# IHS Improved Distributed Hypercube Sampling Datasets

IHS is a dataset directory which contains 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.

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;
The values of M, N, D and SEED are specified as part of the dataset file names.

### Related Data and Programs:

IHS, a C++ library which computes an Improved Hypercube Sampling (IHS) quasirandom sequence;

IHS_DATASET, a C++ program which creates an improved distributed Latin Hypercube dataset and writes it to a file.

### Example dataset:

A typical (but small) dataset looks like this:

```      0.75        0.25
0.35        0.05
0.05        0.35
0.95        0.85
0.65        0.15
0.85        0.55
0.55        0.45
0.45        0.75
0.15        0.65
0.25        0.95
```

### Reference:

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

### Datasets:

You can go up one level to the DATASETS directory.

Last revised on 04 November 2014.