HAMMERSLEY_DATASET
Generate Hammersley Datasets

HAMMERSLEY_DATASET is a FORTRAN90 program, using double precision arithmetic, which creates a Hammersley dataset and writes it to a file.

The program is interactive, and allows the user to choose the parameters that define the sequence.

The program applies the user's data to select elements of a "leaped" subsequence of the Hammersley sequence. The subsequence elements are indexed by a quantity called STEP, which starts at 0. The STEP-th subsequence element is simply the Hammersley sequence element with index

        SEED(1:NDIM) + STEP * LEAP(1:NDIM).
      

The data that the user may set include:

• NDIM, the spatial dimension,
  default: NDIM = 1,
  required: 1 <= NDIM;
• N, the number of entries of the subsequence to compute,
  required: 1 <= N;
• STEP, the subsequence index of the first entry to compute,
  default: STEP = 0,
  required: 0 <= STEP.
• SEED(1:NDIM), the sequence index corresponding to STEP = 0.
  default: SEED(1:NDIM) = (0, 0, ... 0),
  required: 0 <= SEED(1:NDIM);
• LEAP(1:NDIM), the succesive jumps in the sequence.
  default: LEAP(1:NDIM) = (1, 1, ..., 1).
  required: 1 <= LEAP(1:NDIM).
• BASE(1:NDIM), the Hammersley bases.
  default: BASE(1:NDIM) = (2, 3, 5, 7, 11... ), or
  (-N, 2, 3, 5, 7, 11,...) if N is known.
  required: 1 < BASE(I) for any van der Corput dimension I, or BASE(I) < 0 to generate the fractional sequence J/|BASE(I)|.

Once these parameters are set, the program generates the data, and writes it to a file. The user may then specify another set of data, or terminate the program.

Related Data and Programs:

HAMMERSLEY is a FORTRAN90 library which contains routines which compute elements of a Hammersley sequence. A compiled version of this library is necessary in order to build HAMMERSLEY_DATASET.

The HAMMERSLEY dataset directory contains examples of files created by HAMMERSLEY_DATASET.

HAMMERSLEY_DATASET is also available in a C++ version and a MATLAB version.

The TABLE format is used for the output files created by HAMMERSLEY_DATASET.

TABLE_DISCREPANCY is a 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. John Hammersley,
   Monte Carlo methods for solving multivariable problems,
   Proceedings of the New York Academy of Science,
   Volume 86, 1960, pages 844-874.
2. Ladislav Kocis, William Whiten,
   Computational Investigations of Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 23, Number 2, 1997, pages 266-294.

Source Code:

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

Examples and Tests:

• hammersley_dataset_input.txt, is a simple input file for creation of sequences of dimension 2, 3 and 7.
• hammersley_dataset_output.txt, is the printed output from a run of the program with the input file.
• hammersley_02_00020.txt, a leaped Hammersley subsequence dataset with NDIM = 2 and N = 20.
• hammersley_03_00010.txt, a leaped Hammersley subsequence dataset with NDIM = 3 and N = 10.
• hammersley_07_00010.txt, a leaped Hammersley subsequence dataset with NDIM = 7 and N = 10.

List of Routines:

• MAIN is the main program for HAMMERSLEY_DATASET.

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