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bvls.html
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<html>
<head>
<title>
BVLS - Bounded Variable Least Squares Solver
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BVLS <br> Bounded Variable Least Squares Solver
</h1>
<hr>
<p>
<b>BVLS</b>
is a FORTRAN90 library which
solves a least squares problem with bounds on the variables,
by Charles Lawson and Richard Hanson.
</p>
<p>
Given an M by N matrix, A, and an M-vector, B, BVLS computes an
N-vector X that solves the least-squares problem:
<blockquote>
A * X = B<br>
subject to BND(1,J) <= X(J) <= BND(2,J) for 1 <= J <= N.
</blockquote>
</p>
<p>
The program allows the user to bound some or all of the variables.
The user is also free to constrain some variables with only a one-sided
bounded. The values BND(1,J) = -huge(ONE) and BND(2,J) = huge(ONE) are
suggested choices to designate that there is no constraint in that
direction. The parameter ONE is 1.0 in the working precision.
</p>
<p>
This algorithm is a generalization of the routine NNLS, which solves
the least-squares problem:
<blockquote>
A * X = B<br>
subject to 0 <= X(J) for all J.
</blockquote>
</p>
<p>
The subroutine NNLS appeared in 'Solving Least Squares Problems'
by Lawson and Hanson, Prentice-Hall, 1974. Work on BVLS was started
by Charles Lawson and Richard Hanson at Jet Propulsion Laboratory,
1973 June 12. Many modifications were subsequently made.
</p>
<p>
This FORTRAN90 version was completed in April, 1995 by Richard Hanson.
Assumed shape arrays, automatic arrays, array operations, internal
subroutines and FORTRAN90 elemental functions are used. Comments are
prefixed with an exclamation mark. More than 72 characters appear on some lines.
The BVLS package is an additional item for the reprinting of the book
by SIAM Publications and the distribution of the code package
using netlib and Internet or network facilities.
</p>
<p>
The original source code is available through NETLIB at<br>
<a href = "http://www.netlib.org/lawson-hanson/index.html">
http://www.netlib.org/lawson-hanson/index.html</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/brent/brent.html">
BRENT</a>,
a FORTRAN90 library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems.
</p>
<p>
<a href = "../../f_src/lawson/lawson.html">
LAWSON</a>,
a FORTRAN90 library which
solves least squares problems, and computes singular value
decompositions.
</p>
<p>
<a href = "../../f_src/nl2sol/nl2sol.html">
NL2SOL</a>,
a FORTRAN90 library which
implements an adaptive nonlinear least-squares algorithm.
</p>
<p>
<a href = "../../f_src/praxis/praxis.html">
PRAXIS</a>,
a FORTRAN90 library which
minimizes a scalar function of several variables.
</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/toms611/toms611.html">
TOMS611</a>,
a FORTRAN90 library which
seeks the minimizer of a scalar functional
of multiple variables.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Charles Lawson and Richard Hanson.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Charles Lawson, Richard Hanson,<br>
Solving Least Squares Problems,<br>
Revised edition, <br>
SIAM, 1995,<br>
ISBN: 0898713560,<br>
LC: QA275.L38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bvls.f90">bvls.f90</a>, the source code.
</li>
<li>
<a href = "bvls.sh">bvls.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "bvls_prb.f90">bvls_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "bvls_prb.sh">bvls_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "bvls_prb_output.txt">bvls_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BVLS</b> solves a least squares problem with bounds on the variables.
</li>
<li>
<b>INITIALIZE</b> initializes internal data.
</li>
<li>
<b>SELECT_ANOTHER_COEFF_TO!_SOLVE_FOR</b>
</li>
<li>
<b>TEST_COEF_J_FOR_DIAG!_ELT_AND_DIRECTION_OF_CHANGE</b>
</li>
<li>
<b>MOVE_J_FROM_SET_Z_TO_SET_P</b>
</li>
<li>
<b>TEST_SET_P_AGAINST_CONSTRAINTS</b>
</li>
<li>
<b>SEE_IF_ALL_CONSTRAINED_COEFFS!_ARE_FEASIBLE</b>
</li>
<li>
<b>MOVE_COEF_I_FROM_SET_P_TO_SET_Z</b>
</li>
<li>
<b>TERMINATION</b>
</li>
<li>
<b>ROTG</b> performs a Givens rotation.
</li>
<li>
<b>NRM2</b> returns the Euclidean norm of a vector.
</li>
<li>
<b>HTC</b> constructs a Householder transformation.
</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 01 January 2011.
</i>
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