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<html>
<head>
<title>
HAMMERSLEY_DATASET - Generate Hammersley Datasets
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HAMMERSLEY_DATASET <br> Generate Hammersley Datasets
</h1>
<hr>
<p>
<b>HAMMERSLEY_DATASET</b>
is a FORTRAN90 program which
creates a Hammersley dataset and
writes it to a file.
</p>
<p>
The program is interactive, and allows the user to choose
the parameters that define the sequence.
</p>
<p>
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
<pre>
SEED(1:NDIM) + STEP * LEAP(1:NDIM).
</pre>
</p>
<p>
The data that the user may set include:
<ul>
<li>
NDIM, the spatial dimension, <br>
default: NDIM = 1, <br>
required: 1 <= NDIM;
</li>
<li>
N, the number of entries of the subsequence to compute, <br>
required: 1 <= N;
</li>
<li>
STEP, the subsequence index of the first entry to compute,<br>
default: STEP = 0,<br>
required: 0 <= STEP.
</li>
<li>
SEED(1:NDIM), the sequence index corresponding to STEP = 0.<br>
default: SEED(1:NDIM) = (0, 0, ... 0),<br>
required: 0 <= SEED(1:NDIM);
</li>
<li>
LEAP(1:NDIM), the succesive jumps in the sequence.<br>
default: LEAP(1:NDIM) = (1, 1, ..., 1).<br>
required: 1 <= LEAP(1:NDIM).
</li>
<li>
BASE(1:NDIM), the Hammersley bases.<br>
default: BASE(1:NDIM) = (2, 3, 5, 7, 11... ), or<br>
(-N, 2, 3, 5, 7, 11,...) if <b>N</b> is known.<br>
required: 1 < BASE(I) for any van der Corput dimension I, or
BASE(I) < 0 to generate the fractional sequence J/|BASE(I)|.
</li>
</ul>
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>HAMMERSLEY_DATASET</b> is available in
<a href = "../../cpp_src/hammersley_dataset/hammersley_dataset.html">a C++ version</a> and
<a href = "../../f_src/hammersley_dataset/hammersley_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/hammersley_dataset/hammersley_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a FORTRAN90 program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../f_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a FORTRAN90 program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
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 <b>HAMMERSLEY_DATASET</b>.
</p>
<p>
<a href = "../../datasets/hammersley/hammersley.html">
HAMMERSLEY</a>,
a dataset directory which
contains examples of files
created by <b>HAMMERSLEY_DATASET</b>.
</p>
<p>
<a href = "../../f_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a FORTRAN90 program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../f_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a FORTRAN90 program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../f_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a FORTRAN90 program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../f_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a FORTRAN90 program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../f_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a FORTRAN90 program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a FORTRAN90 program which
creates a van der Corput quasirandom sequence and writes it to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
John Hammersley,<br>
Monte Carlo methods for solving multivariable problems,<br>
Proceedings of the New York Academy of Science,<br>
Volume 86, 1960, pages 844-874.
</li>
<li>
Ladislav Kocis, William Whiten,<br>
Computational Investigations of Low-Discrepancy Sequences,<br>
ACM Transactions on Mathematical Software,<br>
Volume 23, Number 2, 1997, pages 266-294.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "hammersley_dataset.f90">hammersley_dataset.f90</a>,
the source code.
</li>
<li>
<a href = "hammersley_dataset.sh">hammersley_dataset.sh</a>,
commands to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "hammersley_dataset_input.txt">hammersley_dataset_input.txt</a>,
is a simple input file for creation of sequences of
dimension 2, 3 and 7.
</li>
<li>
<a href = "hammersley_dataset_output.txt">hammersley_dataset_output.txt</a>,
is the printed output from a run of the program with
the input file.
</li>
<li>
<a href = "../../datasets/hammersley/hammersley_02_00020.txt">
hammersley_02_00020.txt</a>,
a leaped Hammersley subsequence dataset with NDIM = 2 and N = 20.
</li>
<li>
<a href = "../../datasets/hammersley/hammersley_03_00010.txt">
hammersley_03_00010.txt</a>,
a leaped Hammersley subsequence dataset with NDIM = 3 and N = 10.
</li>
<li>
<a href = "../../datasets/hammersley/hammersley_07_00010.txt">
hammersley_07_00010.txt</a>,
a leaped Hammersley subsequence dataset with NDIM = 7 and N = 10.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for HAMMERSLEY_DATASET.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 30 August 2005.
</i>
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