LATIN_RANDOM
Latin Random Squares in M dimensions

LATIN_RANDOM is a library of FORTRAN90 routines, using double precision arithmetic, for making Latin random 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.

A Latin Random Square (I just made up this name) is a set of N points, where one point is taken at random from each of the subsquares of a Latin Square. These points may be regarded as an M dimensional quasirandom pointset.

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

Related Data and Programs:

CVT is a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a FORTRAN90 library which computes elements of a Faure quasirandom sequence.

GRID is a FORTRAN90 library which computes elements of a grid dataset.

HALTON is a FORTRAN90 library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a FORTRAN90 library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a FORTRAN90 library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS is a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is also available in a C++ version and a MATLAB version.

LATIN_RANDOM is a dataset directory which contains a number of examples of datasets created by LATIN_RANDOM.

LCVT is a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a FORTRAN90 library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a FORTRAN90 library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL is a FORTRAN90 library which computes elements of a Sobol quasirandom sequence.

UNIFORM is a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT is a FORTRAN90 library which computes elements of a van der Corput quasirandom sequence.

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
2. C J Colbourn and 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. 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.f90, the source code.
• latin_random.csh, commands to compile the source code.

Examples and Tests:

• latin_random_prb.f90, a sample calling program.
• latin_random_prb.csh, commands to compile and run the sample program.
• latin_random_prb.out, the output from a run of the sample program.
• latin_random.txt, the coordinates of a dataset created by the program;

List of Routines:

• GET_SEED returns a seed for the random number generator.
• GET_UNIT returns a free FORTRAN unit number.
• I4_SWAP swaps two integer values.
• I4_UNIFORM returns a pseudorandom I4.
• LATIN_RANDOM returns points in a Latin Random square.
• LATIN_RANDOM_WRITE writes a Latin Random Square dataset to a file.
• PERM_RANDOM selects a random permutation of N objects.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• RANDOM_INITIALIZE initializes the FORTRAN 90 random number seed.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

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