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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 FORTRAN90 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 = "../../f_src/bvls/bvls.html">
BVLS</a>,
a FORTRAN90 library which
applies least squares methods to solve a linear system for which
lower and upper constraints may have been placed on every variable,
by Charles Lawson and Richard Hanson.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems,
by Richard Hanson and Fred Krogh.
</p>
<p>
<a href = "../../f_src/lawson/lawson.html">
LAWSON</a>,
a FORTRAN90 library which
contains routines for solving least squares problems and singular value
decompositions (SVD),
by Charles Lawson, Richard Hanson.
</p>
<p>
<a href = "../../f_src/llsq/llsq.html">
LLSQ</a>,
a FORTRAN90 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 = "../../f_src/minpack/minpack.html">
MINPACK</a>,
a FORTRAN90 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 = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes a wide variety of numerical software, including
solvers for linear systems of equations, interpolation of data,
numerical quadrature, linear least squares data fitting,
the solution of nonlinear equations, ordinary differential equations,
optimization and nonlinear least squares, simulation and random numbers,
trigonometric approximation and Fast Fourier Transforms (FFT).
</p>
<p>
<a href = "../../f_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a FORTRAN90 library which
computes the least squares solution of a linear system A*x=b.
</p>
<p>
<a href = "../../f_src/r8lib/r8lib.html">
R8LIB</a>,
a FORTRAN90 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.f90">test_ls.f90</a>, the source code.
</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.f90">test_ls_prb.f90</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 04 October 2012.
</i>
<!-- John Burkardt -->
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