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test_ls.html
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<html>
<head>
<title>
TEST_LS - Linear Least Squares Test Problems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_LS <br> Linear Least Squares Test Problems
</h1>
<hr>
<p>
<b>TEST_LS</b>
is a C++ library which
defines a number of linear least squares problems of the form A*x=b,
where A is an M by N matrix.
</p>
<p>
Some linear least squares problems include constraints on the data,
such as requiring that every entry of X be positive. This library
only contains unconstrained problems. For such problems, the task is
typically to find a vector X which minimizes the Euclidean norm of
the residual r=Ax-b, or, in cases where multiple minimizers exist,
to find the minimizer of minimal Euclidean norm.
</p>
<p>
<b>TEST_LS</b> requires access to a compiled copy of the R8LIB library.
</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>TEST_LS</b> is available in
<a href = "../../c_src/test_ls/test_ls.html">a C version</a> and
<a href = "../../cpp_src/test_ls/test_ls.html">a C++ version</a> and
<a href = "../../f77_src/test_ls/test_ls.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_ls/test_ls.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_ls/test_ls.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/llsq/llsq.html">
LLSQ</a>,
a C++ library which
solves the simple linear least squares problem of finding the formula
of a straight line y=a*x+b which minimizes the root-mean-square error
to a set of N data points.
</p>
<p>
<a href = "../../cpp_src/minpack/minpack.html">
MINPACK</a>,
a C++ library which
solves systems of nonlinear equations, or the least squares minimization of the
residual of a set of linear or nonlinear equations.
</p>
<p>
<a href = "../../cpp_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a C++ library which
computes the least squares solution of a linear system A*x=b.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Cleve Moler,<br>
Numerical Computing with MATLAB,<br>
SIAM, 2004,<br>
ISBN13: 978-0-898716-60-3,<br>
LC: QA297.M625,<br>
ebook: http://www.mathworks.com/moler/chapters.html
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_ls.cpp">test_ls.cpp</a>, the source code.
</li>
<li>
<a href = "test_ls.hpp">test_ls.hpp</a>, the include file.
</li>
<li>
<a href = "test_ls.sh">test_ls.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_ls_prb.cpp">test_ls_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "test_ls_prb.sh">test_ls_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_ls_prb_output.txt">test_ls_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_A</b> returns the matrix A for any least squares problem.
</li>
<li>
<b>P00_B</b> returns the right hand side B for any least squares problem.
</li>
<li>
<b>P00_M</b> returns the number of equations M for any least squares problem.
</li>
<li>
<b>P00_N</b> returns the number of variables N for any least squares problem.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of least squares problems.
</li>
<li>
<b>P00_X</b> returns the least squares solution X for any least squares problem.
</li>
<li>
<b>P01_A</b> returns the matrix A for problem 1.
</li>
<li>
<b>P01_B</b> returns the right hand side B for problem 1.
</li>
<li>
<b>P01_M</b> returns the number of equations M for problem 1.
</li>
<li>
<b>P01_N</b> returns the number of variables N for problem 1.
</li>
<li>
<b>P01_X</b> returns the least squares solution X for problem 1.
</li>
<li>
<b>P02_A</b> returns the matrix A for problem 2.
</li>
<li>
<b>P02_B</b> returns the right hand side B for problem 2.
</li>
<li>
<b>P02_M</b> returns the number of equations M for problem 2.
</li>
<li>
<b>P02_N</b> returns the number of variables N for problem 2.
</li>
<li>
<b>P02_X</b> returns the least squares solution X for problem 2.
</li>
<li>
<b>P03_A</b> returns the matrix A for problem 3.
</li>
<li>
<b>P03_B</b> returns the right hand side B for problem 3.
</li>
<li>
<b>P03_M</b> returns the number of equations M for problem 3.
</li>
<li>
<b>P03_N</b> returns the number of variables N for problem 3.
</li>
<li>
<b>P03_X</b> returns the least squares solution X for problem 3.
</li>
<li>
<b>P04_A</b> returns the matrix A for problem 4.
</li>
<li>
<b>P04_B</b> returns the right hand side B for problem 4.
</li>
<li>
<b>P04_M</b> returns the number of equations M for problem 4.
</li>
<li>
<b>P04_N</b> returns the number of variables N for problem 4.
</li>
<li>
<b>P04_X</b> returns the least squares solution X for problem 4.
</li>
<li>
<b>P05_A</b> returns the matrix A for problem 5.
</li>
<li>
<b>P05_B</b> returns the right hand side B for problem 5.
</li>
<li>
<b>P05_M</b> returns the number of equations M for problem 5.
</li>
<li>
<b>P05_N</b> returns the number of variables N for problem 5.
</li>
<li>
<b>P05_X</b> returns the least squares solution X for problem 5.
</li>
<li>
<b>P06_A</b> returns the matrix A for problem 6.
</li>
<li>
<b>P06_B</b> returns the right hand side B for problem 6.
</li>
<li>
<b>P06_M</b> returns the number of equations M for problem 6.
</li>
<li>
<b>P06_N</b> returns the number of variables N for problem 6.
</li>
<li>
<b>P06_X</b> returns the least squares solution X for problem 6.
</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 04 October 2012.
</i>
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