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<html>
<head>
<title>
BAND_QR - LAPACK-Style QR Factorization of Banded Matrices
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BAND_QR <br> LAPACK-Style QR Factorization of Banded Matrices
</h1>
<hr>
<p>
<b>BAND_QR</b>
is a FORTRAN90 library which
includes LAPACK-style routines to compute the QR factorization
of a banded matrix,
by Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti.
</p>
<p>
The distinguishing features of these routines include the fact
that
<ul>
<li>
they accept the banded matrix in the compact "GB"
("General Banded") format
</li>
<li>
the QR factors are also stored compactly, by overwriting
the input matrix storage.
</li>
<li>
large problems are handled efficiently by taking advantage
of the blocked version of the algorithm.
</li>
</ul>
</p>
<p>
The routines, as originally developed, did not include a routine to
solve linear systems A*x=b once the QR factors had been computed.
A routine <b>DGBBQRS</b> has been written to carry out this computation
in cases where the QR factors were computed using <b>DGBBQR2</b>,
that is, the unblocked code.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
This software library includes routines which are distributed under
a separate license. Each such routine is individually marked with
the following information:
<pre>
Copyright (c) 2007, Universidad Jaume I de Castellon
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the <organization> nor the
names of its contributors may be used to endorse or promote
products derived from this software without specific prior written
permission.
This software is provided by <copyright holder> ''as is'' and any
express or implied warranties, including, but not limited to, the
implied warranties of merchantability and fitness for a particular
purpose are disclaimed. In no event shall <copyright holder> be liable
for any direct, indirect, incidental, special, exemplary, or
consequential damages (including, but not limited to, procurement of
substitute goods or services; loss of use, data, or profits; or
business interruption) however caused and on any theory of liability,
whether in contract, strict liability, or tort (including negligence
or otherwise) arising in any way out of the use of this software, even
if advised of the possibility of such damage.
</pre>
</p>
<p>
Code not covered under the above license is made available under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>BAND_QR</b> is available in
<a href = "../../f77_src/band_qr/band_qr.html">a FORTRAN77 version</a> and
<a href = "../../f_src/band_qr/band_qr.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/lapack/lapack.html">
LAPACK</a>,
a FORTRAN90 library which
contains modern linear algebra routines.
</p>
<p>
<a href = "../../f_src/linplus/linplus.html">
LINPLUS</a>,
a FORTRAN90 library which
carries out some linear algebra operations on matrices
in a variety of formats.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Certain routines in this library represent the work of:<br>
Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti,<br>
Dept. de Ingenieria y Ciencia de Computadores, Universidad Jaume I,<br>
12.080 Castellon, Spain,<br>
{gquintan,remon,quintana}@icc.uji.es
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford,
James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum,
Sven Hammarling, Alan McKenney, Danny Sorensen,<br>
LAPACK User's Guide,<br>
Third Edition,<br>
SIAM, 1999,<br>
ISBN: 0898714478,<br>
LC: QA76.73.F25L36
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti,<br>
LAPACK-Style Codes for the QR Factorization of Banded Matrices,<br>
To Appear.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "band_qr.f90">band_qr.f90</a>, the source code.
</li>
<li>
<a href = "band_qr.sh">band_qr.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "band_qr_prb.f90">band_qr_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "band_qr_prb.sh">band_qr_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "band_qr_prb_output.txt">band_qr_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>DGBBQR2</b> QR factors an M by N band matrix in GB format, without blocking.
</li>
<li>
<b>DGBBQRF</b> QR factors an M by N band matrix in GB format, using blocking.
</li>
<li>
<b>DGBBQRS</b> solves A*X = B when A has been factored by DGBBQR2.
</li>
<li>
<b>DGEBQR2</b> QR factors an M by N band matrix in GE format, with no blocking.
</li>
<li>
<b>DGEBQRF</b> QR factors an M by N band matrix stored in GE format, with blocking.
</li>
<li>
<b>DGEQRS</b> solves a linear system factored by DGEQRF.
</li>
<li>
<b>DGEQRS_TWO</b> solves A*X = B when A has been factored by DGEQRF or DGEBQR2.
</li>
<li>
<b>R8GB_PRINT</b> prints an R8GB matrix.
</li>
<li>
<b>R8GB_PRINT_SOME</b> prints some of an R8GB matrix.
</li>
<li>
<b>R8GE_PRINT</b> prints an R8 GE matrix
</li>
<li>
<b>R8GE_PRINT_SOME</b> prints some of an R8 GE matrix.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</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 April 2010.
</i>
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