NIEDERREITER2_DATASET
Create a Niederreiter Dataset, Base = 2.

NIEDERREITER2_DATASET is a FORTRAN90 program, using single precision arithmetic, which creates a Niederreiter quasirandom dataset with base 2.

The program is interactive, and allows the user to choose

• M, the spatial dimension;
• N, the number of points to generate;
• SKIP, the initial number of points to skip over;

A nonzero value of SKIP can be used to allow the sequence to "warm up". A recommended value is 2**12 = 4096.

Related Data and Programs:

NIEDERREITER2 is a FORTRAN90 library of routines which compute the elements of the sequence. A compiled version of that library must be available to build NIEDERREITER2_DATASET.

NIEDERREITER2 is a dataset directory which contains examples of the files created by NIEDERREITER2_DATASET.

TABLE is a file format which is used for the output files.

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

Reference:

1. Paul Bratley, Bennett Fox,
   Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator,
   ACM Transactions on Mathematical Software,
   Volume 14, Number 1, pages 88-100, 1988.
2. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Algorithm 738: Programs to Generate Niederreiter's Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 20, Number 4, pages 494-495, 1994.
3. 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.
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.
5. Rudolf Lidl, Harald Niederreiter,
   Finite Fields,
   Cambridge University Press, 1984, page 553.
6. Harald Niederreiter,
   Low-discrepancy and low-dispersion sequences,
   Journal of Number Theory,
   Volume 30, 1988, pages 51-70.
7. Harald Niederreiter,
   Random Number Generation and quasi-Monte Carlo Methods,
   SIAM, 1992.

Source Code:

• niederreiter2_dataset.f90, the source code.
• niederreiter2_dataset.csh, commands to compile the source code.

List of Routines:

• MAIN is the main program for NIEDERREITER2_DATASET.

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