LATIN_RANDOM
Latin Random Squares in M dimensions

LATIN_RANDOM is a FORTRAN90 library which makes 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.

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 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LATIN_RANDOM_DATASET, a FORTRAN77 program which computes a Latin Hypercube in M dimensions of N points, randomly placed within their subsquares.

NORMAL, a FORTRAN77 library which computes elements of a sequence of pseudorandom normally distributed values.

UNIFORM, a FORTRAN77 library which computes elements of a uniform pseudorandom 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.sh, commands to compile the source code.

Examples and Tests:

• latin_random_prb.f90, a sample calling program.
• latin_random_prb.sh, commands to compile and run the sample program.
• latin_random_prb_output.txt, 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_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.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8MAT_WRITE writes an R8MAT file.
• RANDOM_INITIALIZE initializes the FORTRAN 90 random number seed.
• 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.