CVT_MOD
CVT Datasets on a Logical Torus

CVT_MOD is a dataset directory which contains points on a logical torus, generated by an M-dimensional Centroidal Voronoi Tessellation algorithm.

Each dataset contains N points in M-dimensions, with the points having the property that they are (approximately) the centroids of the Voronoi regions that they generate.

The datasets are distinguished by the values of the following parameters:

• M, the spatial dimension;
• N, the number of points to generate;
• SEED, the initial seed for the random number routine;
• INITIALIZE, UNIFORM/HALTON/GRID/FILE, the method of initializing the generators;
• SAMPLE, UNIFORM/HALTON/GRID, the method of sampling the Voronoi diagram;
• SAMPLE_NUM, the number of points used to sample the Voronoi diagram;
• ITERATIONS, the number of CVT iteration steps;

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:

CVT_MOD_DATASET is an interactive FORTRAN90 program which allows a user to define and compute a CVT_MOD dataset.

TABLE is a file format used to store the data.

PLOT_POINTS is a graphics program which was used to make images of some of the 2D datasets.

TABLE_TOP is a graphics program which was used to make pairwise coordinate plots of some of the higher dimensional datasets

Example dataset:

A typical (but small) dataset looks like this:

#  cvt_mod_02_00010.txt
#  created by routine CVT_MOD_WRITE in CVT_MOD_DATASET.F90
#  at December  7 2003  10:24:20.791 AM
#
#  Spatial dimension M =   2
#  Number of points N =     10
#  EPSILON (unit roundoff) =   0.119209E-06
#
#  Initial SEED =    123456789
#
#  Initialization by UNIFORM.
#  Sampling by UNIFORM.
#  Number of sample points =       500000
#  Number of sampling iterations =    100
#  L2 norm of dataset change on last step =   0.001598
#
  0.378753  0.919641
  0.725977  0.572210
  0.551973  0.246525
  0.264802  0.248364
  0.052727  0.745158
  0.057432  0.457647
  0.395623  0.587517
  0.710814  0.904034
  0.839889  0.240473
  0.046507  0.033340
      

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. Qiang Du, Vance Faber, and Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.

Datasets:

There is a family of datasets in M = 2 dimensions. At least for the lower values of N, it is useful to look at plots of this data.

• cvt_mod_02_00010.inp, is the input file to CVT_MOD_DATASET for an N = 10 dataset;
• cvt_mod_02_00010.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_02_00010.txt, is the computed dataset;
• cvt_mod_02_00010.png, a PNG image of the dataset;
• cvt_mod_02_00100.inp, is the input file to CVT_MOD_DATASET for an N = 100 dataset;
• cvt_mod_02_00100.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_02_00100.txt, is the computed dataset;
• cvt_mod_02_00100.png, a PNG image of the dataset;
• cvt_mod_02_01000.inp, is the input file to CVT_MOD_DATASET for an N = 1000 dataset;
• cvt_mod_02_01000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_02_01000.txt, is the computed dataset;
• cvt_mod_02_01000.png, a PNG image of the dataset;
• cvt_mod_02_10000.inp, is the input file to CVT_MOD_DATASET for an N = 10000 dataset;
• cvt_mod_02_10000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_02_10000.txt, is the computed dataset;

There is a family of datasets in M = 7 dimensions.

• cvt_mod_07_00010.inp, is the input file to CVT_MOD_DATASET for an N = 10 dataset;
• cvt_mod_07_00010.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_07_00010.txt, is the computed dataset;
• cvt_mod_07_00100.inp, is the input file to CVT_MOD_DATASET for an N = 100 dataset;
• cvt_mod_07_00100.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_07_00100.txt, is the computed dataset;
• cvt_mod_07_01000.inp, is the input file to CVT_MOD_DATASET for an N = 1000 dataset;
• cvt_mod_07_01000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_07_01000.txt, is the computed dataset;
• cvt_mod_07_10000.inp, is the input file to CVT_MOD_DATASET for an N = 10000 dataset;
• cvt_mod_07_10000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_07_10000.txt, is the computed dataset;

There is a family of datasets in M = 16 dimensions.

• cvt_mod_16_00010.inp, is the input file to CVT_MOD_DATASET for an N = 10 dataset;
• cvt_mod_16_00010.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_16_00010.txt, is the computed dataset;
• cvt_mod_16_00100.inp, is the input file to CVT_MOD_DATASET for an N = 100 dataset;
• cvt_mod_16_00100.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_16_00100.txt, is the computed dataset;
• cvt_mod_16_01000.inp, is the input file to CVT_MOD_DATASET for an N = 1000 dataset;
• cvt_mod_16_01000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_16_01000.txt, is the computed dataset;
• cvt_mod_16_10000.inp, is the input file to CVT_MOD_DATASET for an N = 10000 dataset;
• cvt_mod_16_10000.out, is the printed output file from CVT_MOD_DATASET;
• cvt_mod_16_10000.txt, is the computed dataset;

You can go up one level to the DATASETS directory.