TABLE_LATINIZE
Force a Dataset to be a Latin Hypercube

TABLE_LATINIZE is a FORTRAN90 program which allows the user to specify a file of data to be read in and adjusted to form a Latin hypercube.

The data in the file represents N points in M-dimensional space.

The algorithm is actually very simple. In each spatial dimension, the point coordinates are sorted, and then replaced by the appropriate values for a Latin hypercube. In particular, if there are four points, then in every coordinate, the four points will be assigned values of 1/8, 3/8, 5/8 and 7/8 (in some order). The hope is that if the initial dataset has some nice dispersion property, then the resulting adjusted dataset will inherit some of this dispersion as well; in particular, more dispersion than typically seen in an arbitrary Latin hypercube.

Usage:

table_latinize file.txt

reads the user's data file file.txt and writes a "latinized" version which will be called file.latin.txt.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TABLE_LATINIZE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LATINIZE, a FORTRAN90 library which supplies the routines that calculate the Latinized data needed by TABLE_LATINIZE.

TABLE_IO, a FORTRAN90 library which supplies the routines used to read the TABLE file.

TABLE_QUALITY, a FORTRAN90 program which reads a file of points and computes the quality of dispersion.

Reference:

1. Michael McKay, William Conover, Richard 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.
2. Yuki Saka, Max Gunzburger, John Burkardt,
   Latinized, Improved LHS, and CVT Point Sets in Hypercubes,
   International Journal of Numerical Analysis and Modeling,
   Volume 4, Number 3-4, 2007, pages 729-743,

Source Code:

• table_latinize.f90, the source code.

Examples and Tests:

CVT_02_00010 is a set of 10 CVT points in 2D:

• cvt_02_00010.txt, the original set of 10 points in 2D.
• cvt_02_00010.png, a PNG image of the points.
• cvt_02_00010.latin.txt, the latinized version of the dataset.
• cvt_02_00010.latin.png, a PNG image of the latinized points.

CVT_03_00007 is a set of 7 CVT points in 3D:

• cvt_03_00007.txt, 7 points in 3D.
• cvt_03_00007.latin.txt, the latinized version of the dataset.
• cvt_03_00007.out, the printed output from the command "latinize cvt_03_00007.txt".

CVT_03_00056 is a set of 56 CVT points in 3D:

• cvt_03_00056.txt, 56 points in 3D.
• cvt_03_00056.latin.txt, the latinized version of the dataset.

CVT_07_00100 is a set of 100 CVT points in 7D:

• cvt_07_00100.txt, 100 points in 7D.
• cvt_07_00100.latin.txt, the latinized version of the dataset.

List of Routines:

• MAIN is the main program for TABLE_LATINIZE.

You can go up one level to the FORTRAN90 source codes.