LATIN_RANDOM
Latin Random Datasets

LATIN_RANDOM is a dataset directory which contains points generated by the M-dimensional Latin Random 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 random one point from each subsquare, we have what we will term a "Latin Random 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;

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:

LATIN_RANDOM, a C++ library which computes elements of a Latin Hypercube dataset, choosing points at random.

LATIN_RANDOM_DATASET, a FORTRAN90 program which allows a user to define and compute a Latin random dataset

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

TABLE, a data format which is used to store the datasets.

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:

#  latin_random_02_00010.txt
#  created by LATIN_RANDOM_DATASET.
#
#  File generated on March 20 2003  11:43:51.082 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Initial seed for UNIFORM =    123456789
#
  0.821842  0.606173
  0.095632  0.044954
  0.282951  0.840131
  0.356170  0.175467
  0.541531  0.979729
  0.906612  0.700184
  0.625758  0.389750
  0.110996  0.435075
  0.404383  0.209454
  0.763397  0.501362
      

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_random_02_00010.txt, M = 2, N = 10, SEED = 123456789;
• latin_random_02_00010.png, a PNG image of the dataset;
• latin_random_02_00100.txt, M = 2, N = 100, SEED = 123456789;
• latin_random_02_00100.png, a PNG image of the dataset;
• latin_random_02_01000.txt, M = 2, N = 1000, SEED = 123456789;
• latin_random_02_01000.png, a PNG image of the dataset;
• latin_random_02_10000.txt, M = 2, N = 10000, SEED = 123456789;

Datasets in M = 7 dimensions include:

• latin_random_07_00010.txt, M = 7, N = 10, SEED = 123456789;
• latin_random_07_00100.txt, M = 7, N = 100, SEED = 123456789;
• latin_random_07_01000.txt, M = 7, N = 1000, SEED = 123456789;
• latin_random_07_10000.txt, M = 7, N = 10000, SEED = 123456789;

Datasets in M = 16 dimensions include:

• latin_random_16_00010.txt, M = 16, N = 10, SEED = 123456789;
• latin_random_16_00100.txt, M = 16, N = 100, SEED = 123456789;
• latin_random_16_01000.txt, M = 16, N = 1000, SEED = 123456789;
• latin_random_16_10000.txt, M = 16, N = 10000, SEED = 123456789;

You can go up one level to the DATASETS directory.