LCVTP
Latinized CVT Datasets
on a Logical Torus

LCVTP is a dataset directory which contains examples of LCVTP's, that is, Latinized Centroidal Voronoi Tessellations over a periodic domain.

The datasets were created in a two step process. First, the program CVTP_DATASET was used to set up a CVTP dataset on a logical torus. Then the program LATINIZE was used to "latinize" the dataset.

The datasets created on the first step contain N points in M-dimensions, with the points having the property that they are (approximately) the centroids of the Voronoi regions that they generate, in the logical torus geometry. On the second step, the points in the dataset are modified (slightly, one hopes) so that they have the Latin square property.

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:

CVTP, a dataset directory which contains examples of CVTP's, that is, Centroidal Voronoi Tessellations on a periodic domain.

CVTP, a FORTRAN90 library which creates a CVTP, that is, a Centroidal Voronoi Tessellation on a periodic domain.

LATINIZE, a FORTRAN90 program which was used to "latinize" the datasets.

LCVT_DATASET, a FORTRAN90 program which allows a user to define and compute a latinized CVT dataset

PLOT_POINTS, a FORTRAN90 program which can plot two dimensional datasets, making Encapsulated PostScript images.

TABLE_TOP, a FORTRAN90 program which can be used to analyze datasets of any dimension, by creating images of pairwise coordinates.

Example dataset:

A typical (but small) dataset looks like this:

      0.45        0.95  
      0.85        0.55  
      0.65        0.25  
      0.35        0.35  
      0.15        0.75  
      0.25        0.45  
      0.55        0.65  
      0.75        0.85  
      0.95        0.15  
      0.05        0.05  
      

Reference:

1. John Burkardt, Max Gunzburger, Janet Peterson and Rebecca Brannon,
   User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Placement and Associated Zeroth, First, and Second Moment Determination,
   Sandia National Laboratories Technical Report SAND2002-0099,
   February 2002.
2. Qiang Du, Vance Faber, and Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.
3. M D McKay, W J Conover, R J Beckman,
   A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,
   Technometrics,
   Volume 21, pages 239-245, 1979.
4. Herbert Ryser,
   Combinatorial Mathematics,
   Mathematical Association of America, 1963.

Datasets:

The first family of points is in M = 2 dimensions.

• cvtp_02_00010.txt, the original CVTP dataset with N = 10;
• lcvtp_02_00010.txt, the latinized dataset for N = 10;
• lcvtp_02_00010.png
• cvtp_02_00100.txt, the original CVTP dataset with N = 100;
• lcvtp_02_00100.txt, the latinized dataset for N = 100;
• lcvtp_02_00100.png
• cvtp_02_01000.txt, the original CVTP dataset with N = 1000;
• lcvtp_02_01000.txt, the latinized dataset for N = 1000;
• lcvtp_02_01000.png
• cvtp_02_10000.txt, the original CVTP dataset with N = 10000;
• lcvtp_02_10000.txt, the latinized dataset for N = 10000;

The second family of points is in M = 7 dimensions.

• cvtp_07_00010.txt, the original CVTP dataset with N = 10;
• lcvtp_07_00010.txt, the latinized dataset for N = 10;
• cvtp_07_00100.txt, the original CVTP dataset with N = 100;
• lcvtp_07_00100.txt, the latinized dataset for N = 100;
• cvtp_07_01000.txt, the original CVTP dataset with N = 1000;
• lcvtp_07_01000.txt, the latinized dataset for N = 1000;
• cvtp_07_10000.txt, the original CVTP dataset with N = 10000;
• lcvtp_07_10000.txt, the latinized dataset for N = 10000;

The third family of points is in M = 16 dimensions.

• cvtp_16_00010.txt, the original CVTP dataset with N = 10;
• lcvtp_16_00010.txt, the latinized dataset for N = 10;
• cvtp_16_00100.txt, the original CVTP dataset with N = 100;
• lcvtp_16_00100.txt, the latinized dataset for N = 100;
• cvtp_16_01000.txt, the original CVTP dataset with N = 1000;
• lcvtp_16_01000.txt, the latinized dataset for N = 1000;
• cvtp_16_10000.txt, the original CVTP dataset with N = 10000;
• lcvtp_16_10000.txt, the latinized dataset for N = 10000;

You can go up one level to the DATASETS directory.