LATIN_EDGE_DATASET
Generate Latin Edge Square Datasets

LATIN_EDGE_DATASET is a FORTRAN90 program, using double precision arithmetic, which creates a Latin Edge Square dataset.

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.

Now suppose that, in each spatial coordinate, we label successive squares by the values 0, 1/N-1, 2/N-1, ..., (N-2)/(N-1), 1. Then each element of our Latin Edge dataset is a vector of N such values, and our dataset contains N such vectors.

The program is interactive, and allows the user to choose

• M, the spatial dimension;
• N, the number of points to generate;
• SEED, a seed for UNIFORM, the portable uniform random number generator used to make choices.

Related Data and Programs:

LATIN_EDGE is a FORTRAN90 library of routines which compute the Latin Edge squares requested by LATIN_EDGE_DATASET.

LATIN_EDGE is a dataset directory which contains sample datasets created by LATIN_EDGE_DATASET.

TABLE is a file format which is used for the output files created by LATIN_EDGE_DATASET.

TABLE_DISCREPANCY is a C++ program which can read a TABLE file of points (presumed to lie in the unit hypercube) and compute bounds on the star discrepancy, a measure of dispersion.

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
2. CJ Colbourn, JH Dinitz,
   CRC Handbook of Combinatorial Design,
   CRC, 1996.
3. Bennett Fox,
   Algorithm 647:
   Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, pages 362-376, 1986.
4. 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.
5. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms,
   Academic Press, 1978, second edition,
   ISBN 0-12-519260-6.
6. Herbert Ryser,
   Combinatorial Mathematics,
   Mathematical Association of America, 1963.

Source Code:

• latin_edge_dataset.f90, the source code.
• latin_edge_dataset.csh, commands to compile and load the source code.

List of Routines:

• MAIN is the main program for LATIN_EDGE_DATASET.

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