LATIN_CENTER
Latin Center Datasets

LATIN_CENTER is a collection of datasets of points generated by the M-dimensional Latin Center Square process.

A Latin square, in M dimensional space, with N points, can be thought of as being constructed by dividing each of the M coordinate dimensions into N equal intervals. The I-th coordinates of the N subsquares are defined by assigning each possible value exactly once to one subsquare. Such a set is called a Latin Square.

If we now select at the center point from each subsquare, we have what we will term a "Latin Center Square".

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 value of the seed used for UNIFORM, a portable uniform random number generator;

Related Data and Programs:

LATIN_CENTER is a library which allows a user program to compute a Latin centered dataset. The library is available in a C++ version, and a FORTRAN90 version, and a MATLAB version.

LATIN_CENTER_DATASET is an interactive program which allows a user to define and compute a Latin center dataset

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

The TABLE data format is used to store the datasets.

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:

#  latin_center_02_00010.txt
#  created by LATIN_CENTER_DATASET.
#
#  File generated on April  8 2003  10:47:39.811 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Initial seed for UNIFORM =    123456789
#
  0.250000  0.050000
  0.950000  0.550000
  0.850000  0.150000
  0.650000  0.850000
  0.350000  0.350000
  0.550000  0.250000
  0.750000  0.950000
  0.450000  0.450000
  0.050000  0.750000
  0.150000  0.650000
      

Reference:

1. C J Colbourn and J H Dinitz,
   CRC Handbook of Combinatorial Design,
   CRC, 1996.
2. 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.
3. Herbert Ryser,
   Combinatorial Mathematics,
   Mathematical Association of America, 1963.

Sample Datasets:

Datasets in M = 2 dimensions include:

• latin_center_02_00010.txt, M = 2, N = 10, SEED = 123456789;
• latin_center_02_00010.png, a PNG image of the dataset;
• latin_center_02_00100.txt, M = 2, N = 100, SEED = 123456789;
• latin_center_02_00100.png, a PNG image of the dataset;
• latin_center_02_01000.txt, M = 2, N = 1000, SEED = 123456789;
• latin_center_02_01000.png, a PNG image of the dataset;
• latin_center_02_10000.txt, M = 2, N = 10000, SEED = 123456789;

Datasets in M = 7 dimensions include:

• latin_center_07_00010.txt, M = 7, N = 10, SEED = 123456789;
• latin_center_07_00100.txt, M = 7, N = 100, SEED = 123456789;
• latin_center_07_01000.txt, M = 7, N = 1000, SEED = 123456789;
• latin_center_07_10000.txt, M = 7, N = 10000, SEED = 123456789;

Datasets in M = 16 dimensions include:

• latin_center_16_00010.txt, M = 16, N = 10, SEED = 123456789;
• latin_center_16_00100.txt, M = 16, N = 100, SEED = 123456789;
• latin_center_16_01000.txt, M = 16, N = 1000, SEED = 123456789;
• latin_center_16_10000.txt, M = 16, N = 10000, SEED = 123456789;

You can go up one level to the DATASETS directory.