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<html>
<head>
<title>
NIEDERREITER2_DATASET - Create a Niederreiter Dataset, Base = 2.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NIEDERREITER2_DATASET <br> Create a Niederreiter Dataset, Base = 2.
</h1>
<hr>
<p>
<b>NIEDERREITER2_DATASET</b>
is a C++ program
which creates a Niederreiter quasirandom dataset with base 2.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>niederreiter2_dataset</b> <i>m</i> <i>n</i> <i>skip</i>
</blockquote>
where
<ul>
<li>
<i>m</i> is the spatial dimension;
</li>
<li>
<i>n</i> is the number of points to generate;
</li>
<li>
<i>skip</i> is the number of initial values to skip.
A recommended value is 4096.
</li>
</ul>
The data is written to the file <b>niederreiter2_<i>m</i>_<i>n</i>.txt</b>.
</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>NIEDERREITER2_DATASET</b> is available in
<a href = "../../cpp_src/niederreiter2_dataset/niederreiter2_dataset.html">a C++ version</a> and
<a href = "../../f_src/niederreiter2_dataset/niederreiter2_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/niederreiter2_dataset/niederreiter2_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a C++ program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../cpp_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a C++ program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a C++ program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a C++ program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a C++ program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../cpp_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a C++ library which
computes the elements of the sequence. A compiled version of that library
must be available to build <b>NIEDERREITER2_DATASET</b>.
</p>
<p>
<a href = "../../datasets/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a dataset directory which
contains
examples of the files created by <b>NIEDERREITER2_DATASET</b>.
</p>
<p>
<a href = "../../cpp_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a C++ program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../cpp_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a C++ program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../cpp_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a C++ program which
generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../cpp_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a C++ program which
creates a van der Corput quasirandom sequence and writes it to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox,<br>
Algorithm 659:
Implementing Sobol's Quasirandom Sequence Generator,<br>
ACM Transactions on Mathematical Software,<br>
Volume 14, Number 1, pages 88-100, 1988.
</li>
<li>
Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
Algorithm 738:
Programs to Generate Niederreiter's Low-Discrepancy Sequences,<br>
ACM Transactions on Mathematical Software,<br>
Volume 20, Number 4, pages 494-495, 1994.
</li>
<li>
Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
Implementation and Tests of Low Discrepancy Sequences,<br>
ACM Transactions on Modeling and Computer Simulation,<br>
Volume 2, Number 3, pages 195-213, 1992.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, pages 362-376, 1986.
</li>
<li>
Rudolf Lidl, Harald Niederreiter,<br>
Finite Fields,<br>
Cambridge University Press, 1984, page 553.
</li>
<li>
Harald Niederreiter,<br>
Low-discrepancy and low-dispersion sequences,<br>
Journal of Number Theory,<br>
Volume 30, 1988, pages 51-70.
</li>
<li>
Harald Niederreiter,<br>
Random Number Generation and quasi-Monte Carlo Methods,<br>
SIAM, 1992.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "niederreiter2_dataset.cpp">niederreiter2_dataset.cpp</a>, the source code.
</li>
<li>
<a href = "niederreiter2_dataset.sh">niederreiter2_dataset.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for NIEDERREITER2_DATASET.
</li>
<li>
<b>CALCC2</b> computes values of the constants C(I,J,R).
</li>
<li>
<b>CALCV2</b> calculates the value of the constants V(J,R).
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>NIEDERREITER2</b> returns an element of the Niederreiter sequence base 2.
</li>
<li>
<b>NIEDERREITER2_GENERATE</b> generates a set of Niederreiter values.
</li>
<li>
<b>PLYMUL2</b> multiplies two polynomials in the field of order 2
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>SETFLD2</b> sets up arithmetic tables for the finite field of order 2.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 11 December 2009.
</i>
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