NIEDERREITER2_DATASET
Create a Niederreiter Dataset, Base = 2.

NIEDERREITER2_DATASET is a C++ program which creates a Niederreiter quasirandom dataset with base 2.

Usage:

niederreiter2_dataset m n skip

• m is the spatial dimension;
• n is the number of points to generate;
• skip is the number of initial values to skip. A recommended value is 4096.

Licensing:

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

Languages:

NIEDERREITER2_DATASET is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FAURE_DATASET, a C++ program which creates a Faure quasirandom dataset;

GRID_DATASET, a C++ program which creates a grid sequence and writes it to a file.

LATIN_CENTER_DATASET, a C++ program which creates a Latin Center Hypercube dataset;

LATIN_EDGE_DATASET, a C++ program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM_DATASET, a C++ program which creates a Latin Random Hypercube dataset;

NIEDERREITER2, a C++ library which computes the elements of the sequence. A compiled version of that library must be available to build NIEDERREITER2_DATASET.

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

NORMAL_DATASET, a C++ program which generates a dataset of multivariate normal pseudorandom values and writes them to a file.

SOBOL_DATASET, a C++ program which computes a Sobol quasirandom sequence and writes it to a file.

UNIFORM_DATASET, a C++ program which generates a dataset of multivariate uniform pseudorandom values and writes them to a file.

VAN_DER_CORPUT_DATASET, a C++ program which creates a van der Corput quasirandom sequence and writes it to a file.

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.cpp, the source code.

List of Routines:

• MAIN is the main program for NIEDERREITER2_DATASET.
• CALCC2 computes values of the constants C(I,J,R).
• CALCV2 calculates the value of the constants V(J,R).
• I4_POWER returns the value of I^J.
• NIEDERREITER2 returns an element of the Niederreiter sequence base 2.
• NIEDERREITER2_GENERATE generates a set of Niederreiter values.
• PLYMUL2 multiplies two polynomials in the field of order 2
• R8MAT_WRITE writes an R8MAT file.
• SETFLD2 sets up arithmetic tables for the finite field of order 2.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.