01-Jun-2023 18:08:27 random_data_test(): MATLAB/Octave version 5.2.0 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: 4.00000 1.00000 1.00000 0.50000 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 = 0.29623518 -0.62163374 0.03885297 -0.06489149 -0.12713802 0.50567383 -0.03686592 0.03496010 0.28409766 -0.19804922 0.17314504 0.13117508 -0.25048540 0.56349008 -0.16771860 0.50298694 0.29323634 -0.30766179 0.30026886 -0.26222230 -0.24639317 -0.03369071 -0.22986827 -0.01777126 0.07920072 0.34733250 0.29330011 -0.26830254 -0.06899019 0.00187428 0.14376596 0.22067761 -0.04434618 0.18511718 -0.07674474 -0.20001592 0.08560399 0.27523852 -0.06310793 -0.37905526 -0.33516412 0.45975011 0.24020380 -0.07746150 -0.39285396 0.50300343 0.11350683 0.27130860 0.16119012 0.16983849 0.06019714 -0.44286456 0.16364915 -0.46957430 0.34682125 -0.31312022 -0.33922700 0.28212216 0.25796247 -0.42935420 -0.37143578 0.51449339 0.11632049 -0.04221870 -0.07653018 0.50836335 0.24984412 -0.24969378 0.07996928 -0.20262523 0.10203170 -0.21186501 0.23843561 -0.59091485 -0.08970985 0.14816604 -0.17922530 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-0.10511776 -0.26678116 0.33162153 0.04464424 0.17464847 0.06205531 -0.16175798 0.21490347 0.16620832 0.34973876 -0.20385083 -0.06802090 -0.04610970 0.20001264 0.06045864 0.02972217 -0.30066350 -0.06313205 -0.22110156 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: 0.00000 0.00000 0.50000 0.30000 1.00000 0.00000 0.70000 0.40000 1.00000 0.60000 0.60000 0.60000 0.50000 1.00000 0.40000 0.60000 0.00000 0.60000 0.30000 0.40000 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. 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_test(): uniform_on_sphere_patch(): maps uniform points onto a 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.png". uniform_on_sphere_triangle_test(): uniform_on_sphere_triangle() 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.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. 01-Jun-2023 18:08:34