LATIN_RANDOM_DATASET
Generate Latin Random Square Datasets

LATIN_RANDOM_DATASET is a FORTRAN90 library which creates a Latin Random 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.

If we now select at random one point from each subsquare, we have what we will term a "Latin Random Square".

Usage:

latin_random_dataset m n seed

• m is the spatial dimension;
• n is the number of points to generate;
• seed is the initial seed value.

Licensing:

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

Languages:

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

Related Data and Programs:

FAURE_DATASET, a FORTRAN90 program which creates a Faure quasirandom dataset;

GRID_DATASET, a FORTRAN90 program which creates a grid sequence and writes it to a file.

LATIN_CENTER_DATASET, a FORTRAN90 program which creates a Latin Center Hypercube dataset;

LATIN_COVER, a FORTRAN90 library which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube.

LATIN_EDGE_DATASET, a FORTRAN90 program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM, a FORTRAN90 library which contains the computational routines needed by LATIN_RANDOM_DATASET, and a compiled version of that library must be available to build the program.

LATIN_RANDOM, a dataset directory which contains sample datasets created by LATIN_RANDOM_DATASET.

NIEDERREITER2_DATASET, a FORTRAN90 program which creates a Niederreiter quasirandom dataset with base 2;

NORMAL_DATASET, a FORTRAN90 program which generates a dataset of multivariate normal pseudorandom values and writes them to a file.

SOBOL_DATASET, a FORTRAN90 program which computes a Sobol quasirandom sequence and writes it to a file.

UNIFORM_DATASET, a FORTRAN90 program which generates a dataset of multivariate uniform pseudorandom values and writes them to a file.

VAN_DER_CORPUT_DATASET, a FORTRAN90 program which creates a van der Corput quasirandom sequence and writes it to a file.

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_random_dataset.f90, the source code.

Examples and Data:

• latin_random_02_00100.txt, is the file created by the command latin_random_dataset 2 100 12346789.

List of Routines:

• MAIN is the main program for LATIN_RANDOM_DATASET.
• GET_SEED returns a seed for the random number generator.
• GET_UNIT returns a free FORTRAN unit number.
• I4_UNIFORM returns a scaled pseudorandom I4.
• LATIN_RANDOM returns points in a Latin Random Square.
• PERM_UNIFORM selects a random permutation of N objects.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R8MAT_WRITE writes an R8MAT file.
• S_TO_I4 reads an integer value from a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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