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<html>
<head>
<title>
TOMS743 - Evaluation of Lambert's W function.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS743 <br> Evaluation of Lambert's W function.
</h1>
<hr>
<p>
<b>TOMS743</b>
is a MATLAB library which
evaluates Lambert's W function.
This is a version of ACM TOMS algorithm 743,
by Barry, Barry and Culligan-Hensley.
</p>
<p>
Lambert's W function W(X) satisfies the equation
<pre>
W(x) * exp ( W(x) ) = x
</pre>
</p>
<p>
The text of many ACM TOMS algorithms is available online
through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>TOMS743</b> is available in
<a href = "../../c_src/toms743/toms743.html">a C version</a> and
<a href = "../../cpp_src/toms743/toms743.html">a C++ version</a> and
<a href = "../../f77_src/toms743/toms743.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms743/toms743.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms743/toms743.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/test_values/test_values.html">
TEST_VALUES</a>,
a MATLAB library which
contains routines which return sample values of various functions,
including the modified beta function, and the logarithm of the
gamma function.
</p>
<p>
<a href = "../../m_src/toms443/toms443.html">
TOMS443</a>,
a MATLAB library which
evaluates Lambert's W function.
This is a version of ACM TOMS algorithm 443.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Fred Fritsch, RE Shafer, WP Crowley,<br>
Algorithm 443:
Solution of the Transcendental Equation W*exp(W)=X,<br>
Communications of the ACM,<br>
Volume 16, Number 1, February 1973, pages 123-124.
</li>
<li>
Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,<br>
Algorithm 743: WAPR - A Fortran routine for calculating real
values of the W-function,<br>
ACM Transactions on Mathematical Software,<br>
Volume 21, Number 2, June 1995, pages 172-181.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
</li>
<li>
<a href = "bisect.m">bisect.m</a>,
approximates the W function using bisection.
</li>
<li>
<a href = "crude.m">crude.m</a>,
returns a crude approximation for the W function.
</li>
<li>
<a href = "nbits_compute.m">nbits_compute.m</a>,
computes the mantissa length minus one.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints out the current YMDHMS date as a timestamp.
</li>
<li>
<a href = "wapr.m">wapr.m</a>,
approximates the W function.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms743_test.m">toms743_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "toms743_test_output.txt">toms743_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "toms743_test01.m">toms743_test01.m</a>,
compares wapr() with some tabulated values;
</li>
<li>
<a href = "toms743_test02.m">toms743_test02.m</a>,
tests wapr() when the input is an increment from -exp(-1).
</li>
<li>
<a href = "toms743_test03.m">toms743_test03.m</a>,
tests wapr() when the input is simply the argument.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 15 June 2014.
</i>
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</body>
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</html>