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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 MATLAB 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 = "../../m_src/llsq/llsq.html">
LLSQ</a>,
a MATLAB 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 = "../../m_src/r8lib/r8lib.html">
R8LIB</a>,
a MATLAB 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 = "p00_a.m">p00_a.m</a>
returns the matrix A for any least squares problem.
</li>
<li>
<a href = "p00_b.m">p00_b.m</a>
returns the right hand side B for any least squares problem.
</li>
<li>
<a href = "p00_m.m">p00_m.m</a>
returns the number of equations M for any least squares problem.
</li>
<li>
<a href = "p00_n.m">p00_n.m</a>
returns the number of variables N for any least squares problem.
</li>
<li>
<a href = "p00_prob_num.m">p00_prob_num.m</a>
returns the number of least squares problems.
</li>
<li>
<a href = "p00_x.m">p00_x.m</a>
returns the least squares solution X for any least squares problem.
</li>
<li>
<a href = "p01_a.m">p01_a.m</a>
returns the matrix A for problem 1.
</li>
<li>
<a href = "p01_b.m">p01_b.m</a>
returns the right hand side B for problem 1.
</li>
<li>
<a href = "p01_m.m">p01_m.m</a>
returns the number of equations M for problem 1.
</li>
<li>
<a href = "p01_n.m">p01_n.m</a>
returns the number of variables N for problem 1.
</li>
<li>
<a href = "p01_x.m">p01_x.m</a>
returns the least squares solution X for problem 1.
</li>
<li>
<a href = "p02_a.m">p02_a.m</a>
returns the matrix A for problem 2.
</li>
<li>
<a href = "p02_b.m">p02_b.m</a>
returns the right hand side B for problem 2.
</li>
<li>
<a href = "p02_m.m">p02_m.m</a>
returns the number of equations M for problem 2.
</li>
<li>
<a href = "p02_n.m">p02_n.m</a>
returns the number of variables N for problem 2.
</li>
<li>
<a href = "p02_x.m">p02_x.m</a>
returns the least squares solution X for problem 2.
</li>
<li>
<a href = "p03_a.m">p03_a.m</a>
returns the matrix A for problem 3.
</li>
<li>
<a href = "p03_b.m">p03_b.m</a>
returns the right hand side B for problem 3.
</li>
<li>
<a href = "p03_m.m">p03_m.m</a>
returns the number of equations M for problem 3.
</li>
<li>
<a href = "p03_n.m">p03_n.m</a>
returns the number of variables N for problem 3.
</li>
<li>
<a href = "p03_x.m">p03_x.m</a>
returns the least squares solution X for problem 3.
</li>
<li>
<a href = "p04_a.m">p04_a.m</a>
returns the matrix A for problem 4.
</li>
<li>
<a href = "p04_b.m">p04_b.m</a>
returns the right hand side B for problem 4.
</li>
<li>
<a href = "p04_m.m">p04_m.m</a>
returns the number of equations M for problem 4.
</li>
<li>
<a href = "p04_n.m">p04_n.m</a>
returns the number of variables N for problem 4.
</li>
<li>
<a href = "p04_x.m">p04_x.m</a>
returns the least squares solution X for problem 4.
</li>
<li>
<a href = "p05_a.m">p05_a.m</a>
returns the matrix A for problem 5.
</li>
<li>
<a href = "p05_b.m">p05_b.m</a>
returns the right hand side B for problem 5.
</li>
<li>
<a href = "p05_m.m">p05_m.m</a>
returns the number of equations M for problem 5.
</li>
<li>
<a href = "p05_n.m">p05_n.m</a>
returns the number of variables N for problem 5.
</li>
<li>
<a href = "p05_x.m">p05_x.m</a>
returns the least squares solution X for problem 5.
</li>
<li>
<a href = "p06_a.m">p06_a.m</a>
returns the matrix A for problem 6.
</li>
<li>
<a href = "p06_b.m">p06_b.m</a>
returns the right hand side B for problem 6.
</li>
<li>
<a href = "p06_m.m">p06_m.m</a>
returns the number of equations M for problem 6.
</li>
<li>
<a href = "p06_n.m">p06_n.m</a>
returns the number of variables N for problem 6.
</li>
<li>
<a href = "p06_x.m">p06_x.m</a>
returns the least squares solution X for problem 6.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_ls_test.m">test_ls_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "test_ls_test00.m">test_ls_test00.m</a>,
tries out MATLAB's A\b solver on the data.
</li>
<li>
<a href = "test_ls_test01.m">test_ls_test01.m</a>,
summarizes the test data.
</li>
<li>
<a href = "test_ls_test_output.txt">test_ls_test_output.txt</a>,
the output file.
</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 18 April 2012.
</i>
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