HAMMERSLEY_DATASET
Generate Hammersley Datasets

HAMMERSLEY_DATASET is a MATLAB program 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.

Licensing:

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

Languages:

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

Related Data and Programs:

FAURE_DATASET, a MATLAB program which creates a Faure quasirandom dataset;

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

HAMMERSLEY, a MATLAB library which computes the sequences needed by HAMMERSLEY_DATASET.

HAMMERSLEY, a dataset directory which contains sample datasets created by HAMMERSLEY_DATASET.

LATIN_CENTER_DATASET, a MATLAB program which creates a Latin Center Hypercube dataset;

LATIN_EDGE_DATASET, a MATLAB program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM_DATASET, a MATLAB program which creates a Latin Random Hypercube dataset;

NIEDERREITER2_DATASET, a MATLAB program which creates a Niederreiter quasirandom dataset with base 2;

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

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

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

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

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.m, the main program.

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_2_20.txt, a leaped Hammersley subsequence dataset with NDIM = 2 and N = 20.
• hammersley_3_10.txt, a leaped Hammersley subsequence dataset with NDIM = 3 and N = 10.
• hammersley_7_10.txt, a leaped Hammersley subsequence dataset with NDIM = 7 and N = 10.

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