LATIN_EDGE
Latin Edge Datasets

LATIN_EDGE is a collection of datasets of points generated by the M-dimensional Latin Edge 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, but then remap these points to the unit hypercube so that the least coordinate is 0.0 and the greatest is 1.0, we have what we will term a "Latin Edge 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_EDGE is a library which allows a user program to compute a Latin edge dataset. The library is available in a C++ version, and a FORTRAN90 version, and a MATLAB version.

LATIN_EDGE_DATASET is an interactive program which allows a user to define and compute a Latin edge dataset

PLOT_POINTS is a FORTRAN90 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_edge_02_00010.txt
#  created by LATIN_EDGE_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.

Datasets:

Datasets in M = 2 dimensions include:

• latin_edge_02_00010.txt, M = 2, N = 10, SEED = 123456789;
• latin_edge_02_00010.png, a PNG image of the dataset;
• latin_edge_02_00100.txt, M = 2, N = 100, SEED = 123456789;
• latin_edge_02_00100.png, a PNG image of the dataset;
• latin_edge_02_01000.txt, M = 2, N = 1000, SEED = 123456789;
• latin_edge_02_01000.png, a PNG image of the dataset;
• latin_edge_02_10000.txt, M = 2, N = 10000, SEED = 123456789;

Datasets in M = 7 dimensions include:

• latin_edge_07_00010.txt, M = 7, N = 10, SEED = 123456789;
• latin_edge_07_00100.txt, M = 7, N = 100, SEED = 123456789;
• latin_edge_07_01000.txt, M = 7, N = 1000, SEED = 123456789;
• latin_edge_07_10000.txt, M = 7, N = 10000, SEED = 123456789;

Datasets in M = 16 dimensions include:

• latin_edge_16_00010.txt, M = 16, N = 10, SEED = 123456789;
• latin_edge_16_00100.txt, M = 16, N = 100, SEED = 123456789;
• latin_edge_16_01000.txt, M = 16, N = 1000, SEED = 123456789;
• latin_edge_16_10000.txt, M = 16, N = 10000, SEED = 123456789;

You can go up one level to the DATASETS directory.