# LHS Latin Hypercube Sampling Datasets

LHS is a dataset directory which collects Latin Hypercube Sampling datasets.

The datasets are lists of points. The points have spatial dimension M, and there the number of points in a dataset is denoted by N. Generally, a randomizing technique is used to make choices when creating the dataset, so the initial value of the random number seed, called SEED, may be useful in characterizing the data as well.

The "Latin" property is a generalization of the following idea. It is possible to place 8 rooks on an 8 by 8 chess board in such a way that no rook attacks any other. In that case, there is a rook in every column and every row. We say that the positions of the rooks constitute a Latin square sampling of the chessboard, in the sense that the N = 8 "points" have the property that every row rank and every column rank is "sampled" by exactly one of the points.

To generalize, we allow our sampling space to have an arbitrary dimension M. In the rook example, we only have 8 values to sample, but in general the data covers a range of real values. It is possible to require that the sampling data fall exactly on the midpoints of N equal intervals into which we divide the coordinate range in each dimension. We could also simply required that a sampling point fall somewhere within each of the N equal intervals. Also, we could divide the range into N-1 equal subintervals, and require that the data fall exactly on the endpoints of these subintervals. In this case, the extreme values of the ranges will be guaranteed to be sampled.

### Related Data and Programs:

IHS, a FORTRAN90 library which uses the improved Hypercube Sampling technique.

LATIN_CENTER, a FORTRAN90 library which computes Latin hypercubes using a centered choice.

LATIN_EDGE, a FORTRAN90 library which computes Latin hypercubes using an edge choice.

LATIN_RANDOM, a FORTRAN90 library which computes Latin hypercubes using a random choice.

PLOT_POINTS, a FORTRAN90 program which can make simple plots of the data in the LHS files.

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

### 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:

LATIN_CENTER has dimension M = 2, number of points N = 41, and was created by the LATIN_CENTER library:

LATIN_EDGE has dimension M = 2, number of points N = 41, and was created by the LATIN_EDGE library:

LATIN_RANDOM has dimension M = 2, number of points N = 41, and was created by the LATIN_RANDOM library:

LHS_02_00009_1 has dimension M = 2, number of points N = 9, a random number generator SEED = 123456789, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00009_2 has dimension M = 2, number of points N = 9, a random number generator SEED = 192837465, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00009_3 has dimension M = 2, number of points N = 9, a random number generator SEED = 987654321, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00013_1 has dimension M = 2, number of points N = 13, a random number generator SEED = 123456789, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00013_2 has dimension M = 2, number of points N = 13, a random number generator SEED = 192837465, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00013_3 has dimension M = 2, number of points N = 13, a random number generator SEED = 987654321, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00025_1 has dimension M = 2, number of points N = 25, a random number generator SEED = 123456789, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00025_2 has dimension M = 2, number of points N = 25, a random number generator SEED = 192837465, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00025_3 has dimension M = 2, number of points N = 25, a random number generator SEED = 987654321, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00041_1 has dimension M = 2, number of points N = 41, a random number generator SEED = 123456789, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00041_2 has dimension M = 2, number of points N = 41, a random number generator SEED = 192837465, supplied by Vicente Romero of Sandia National Laboratory:

LHS_02_00041_3 has dimension M = 2, number of points N = 41, a random number generator SEED = 987654321, supplied by Vicente Romero of Sandia National Laboratory:

You can go up one level to the DATASETS directory.

Last revised on 02 November 2005.