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<html>
<head>
<title>
NIEDERREITER2 - The Niederreiter Quasirandom Sequence [Base 2]
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NIEDERREITER2 <br> The Niederreiter Quasirandom Sequence [Base 2]
</h1>
<hr>
<p>
<b>NIEDERREITER2</b>
is a C++ library which
implements the Niederreiter
quasirandom sequence, using a base of 2.
</p>
<p>
A quasirandom or low discrepancy sequence, such as the Faure,
Halton, Hammersley, Niederreiter or Sobol sequences, is
"less random" than a pseudorandom number sequence, but
more useful for such tasks as approximation of integrals in
higher dimensions, and in global optimization.
This is because low discrepancy sequences tend to sample
space "more uniformly" than random numbers. Algorithms
that use such sequences may have superior convergence.
</p>
<p>
<b>NIEDERREITER2</b> is an adapation of the INLO2 and GOLO2 routines
in ACM TOMS Algorithm 738. The original code can only
compute the "next" element of the sequence. The revised code
allows the user to specify the index of the desired element.
</p>
<p>
The original, true, correct version of ACM TOMS Algorithm 738
is available in the TOMS subdirectory of
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</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</b> is available in
<a href = "../../cpp_src/niederreiter2/niederreiter2.html">a C++ version</a> and
<a href = "../../f_src/niederreiter2/niederreiter2.html">a FORTRAN90 version</a> and
<a href = "../../m_src/niederreiter2/niederreiter2.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/box_behnken/box_behnken.html">
BOX_BEHNKEN</a>,
a C++ library which
computes a Box-Behnken design,
that is, a set of arguments to sample the behavior
of a function of multiple parameters;
</p>
<p>
<a href = "../../cpp_src/cvt/cvt.html">
CVT</a>,
a C++ library which
computes points in
a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../cpp_src/faure/faure.html">
FAURE</a>,
a C++ library which
computes Faure
sequences.
</p>
<p>
<a href = "../../cpp_src/grid/grid.html">
GRID</a>,
a C++ library which
computes points on a grid.
</p>
<p>
<a href = "../../cpp_src/halton/halton.html">
HALTON</a>,
a C++ library which
computes Halton
sequences.
</p>
<p>
<a href = "../../cpp_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a C++ library which
computes Hammersley
sequences.
</p>
<p>
<a href = "../../cpp_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a C++ library which
computes sets of points in a 2D hexagonal grid.
</p>
<p>
<a href = "../../cpp_src/ihs/ihs.html">
IHS</a>,
a C++ library which
computes improved Latin Hypercube datasets.
</p>
<p>
<a href = "../../cpp_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a C++ library which
computes Latin square data choosing the center value.
</p>
<p>
<a href = "../../cpp_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a C++ library which
computes Latin square data choosing the edge value.
</p>
<p>
<a href = "../../cpp_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a C++ library which
computes Latin square data choosing a random value in the square.
</p>
<p>
<a href = "../../cpp_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a C++ program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../cpp_src/normal/normal.html">
NORMAL</a>,
a C++ library which
computes elements of a
sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../cpp_src/sobol/sobol.html">
SOBOL</a>,
a C++ library which
computes Sobol sequences.
</p>
<p>
<a href = "../../f_src/toms738/toms738.html">
TOMS738</a>,
a FORTRAN90 library which
is a version of ACM TOMS algorithm 738,
for evaluating Niederreiter sequences.
</p>
<p>
<a href = "../../cpp_src/uniform/uniform.html">
UNIFORM</a>,
a C++ library which
computes uniform random values.
</p>
<p>
<a href = "../../cpp_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a C++ library which
computes van der Corput sequences.
</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>
R 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.cpp">niederreiter2.cpp</a>, the source code;
</li>
<li>
<a href = "niederreiter2.hpp">niederreiter2.hpp</a>, the include file;
</li>
<li>
<a href = "niederreiter2.sh">niederreiter2.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "niederreiter2_prb.cpp">niederreiter2_prb.cpp</a>,
the sample test code;
</li>
<li>
<a href = "niederreiter2_prb.sh">niederreiter2_prb.sh</a>,
commands to compile the test code;
</li>
<li>
<a href = "niederreiter2_prb_output.txt">niederreiter2_prb_output.txt</a>,
the output file;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<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>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>
<!-- John Burkardt -->
</body>
</html>