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<html>
<head>
<title>
NORMAL - Normal Random Number Generators
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NORMAL <br> Normal Random Number Generators
</h1>
<hr>
<p>
<b>NORMAL</b>
is a C++ library which
returns a sequence of normally distributed pseudorandom numbers.
</p>
<p>
<b>NORMAL</b> is based on two simple ideas:
<ul>
<li>
the use of a fairly simple uniform pseudorandom number generator,
which can be implemented in software;
</li>
<li>
the use of the Box-Muller transformation to convert pairs of
uniformly distributed random values to pairs of normally distributed
random values.
</li>
</ul>
</p>
<p>
Using these ideas, it is not too hard to generate normal sequences
of real or complex values, of single or double precision. These
values can be generated as single quantities, vectors or matrices.
An associated seed actually determines the sequence. Varying
the seed will result in producing a different sequence.
</p>
<p>
The fundamental underlying random number generator used here
is based on a simple, old, and limited linear congruential random
number generator originally used in the IBM System 360.
</p>
<p>
This library makes it possible to compare certain computations
that use normal random numbers, written in C, C++, FORTRAN77,
FORTRAN90, MATLAB or Python.
</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>NORMAL</b> is available in
<a href = "../../c_src/normal/normal.html">a C version</a> and
<a href = "../../cpp_src/normal/normal.html">a C++ version</a> and
<a href = "../../f77_src/normal/normal.html">a FORTRAN77 version</a> and
<a href = "../../f_src/normal/normal.html">a FORTRAN90 version</a> and
<a href = "../../m_src/normal/normal.html">a MATLAB version</a> and
<a href = "../../py_src/normal/normal.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/asa183/asa183.html">
ASA183</a>,
a C++ library which
implements the Wichman-Hill pseudorandom number generator.
</p>
<p>
<a href = "../../cpp_src/cpp_random/cpp_random.html">
CPP_RANDOM</a>,
C++ programs which
illustrate the use of the C++ random number generator routines.
</p>
<p>
<a href = "../../cpp_src/ranlib/ranlib.html">
RANLIB</a>,
a C++ library which
produces random samples from Probability Density Functions (PDF's),
including Beta, Chi-square Exponential, F, Gamma, Multivariate normal,
Noncentral chi-square, Noncentral F, Univariate normal, random permutations,
Real uniform, Binomial, Negative Binomial, Multinomial, Poisson
and Integer uniform,
by Barry Brown and James Lovato.
</p>
<p>
<a href = "../../cpp_src/rnglib/rnglib.html">
RNGLIB</a>,
a C++ library which
implements a random number generator (RNG) with splitting facilities,
allowing multiple independent streams to be computed,
by L'Ecuyer and Cote.
</p>
<p>
<a href = "../../cpp_src/truncated_normal/truncated_normal.html">
TRUNCATED_NORMAL</a>,
a C++ library which
works with the truncated normal distribution over [A,B], or
[A,+oo) or (-oo,B], returning the probability density function (PDF),
the cumulative density function (CDF), the inverse CDF, the mean,
the variance, and sample values.
</p>
<p>
<a href = "../../cpp_src/uniform/uniform.html">
UNIFORM</a>,
a C++ library which
computes elements of a
sequence of pseudorandom uniformly distributed 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, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673.
</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, December 1986, pages 362-376.
</li>
<li>
Donald Knuth,<br>
The Art of Computer Programming,<br>
Volume 2, Seminumerical Algorithms,<br>
Third Edition,<br>
Addison Wesley, 1997,<br>
ISBN: 0201896842.
</li>
<li>
Pierre LEcuyer,<br>
Random Number Generation,<br>
in Handbook of Simulation,<br>
edited by Jerry Banks,<br>
Wiley, 1998,<br>
ISBN: 0471134031,<br>
LC: T57.62.H37.
</li>
<li>
Peter Lewis, Allen Goodman, James Miller,<br>
A Pseudo-Random Number Generator for the System/360,<br>
IBM Systems Journal,<br>
Volume 8, 1969, pages 136-143.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "normal.cpp">normal.cpp</a>,
the source code.
</li>
<li>
<a href = "normal.hpp">normal.hpp</a>,
the include file.
</li>
<li>
<a href = "normal.sh">normal.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "normal_prb.cpp">normal_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "normal_prb.sh">normal_prb.sh</a>,
commands to compile, link and run the sample calling program.
</li>
<li>
<a href = "normal_prb_output.txt">normal_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_NORMAL_01</b> returns a unit pseudonormal C4.
</li>
<li>
<b>C8_NORMAL_01</b> returns a unit pseudonormal C8.
</li>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>I4_NORMAL_AB</b> returns a scaled pseudonormal I4.
</li>
<li>
<b>I8_NORMAL_AB</b> returns a scaled pseudonormal I8.
</li>
<li>
<b>R4_NINT</b> returns the nearest I4 to an R4.
</li>
<li>
<b>R4_NORMAL_01</b> returns a unit pseudonormal R4.
</li>
<li>
<b>R4_NORMAL_AB</b> returns a scaled pseudonormal R4.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R8_NORMAL_01</b> returns a unit pseudonormal R8.
</li>
<li>
<b>R8_NORMAL_AB</b> returns a scaled pseudonormal R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_NORMAL_01</b> returns a unit pseudonormal R8MAT.
</li>
<li>
<b>R8MAT_NORMAL_01_NEW</b> returns a unit pseudonormal R8MAT.
</li>
<li>
<b>R8MAT_NORMAL_AB</b> returns a scaled pseudonormal R8MAT.
</li>
<li>
<b>R8MAT_NORMAL_AB_NEW</b> returns a scaled pseudonormal R8MAT.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_NORMAL_01_NEW</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_NORMAL_AB</b> returns a scaled pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_NORMAL_AB_NEW</b> returns a scaled pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</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 06 August 2013.
</i>
<!-- John Burkardt -->
</body>
</html>