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toms552.html
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<html>
<head>
<title>
TOMS552 - Constrained Overdetermined Linear Systems in L1.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS552 <br> Constrained Overdetermined Linear Systems in L1.
</h1>
<hr>
<p>
<b>TOMS552</b>
is a FORTRAN90 library which
computes a solution of an overdetermined constrained
linear system, minimizing the error in the L1 norm.
</p>
<p>
<b>TOMS552</b> is an implementation of ACM TOMS algorithm 552.
</p>
<p>
The overdetermined linear system being solved is
<blockquote><b>
A * X = B.
</b></blockquote>
The equality constraints have the form:
<blockquote><b>
C * X = D
</b></blockquote>
and the inequality constraints have the form:
<blockquote><b>
E * X >= F.
</b></blockquote>
The program is required to seek a solution <b>X</b> which satisfies
the constraints, and which minimizes the L1 norm (sum of
absolute values of components) of <b>A*X-B</b>.
</p>
<p>
The original, true, correct version of ACM TOMS 552 is available
in the TOMS subdirectory of
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS552</b> is available in
<a href = "../../f77_src/toms552/toms552.html"> a FORTRAN77 version</a> and
<a href = "../../f_src/toms552/toms552.html">a FORTRAN90 version.</a>
</p>
<h3 align = "center">
Author:
</h3>
<p>
Ian Barrodale,<br>
Frank Roberts.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Ian Barrodale, Frank Roberts,<br>
Algorithm 552:
Solution of the Constrained L1 Approximation Problem,<br>
ACM Transactions on Mathematical Software,<br>
Volume 6, Number 2, March 1980, pages 231-235.
</li>
<li>
Helmuth Spaeth,<br>
Mathematical Algorithms for Linear Regression,<br>
Academic Press, 1991,<br>
ISBN: 0-12-656460-4,<br>
LC: QA278.2.S6313.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms552.f90">toms552.f90</a>, the source code.
</li>
<li>
<a href = "toms552.sh">toms552.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms552_prb.f90">toms552_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "toms552_prb.sh">toms552_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "toms552_prb_input.txt">toms552_prb_input.txt</a>,
an input file for use with the sample program.
</li>
<li>
<a href = "toms552_prb_output.txt">toms552_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CL1</b> solves a linear programming problem.
</li>
<li>
<b>COL</b> adds a multiple of vector V2 to vector V1.
</li>
<li>
<b>L1ORTH</b> carries out orthogonal regression for the L1 norm.
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 28 December 2007.
</i>
<!-- John Burkardt -->
</body>
</html>