IHS
Improved Distributed Hypercube Sampling Datasets

IHS is a collection of datasets of points generated by the M-dimensional Improved Distributed Hypercube Sampling process.

A Latin hypercube, 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 J-th coordinate of the I-th point can be constructed by choosing, in the J-th dimension, an interval that has not been used, and then choosing any value in that interval.

This algorithm differs in that it tries to pick a solution which has the property that the points are "spread out" as evenly as possible. It does this by determining an optimal even spacing, and using the duplication factor D to allow it to choose the best of the various options available to it (the more duplication, the better chance of optimization).

The IHS algorithm, at least as currently programmed, uses time that is quadratic in the number of points. This means that, for large N, it is much slower than most quasirandom sequence methods. In particular, while comparable sets for other sequences were computed in a couple minutes at most, the dataset ihs_02_01000.txt took almost an hour, the dataset ihs_02_10000.txt took about a day, and the dataset ihs_07_10000.txt took three days to compute.

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

• M, the spatial dimension;
• N, the number of points to generate;
• D, the duplication factor, which controls how many "chances" the algorithm has to find good candidates;
• SEED, the initial value of the seed used for UNIFORM, a portable uniform random number generator;

Related Data and Programs:

IHS_DATASET is an interactive program used to generate these datasets. The program is available in a C++ version, and a FORTRAN90 version, and a MATLAB version,

PLOT_POINTS is a FORTRAN90 program which can create Encapsulated PostScript images (EPS) of some of the two dimensional datasets.

TABLE is a file format which is used to store the data.

TABLE_TOP is a graphics program which can display pairwise coordinate plots of higher dimensional datasets.

Example dataset:

A typical (but small) dataset looks like this:

#  ihs_02_00010.txt
#  created by IHS_DATASET.
#
#  File generated on April  2 2003   8:44:23.798 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Duplication factor D =      5
#  Initial seed for UNIFORM =    123456789
#
  0.950000  0.850000
  0.850000  0.150000
  0.750000  0.450000
  0.650000  0.750000
  0.550000  0.050000
  0.450000  0.350000
  0.150000  0.250000
  0.050000  0.550000
  0.350000  0.650000
  0.250000  0.950000
      

Reference:

1. Brian Beachkofski, Ramana Grandhi,
   Improved Distributed Hypercube Sampling,
   American Institute of Aeronautics and Astronautics Paper 2002-1274.

Datasets:

Datasets in M = 2 dimensions include:

• ihs_02_00010.txt, M = 2, N = 10, D = 5, SEED = 123456789;
• ihs_02_00010.png, a PNG image of the dataset;
• ihs_02_00100.txt, M = 2, N = 100, D = 5, SEED = 123456789;
• ihs_02_00100.png, a PNG image of the dataset;
• ihs_02_01000.txt, M = 2, N = 1000, D = 5, SEED = 123456789;
• ihs_02_01000.png, a PNG image of the dataset;
• ihs_02_10000.txt, M = 2, N = 10000, D = 5, SEED = 123456789;

A second family of datasets in M = 2 dimensions, using a seed of 987654321, includes:

• ihs_02_00010_a.txt, M = 2, N = 10, D = 5, SEED = 987654321;
• ihs_02_00100_a.txt, M = 2, N = 100, D = 5, SEED = 987654321;
• ihs_02_01000_a.txt, M = 2, N = 1000, D = 5, SEED = 987654321;
• ihs_02_10000_a.txt, M = 2, N = 10000, D = 5, SEED = 987654321;

Datasets in M = 7 dimensions include:

• ihs_07_00010.txt, M = 7, N = 10, D = 5, SEED = 123456789;
• ihs_07_00100.txt, M = 7, N = 100, D = 5, SEED = 123456789;
• ihs_07_01000.txt, M = 7, N = 1000, D = 5, SEED = 123456789;
• ihs_07_10000.txt, M = 7, N = 10000, D = 5, SEED = 123456789;

A second family of datasets in M = 7 dimensions, using a seed of 987654321, includes:

• ihs_07_00010_a.txt, M = 7, N = 10, D = 5, SEED = 987654321;
• ihs_07_00100_a.txt, M = 7, N = 100, D = 5, SEED = 987654321;
• ihs_07_01000_a.txt, M = 7, N = 1000, D = 5, SEED = 987654321;

Datasets in M = 16 dimensions include:

• ihs_16_00010.txt, M = 16, N = 10, D = 5, SEED = 123456789;
• ihs_16_00100.txt, M = 16, N = 100, D = 5, SEED = 123456789;
• ihs_16_01000.txt, M = 16, N = 1000, D = 5, SEED = 123456789;
• ihs_16_10000.txt, M = 16, N = 10000, D = 5, SEED = 123456789;

A second family of datasets in M = 16 dimensions, using a seed of 987654321, includes:

• ihs_16_00010_a.txt, M = 16, N = 10, D = 5, SEED = 987654321;
• ihs_16_00100_a.txt, M = 16, N = 100, D = 5, SEED = 987654321;
• ihs_16_01000_a.txt, M = 16, N = 1000, D = 5, SEED = 987654321;

You can go up one level to the DATASETS directory.