FAURE_DATASET
Generate Datasets
of Faure Quasirandom Sequences

FAURE_DATASET is a FORTRAN90 program, using double precision arithmetic, which creates a Faure Quasirandom sequence and writes it to a file.

The program is interactive, and allows the user to choose

• M, the spatial dimension (this implicitly determines BASE, which is the smallest prime number greater than or equal to M);
• N, the number of points to generate;
• SKIP, the initial number of points to skip over;

The value of SKIP may be set nonzero in order to allow the sequence to "warm up". A recommended value is (BASE**4)-1.

Related Data and Programs:

FAURE is a dataset directory which contains examples of the datasets created by FAURE_DATASET.

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

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

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

Reference:

1. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Implementation and Tests of Low Discrepancy Sequences,
   ACM Transactions on Modeling and Computer Simulation,
   Volume 2, Number 3, pages 195-213, 1992.
2. Henri Faure,
   Discrepance de suites associees a un systeme de numeration (en dimension s),
   Acta Arithmetica,
   Volume XLI, 1982, pages 337-351, especially page 342.
3. Henri Faure,
   Good permutations for extreme discrepancy,
   Journal of Number Theory,
   Volume 42, 1992, pages 47-56.
4. 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.

Source Code:

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

List of Routines:

• MAIN is the main program for FAURE_DATASET.

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