LCVT_MOD
Latinized CVT Datasets
on a Logical Torus

LCVT_MOD is a collection of datasets of points on a logical torus, generated by an M-dimensional Centroidal Voronoi Tessellation algorithm, and then "latinized".

The datasets were created in a two step process. First, the interactive FORTRAN90 program CVT_MOD_DATASET was used to set up a CVT dataset on a logical torus. Then the interactive FORTRAN90 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.

Related Data and Programs:

CVT_MOD_DATASET was used to in the first step of the creation of these datasets.

LATINIZE was used to "latinize" the datasets.

LCVT_DATASET is an interactive program which allows a user to define and compute a latinized CVT dataset

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

TABLE is a file format used to store the data.

TABLE_TOP is a graphics program that 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:

#  cvt_mod_02_00010.latin.txt
#  created by TABLE_HEADER_WRITE in TABLE_IO.CC
#  at 14 January 2004 02:30:32 PM
#
#  Spatial dimension M = 2
#  Number of points N = 10
#
#  This data was created by the C++ LATINIZE program.
#  The data was read from cvt_mod_02_00010.txt by DTABLE_DATA_READ.C
#  The data was latinized by DTABLE_LATINIZE.C.
#  The data was written to cvt_mod_02_00010.latin.txt by DTABLE_DATA_WRITE.C.
#
      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.
   Online ordering
2. C J Colbourn and J H Dinitz,
   CRC Handbook of Combinatorial Design,
   CRC, 1996.
3. Qiang Du, Vance Faber, and Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.
4. 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.
5. Herbert Ryser,
   Combinatorial Mathematics,
   Mathematical Association of America, 1963.

Datasets:

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

• cvt_mod_02_00010.txt, the original CVT_MOD dataset with N = 10;
• lcvt_mod_02_00010.txt, the latinized dataset for N = 10;
• lcvt_mod_02_00010.png, a PNG image of the dataset;
• cvt_mod_02_00100.txt, the original CVT_MOD dataset with N = 100;
• lcvt_mod_02_00100.txt, the latinized dataset for N = 100;
• lcvt_mod_02_00100.png, a PNG image of the dataset;
• cvt_mod_02_01000.txt, the original CVT_MOD dataset with N = 1000;
• lcvt_mod_02_01000.txt, the latinized dataset for N = 1000;
• lcvt_mod_02_01000.png, a PNG image of the dataset;
• cvt_mod_02_10000.txt, the original CVT_MOD dataset with N = 10000;
• lcvt_mod_02_10000.txt, the latinized dataset for N = 10000;

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

• cvt_mod_07_00010.txt, the original CVT_MOD dataset with N = 10;
• lcvt_mod_07_00010.txt, the latinized dataset for N = 10;
• cvt_mod_07_00100.txt, the original CVT_MOD dataset with N = 100;
• lcvt_mod_07_00100.txt, the latinized dataset for N = 100;
• cvt_mod_07_01000.txt, the original CVT_MOD dataset with N = 1000;
• lcvt_mod_07_01000.txt, the latinized dataset for N = 1000;
• cvt_mod_07_10000.txt, the original CVT_MOD dataset with N = 10000;
• lcvt_mod_07_10000.txt, the latinized dataset for N = 10000;

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

• cvt_mod_16_00010.txt, the original CVT_MOD dataset with N = 10;
• lcvt_mod_16_00010.txt, the latinized dataset for N = 10;
• cvt_mod_16_00100.txt, the original CVT_MOD dataset with N = 100;
• lcvt_mod_16_00100.txt, the latinized dataset for N = 100;
• cvt_mod_16_01000.txt, the original CVT_MOD dataset with N = 1000;
• lcvt_mod_16_01000.txt, the latinized dataset for N = 1000;
• cvt_mod_16_10000.txt, the original CVT_MOD dataset with N = 10000;
• lcvt_mod_16_10000.txt, the latinized dataset for N = 10000;

You can go up one level to the DATASETS directory.