniform_walk.txt". RANDOM_DATA_TEST Normal end of execution. 03 March 2022 09:38:51 PM