LATIN_EDGE
Latin Edge Squares in M dimensions

LATIN_EDGE is a C++ library which makes Latin Edge Squares.

A Latin square is a selection of one point from each row and column of a square matrix or table. In M dimensions, the corresponding item is a set of N points, where, in each dimension, there is exactly one point whose coordinates are in a given "column" or range of values. To emphasize the use of higher dimensions, these objects are sometimes called Latin hypersquares.

Once a Latin square has been selected, the center of each subsquare is chosen to yield a Latin Edge Square dataset. This is the same technique that yields a Latin Center Square dataset, with the difference that the mapping from the Latin Square to the unit square is shifted in such a way that the lowest and highest possible coordinate values are 0.0 and 1.0, instead of 1/(2*N) and (2*N-1)/(2*N).

Here is an image of a Latin edge grid with spatial dimension M = 2 and number of points N = 10.

Licensing:

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

Languages:

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

Related Data and Programs:

BOX_BEHNKEN, a C++ library which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;

CVT, a C++ library which computes points in a Centroidal Voronoi Tessellation.

FAURE, a C++ library which computes Faure sequences.

GRID, a C++ library which computes points on a grid.

HALTON, a C++ library which computes Halton sequences.

HAMMERSLEY, a C++ library which computes Hammersley sequences.

HEX_GRID, a C++ library which computes sets of points in a 2D hexagonal grid.

IHS, a C++ library which computes improved Latin Hypercube datasets.

LATIN_CENTER, a C++ library which computes Latin square data choosing the center value.

LATIN_COVER, a C++ library which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube.

LATIN_EDGE_DATASET, a C++ program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM, a C++ library which computes Latin square data choosing a random value in the square.

NIEDERREITER2, a C++ library which computes Niederreiter sequences with base 2.

NORMAL, a C++ library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL, a C++ library which computes Sobol sequences.

UNIFORM, a C++ library which computes uniform random values.

VAN_DER_CORPUT, a C++ library which computes van der Corput sequences.

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
2. C J Colbourn, J H 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. 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.
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.cpp, the source code.
• latin_edge.hpp, the include file.
• latin_edge.sh, commands to compile the source code.

Examples and Tests:

• latin_edge_prb.cpp, a sample calling program.
• latin_edge_prb.sh, commands to compile and run the sample program.
• latin_edge_prb_output.txt, the output file.

List of Routines:

• GET_SEED returns a random seed for the random number generator.
• I4_RANDOM returns a random integer in a given range.
• I4_SWAP switches two integer values.
• LATIN_EDGE returns edge points in a Latin square.
• PERM_RANDOM selects a random permutation of N objects.
• R8_UNIFORM_01 is a portable pseudorandom number generator.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.