FAURE_DATASET
Generate Datasets
of Faure Quasirandom Sequences

FAURE_DATASET is a FORTRAN90 program which creates a Faure quasirandom sequence and writes it to a file.

Usage:

faure_dataset m n skip

• m is the spatial dimension. This implicitly determines base, which is the smallest prime number greater than or equal to m;
• n is the number of points to generate;
• skip is the initial number of points to skip over. The recommended value of skip is base^4-1.

Licensing:

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

Languages:

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

Related Data and Programs:

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

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

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

LATIN_RANDOM_DATASET, a FORTRAN90 program which creates a Latin Random Hypercube 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, 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.

List of Routines:

• MAIN is the main program for FAURE_DATASET.
• BINOMIAL_TABLE computes a table of bionomial coefficients MOD QS.
• FAURE generates a new quasirandom Faure vector with each call.
• FAURE_GENERATE generates a Faure dataset.
• GET_UNIT returns a free FORTRAN unit number.
• I4_LOG_I4 returns the logarithm of an I4 to an I4 base.
• PRIME_GE returns the smallest prime greater than or equal to N.
• PRIME returns any of the first PRIME_MAX prime numbers.
• R8MAT_WRITE writes an R8MAT file.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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