quality, a MATLAB code which computes some measures of the quality of dispersion of a set of N points in an M dimensional region.
The region to be analyzed is defined by a single routine which the user may specify. We will refer to that routine as sample_routine. This routine is simply required to return sample points from the region.
The library includes routines for two simple regions, namely the unit hypercube and the unit hypersphere. If either of these regions is of interest, then the user simply has to pass the appropriate name, either sample_hypercube_uniform or sample_sphere_uniform. For other regions, the user should write the appropriate version of a sampling routine.
The unit hypercube in M dimensional space is simply the set of all vectors whose entries are between 0 and 1. It is a natural abstraction of the unit line segment, the unit square, and the unit cube, and represents a very simple chunk of M dimensional space.
The unit hypersphere in M dimensional space is simply the set of all points whose distance from the origin is 1 or less.
The quality measures computed include:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
quality is available in a C++ version and a FORTRAN90 version and a MATLAB version.
diaphony, a MATLAB code which reads a file of N points in M dimensions and computes its diaphony, a measure of point dispersion.
tet_mesh, a MATLAB code which includes some quality measures for tetrahedral meshes.