TABLE_QUALITY
Interactive Program for
Point Dispersion Quality

TABLE_QUALITY is a FORTRAN90 program which reads a data file containing the coordinates of N points in an M dimensional region, and computes some measures of the quality of dispersion of the points.

The program assumes that the pointset lies in the unit hypercube. However, it is easy to modify the program to handle other regions. A single routine, named sample_routine, is required to return sample points in the region. To handle a different region, simply modify this routine, and rebuild the program. One other built-in routine is already available, for sampling the unit sphere.

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 quality measures computed include:

• Beta, the standard deviation of the minimum spacing between nodes, normalized by the average spacing;
• Chi, the regularity measure;
• D, the second moment determinant measure;
• E, the Voronoi energy measure;
• Gamma, the mesh ratio;
• H, the point distribution norm;
• Lambda, the COV measure;
• Mu, the point distribution ratio;
• Nu, the cell volume deviation;
• R0, the Riesz S=0 energy;
• S, the sphere volume measure (unit hypercube datasets only).
• Tau, the second moment trace measure;

The program also prints:

• Gamma_min, the minimum spacing between nodes;
• Gamma_ave, the average spacing between nodes;
• Gamma_max, the maximum spacing between nodes;
• Gamma_std, the standard deviation of the spacing between nodes;

Usage:

table_quality filename

reads the pointset coordinates from filename and computes the quality.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

QUALITY is a FORTRAN90 library which supplies the routines that compute the quality measures needed by TABLE_QUALITY.

TABLE is the data format which is used for the input to this program.

TABLE_BARPLOT_PPMA is a FORTRAN90 program which reads a table file and creates a PPMA bargraph of the data.

TABLE_BORDER is a FORTRAN90 program which can be used to add a border (of zero values) to a table file.

TABLE_COLUMNS is a FORTRAN90 program which can extract specific columns of data from a table file.

TABLE_COLUMNS_PERMUTE is a FORTRAN90 program which permutes the columns of a table file.

TABLE_DELAUNAY is a FORTRAN90 program which computes the Delaunay triangulation of a set of points.

TABLE_DIAPHONY is a FORTRAN90 program which computes the diaphony of a set of points stored in a table file.

TABLE_HISTOGRAM is a FORTRAN90 program which can make a histogram of a set of points stored in a table file.

TABLE_IO is a FORTRAN90 library which supplies the routines used to read the TABLE file.

TABLE_LATINIZE is a FORTRAN90 program which reads a file of points and creates a "latinized" version by adjusting the data.

TABLE_MERGE is a FORTRAN90 program which reads a file of points, and removes duplicates, and points that are close to each other.

TABLE_ORTHONORMALIZE is a FORTRAN90 program which reads a file of points and orthonormalizes the columns.

TABLE_QUALITY is available in a C++ version and a FORTRAN90 version and a MATLAB version.

TABLE_READ is a MATLAB program which can read in a TABLE file.

TABLE_RECORD_MATCH is a FORTRAN90 program which can be used to find close records in a table file.

TABLE_SCALE is a FORTRAN90 program which can be used to multiply the entries of a table file by a scale vector.

TABLE_SHIFT is a FORTRAN90 program which can be used to shift the entries of a table file by a shift vector.

TABLE_STATS is a FORTRAN90 program which can read a table file and compute certain statistics.

TABLE_TET_MESH is a FORTRAN90 program which can read a table file of 3D data, and compute a tetrahedral mesh.

TABLE_TOP is a FORTRAN90 program which can read a table file of M-dimensional data and make a table of plots of all pairs of coordinates.

TABLE_UNBORDER is a FORTRAN90 program which can be used to remove the border from a table file.

TABLE_UNIFORM_NOISE is a FORTRAN90 program which can be used to add a uniform noise term to the data in a table file.

TABLE_VORONOI is a FORTRAN90 program which can be used to compute information about the Voronoi diagram of the points.

TRIANGULATION_QUALITY is a FORTRAN90 program which can evaluate a triangulation of a given set of nodes.

Reference:

1. David Field,
   Qualitative Measures for Initial Meshes,
   International Journal of Numerical Methods in Engineering,
   Volume 47, 2000, pages 887-906.
2. Max Gunzburger,
   Uniformity Measures for Point Samples in Hypercubes,
   PDF version.
3. Douglas Hardin and Edward Saff,
   Discretizing Manifolds via Minimum Energy Points,
   Notices of the AMS,
   Volume 51, Number 10, November 2004, pages 1186-1194.
4. Per-Olof Persson and Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, pages 329-345, June 2004.

Source Code:

• table_quality.f90, the source code.
• table_quality.csh, commands to compile, link and load the source code.

Examples and Tests:

• cvt_02_00100.txt, a set of 100 CVT points in 2D.
• cvt_02_00100_quality.txt, the quality analysis.
• cvt_07_00010.txt, a set of 10 CVT points in 7D.
• cvt_07_00010_quality.txt, the quality analysis.
• halton_02_00100.txt, a set of 100 Halton points in 2D.
• halton_02_00100_quality.txt, the quality analysis.
• degen_02_00130.txt, a set of 130 points in 2D, which involve a degenerate triangulation.
• degen_02_00130_quality.txt, the quality analysis.

List of Routines:

• MAIN is the main program for TABLE_QUALITY.
• SAMPLE_ROUTINE returns sample points in the user's region.

You can go up one level to the FORTRAN90 source codes.