Mon Apr 25 06:54:20 2022 random_data_test(): Python version: 3.6.9 random_data() samples points in various geometric objects. uniform_in_annulus_test(): uniform_in_annulus() returns uniform random points from inside a circular annulus. Number of points N = 400 Inner radius = 1.0 Outer radius = 3.0 Annulus center = [10. 5.] Graphics saved as "uniform_in_annulus.png" uniform_in_annulus_sector_test(): uniform_in_annulus_sector() returns uniform random points from inside a sector of a circular annulus. Number of points N = 400 Inner radius = 1.0 Outer radius = 3.0 Annulus center = [10. 5.] theta1 = 0.0 theta2 = 1.5707963267948966 Graphics saved as "uniform_in_annulus_sector.png" uniform_in_circle_test(): uniform_in_circle() returns uniform random points inside a unit circle. Number of points N = 400 Graphics saved as "uniform_in_circle.png" uniform_in_ellipse_test(): uniform_in_ellipse() returns uniform random points from inside an ellipse. Number of points N = 400 R = 1.0 matrix A: [[4. 1. ] [1. 0.5]] Graphics saved as "uniform_in_ellipse.png" uniform_in_ellipsoid_test(): uniform_in_ellipsoid() returns uniform random points from inside an ellipsoid xAx <= r^2. Number of points N = 500 R = 1.0 matrix A: [[4. 1. 0. ] [1. 4. 1. ] [0. 1. 0.5]] Graphics saved as "uniform_in_ellipsoid.png" uniform_in_hexagon_test(): uniform_in_hexagon01() returns uniform random points from inside the unit hexagon. Number of points N = 400 Graphics saved as "uniform_in_hexagon.png" uniform_in_hypercube_test(): uniform_in_hypercube() returns uniform random points from inside the unit hypercube in D-space. Number of points N = 800 Space dimension D = 3 Graphics saved as "uniform_in_hypercube.png" uniform_in_hypersphere_test(): uniform_in_hypersphere() returns uniform random points from inside the D-dimensional unit hypersphere. Number of points N = 500 Space dimension D = 3 Graphics saved as "uniform_in_hypersphere.png" uniform_in_parallelogram_test(): uniform_in_parallelogram() returns uniform random points from inside a parallelogram. Number of points N = 200 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. ] [0.5 0.3] [1. 0. ] [0.7 0.4] [1. 0.6] [0.6 0.6] [0.5 1. ] [0.4 0.6] [0. 0.6] [0.3 0.4]] Graphics saved as "uniform_in_polygon.png" uniform_in_sector_test(): uniform_in_sector() returns uniform random points from inside a circular sector. N = 300 R = 2.0 T1 = 0.78 T2 = 2.35 Graphics saved as "uniform_in_sector.png" uniform_in_simplex_test(): uniform_in_simplex() returns uniform random points from inside the unit simplex. Number of points N = 200 Spatial dimension D = 2 Graphics saved as "uniform_in_simplex.png" uniform_in_tetrahedron_test uniform_in_tetrahedron() returns uniform random points from inside an arbitrary tetrahedron. Number of points N = 200 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() returns uniform random points from inside a triangle. Number of points N = 200 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 the surface of 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 the surface of 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() returns uniform random points on the surface of the D-dimensional ellipsoid xAx=r^2. Number of points N = 500 Space dimension D = 3 Radius R = 1.0 Matrix A: [[3. 1. 0.] [1. 2. 1.] [0. 1. 4.]] Graphics saved as "uniform_on_ellipsoid.png" uniform_on_hemisphere_phong_test(): uniform_on_hemisphere_phong() returns uniform random points on the surface of 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() returns uniform random points on the surface of the unit hypercube in D-space. Number of points N = 800 Space dimension D = 3 Graphics saved as "uniform_on_hypercube.png" uniform_on_hypersphere_test(): uniform_on_hypersphere() computes points uniformly distributed on the surface of the unit hypersphere. Number of points N = 200 Space dimension D = 3 Graphics saved as "uniform_on_hypersphere.png" uniform_on_simplex_test(): uniform_on_simplex() returns uniform random points from inside the unit simplex. Number of points N = 200 Spatial dimension D = 2 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. The points are returned as (X,Y,Z) coordinates. Number of points N = 500 Latitudinal angle PHI1 = 1.3962634015954636 Latitudinal angle PHI2 = 1.7453292519943295 Longitudinal angle THETA1 = 0.0 Longitudinal angle THETA2 = 6.283185307179586 Graphics saved as "uniform_on_sphere_patch.png" uniform_on_sphere_triangle_test(): uniform_on_sphere_triangle() maps uniform points onto a triangle of the unit sphere. The points are returned as (X,Y,Z) coordinates. Number of points N = 500 Vertex V1 = [1. 0. 0.] Vertex V2 = [0. 1. 0.] Vertex V3 = [0. 0. 1.] Graphics saved as "uniform_on_sphere_triangle.png" uniform_on_triangle_test(): uniform_in_triangle() returns uniform random points on the surface of a triangle. Number of points N = 100 Triangle vertices: [[0.75 0.9 ] [0. 0.2 ] [0.95 0.65]] 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 = 100 Spatial dimension D = 2 Graphics saved as "uniform_walk.png" random_data_test(): Normal end of execution. Mon Apr 25 06:54:23 2022