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index.html
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<meta http-equiv="Content-Type" content="application/xhtml+xml; charset=UTF-8" />
<meta name="generator" content="AsciiDoc 10.1.1" />
<title>LAPACK — Linear Algebra PACKage</title>
<style type="text/css">
/* Shared CSS for AsciiDoc xhtml11 and html5 backends */
/* Default font. */
body {
font-family: Georgia,serif;
}
/* Title font. */
h1, h2, h3, h4, h5, h6,
div.title, caption.title,
thead, p.table.header,
#toctitle,
#author, #revnumber, #revdate, #revremark,
#footer {
font-family: Arial,Helvetica,sans-serif;
}
body {
margin: 1em 5% 1em 5%;
}
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color: blue;
text-decoration: underline;
}
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color: fuchsia;
}
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font-style: italic;
color: navy;
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font-weight: bold;
color: #083194;
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color: #527bbd;
margin-top: 1.2em;
margin-bottom: 0.5em;
line-height: 1.3;
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border-bottom: 2px solid silver;
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padding-top: 0.5em;
}
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float: left;
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clear: left;
}
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font-size: 1.0em;
}
div.sectionbody {
margin-left: 0;
}
hr {
border: 1px solid silver;
}
p {
margin-top: 0.5em;
margin-bottom: 0.5em;
}
ul, ol, li > p {
margin-top: 0;
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ul > li > * { color: black; }
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font-family: "Courier New", Courier, monospace;
font-size: inherit;
color: navy;
padding: 0;
margin: 0;
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pre {
white-space: pre-wrap;
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color: #527bbd;
font-weight: bold;
font-size: 1.1em;
}
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}
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}
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font-size: small;
border-top: 2px solid silver;
padding-top: 0.5em;
margin-top: 4.0em;
}
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padding-bottom: 0.5em;
}
#footer-badges {
float: right;
padding-bottom: 0.5em;
}
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margin-top: 1.5em;
margin-bottom: 1.5em;
}
div.imageblock, div.exampleblock, div.verseblock,
div.quoteblock, div.literalblock, div.listingblock, div.sidebarblock,
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margin-top: 1.0em;
margin-bottom: 1.5em;
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div.admonitionblock {
margin-top: 2.0em;
margin-bottom: 2.0em;
margin-right: 10%;
color: #606060;
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div.content { /* Block element content. */
padding: 0;
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/* Block element titles. */
div.title, caption.title {
color: #527bbd;
font-weight: bold;
text-align: left;
margin-top: 1.0em;
margin-bottom: 0.5em;
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div.title + * {
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td div.title:first-child {
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span.image img { border-style: none; vertical-align: text-bottom; }
a.image:visited { color: white; }
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margin-bottom: 0.8em;
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td > div.verse {
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margin-bottom: 0.8em;
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td.hdlist2 {
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margin: 0;
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.comment {
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.footnote, .footnoteref {
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}
span.footnote, span.footnoteref {
vertical-align: super;
}
#footnotes {
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padding: 7px 0 0 0;
}
#footnotes div.footnote {
margin: 0 0 5px 0;
}
#footnotes hr {
border: none;
border-top: 1px solid silver;
height: 1px;
text-align: left;
margin-left: 0;
width: 20%;
min-width: 100px;
}
div.colist td {
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vertical-align: top;
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div.colist td img {
margin-top: 0.3em;
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@media print {
#footer-badges { display: none; }
}
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color: #527bbd;
font-size: 1.1em;
font-weight: bold;
margin-top: 1.0em;
margin-bottom: 0.1em;
}
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margin-bottom: 0;
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span.olive { color: olive; }
span.purple { color: purple; }
span.red { color: red; }
span.silver { color: silver; }
span.teal { color: teal; }
span.white { color: white; }
span.yellow { color: yellow; }
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span.purple-background { background: purple; }
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span.teal-background { background: teal; }
span.white-background { background: white; }
span.yellow-background { background: yellow; }
span.big { font-size: 2em; }
span.small { font-size: 0.6em; }
span.underline { text-decoration: underline; }
span.overline { text-decoration: overline; }
span.line-through { text-decoration: line-through; }
div.unbreakable { page-break-inside: avoid; }
/*
* xhtml11 specific
*
* */
div.tableblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
div.tableblock > table {
border: 3px solid #527bbd;
}
thead, p.table.header {
font-weight: bold;
color: #527bbd;
}
p.table {
margin-top: 0;
}
/* Because the table frame attribute is overridden by CSS in most browsers. */
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border-style: none;
}
div.tableblock > table[frame="hsides"] {
border-left-style: none;
border-right-style: none;
}
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border-top-style: none;
border-bottom-style: none;
}
/*
* html5 specific
*
* */
table.tableblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
thead, p.tableblock.header {
font-weight: bold;
color: #527bbd;
}
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margin-top: 0;
}
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border-width: 3px;
border-spacing: 0px;
border-style: solid;
border-color: #527bbd;
border-collapse: collapse;
}
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border-width: 1px;
padding: 4px;
border-style: solid;
border-color: #527bbd;
}
table.tableblock.frame-topbot {
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border-right-style: hidden;
}
table.tableblock.frame-sides {
border-top-style: hidden;
border-bottom-style: hidden;
}
table.tableblock.frame-none {
border-style: hidden;
}
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text-align: left;
}
th.tableblock.halign-center, td.tableblock.halign-center {
text-align: center;
}
th.tableblock.halign-right, td.tableblock.halign-right {
text-align: right;
}
th.tableblock.valign-top, td.tableblock.valign-top {
vertical-align: top;
}
th.tableblock.valign-middle, td.tableblock.valign-middle {
vertical-align: middle;
}
th.tableblock.valign-bottom, td.tableblock.valign-bottom {
vertical-align: bottom;
}
/*
* manpage specific
*
* */
body.manpage h1 {
padding-top: 0.5em;
padding-bottom: 0.5em;
border-top: 2px solid silver;
border-bottom: 2px solid silver;
}
body.manpage h2 {
border-style: none;
}
body.manpage div.sectionbody {
margin-left: 3em;
}
@media print {
body.manpage div#toc { display: none; }
}
</style>
<script type="text/javascript">
/*<+'])');
// Function that scans the DOM tree for header elements (the DOM2
// nodeIterator API would be a better technique but not supported by all
// browsers).
var iterate = function (el) {
for (var i = el.firstChild; i != null; i = i.nextSibling) {
if (i.nodeType == 1 /* Node.ELEMENT_NODE */) {
var mo = re.exec(i.tagName);
if (mo && (i.getAttribute("class") || i.getAttribute("className")) != "float") {
result[result.length] = new TocEntry(i, getText(i), mo[1]-1);
}
iterate(i);
}
}
}
iterate(el);
return result;
}
var toc = document.getElementById("toc");
if (!toc) {
return;
}
// Delete existing TOC entries in case we're reloading the TOC.
var tocEntriesToRemove = [];
var i;
for (i = 0; i < toc.childNodes.length; i++) {
var entry = toc.childNodes[i];
if (entry.nodeName.toLowerCase() == 'div'
&& entry.getAttribute("class")
&& entry.getAttribute("class").match(/^toclevel/))
tocEntriesToRemove.push(entry);
}
for (i = 0; i < tocEntriesToRemove.length; i++) {
toc.removeChild(tocEntriesToRemove[i]);
}
// Rebuild TOC entries.
var entries = tocEntries(document.getElementById("content"), toclevels);
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var entry = entries[i];
if (entry.element.id == "")
entry.element.id = "_toc_" + i;
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div.className = "toclevel" + entry.toclevel;
toc.appendChild(div);
}
if (entries.length == 0)
toc.parentNode.removeChild(toc);
},
/////////////////////////////////////////////////////////////////////
// Footnotes generator
/////////////////////////////////////////////////////////////////////
/* Based on footnote generation code from:
* http://www.brandspankingnew.net/archive/2005/07/format_footnote.html
*/
footnotes: function () {
// Delete existing footnote entries in case we're reloading the footnodes.
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var noteholder = document.getElementById("footnotes");
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entriesToRemove.push(entry);
}
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<div id="header">
<h1>LAPACK — Linear Algebra PACKage</h1>
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<div id="content">
<div id="preamble">
<div class="sectionbody">
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<td align="center" valign="top"><p class="table"><span class="image">
<img src="images/lapack1.jpg" alt="LAPACK" />
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<td align="center" valign="top"><p class="table"><strong>Version 3.12.0</strong><br />
<a href="https://github.com/Reference-LAPACK/lapack"><strong>LAPACK on GitHub</strong></a><br />
<a href="http://icl.cs.utk.edu/lapack-forum"><strong>Browse the LAPACK User Forum</strong></a><br />
<a href="http://icl.cs.utk.edu/lapack-forum"><strong>Browse the LAPACK User Forum</strong></a><br />
<a href="mailto:[email protected]"><strong>Contact the LAPACK team</strong></a><br />
<br />
<a href="mailto:[email protected]"><strong>Get the latest LAPACK News</strong></a><br />
<br />
<a href="http://www.netlib.org/master_counts2.html#lapack"># access</a></p></td>
<td align="center" valign="top"><p class="table"><span class="image">
<img src="images/lapack2.jpg" alt="LAPACK" />
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</table>
</div>
<div class="paragraph"><p>LAPACK is a software package provided by Univ. of Tennessee; Univ. of California, Berkeley; Univ. of Colorado Denver; and NAG Ltd..</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_presentation">Presentation</h2>
<div class="sectionbody">
<div class="paragraph"><p>LAPACK is written in Fortran 90 and provides routines for solving systems of
simultaneous linear equations, least-squares solutions of linear systems of
equations, eigenvalue problems, and singular value problems. The associated
matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are
also provided, as are related computations such as reordering of the Schur
factorizations and estimating condition numbers. Dense and banded matrices are
handled, but not general sparse matrices. In all areas, similar functionality
is provided for real and complex matrices, in both single and double precision.</p></div>
<div class="paragraph"><p>The original goal of the LAPACK project was to make the widely used EISPACK and
LINPACK libraries run efficiently on shared-memory vector and parallel
processors. On these machines, LINPACK and EISPACK are inefficient because
their memory access patterns disregard the multi-layered memory hierarchies of
the machines, thereby spending too much time moving data instead of doing
useful floating-point operations. LAPACK addresses this problem by reorganizing
the algorithms to use block matrix operations, such as matrix multiplication,
in the innermost loops. These block operations can be optimized for each
architecture to account for the memory hierarchy, and so provide a
transportable way to achieve high efficiency on diverse modern machines. We use
the term "transportable" instead of "portable" because, for fastest possible
performance, LAPACK requires that highly optimized block matrix operations be
already implemented on each machine.</p></div>
<div class="paragraph"><p>LAPACK routines are written so that as much as possible of the computation is
performed by calls to the Basic Linear Algebra Subprograms (BLAS).
LAPACK is designed at the outset to exploit the Level 3 BLAS — a set of
specifications for Fortran subprograms that do various types of matrix
multiplication and the solution of triangular systems with multiple right-hand
sides. Because of the coarse granularity of the Level 3 BLAS operations, their
use promotes high efficiency on many high-performance computers, particularly
if specially coded implementations are provided by the manufacturer.</p></div>
<div class="paragraph"><p>Highly efficient machine-specific implementations of the BLAS are available for
many modern high-performance computers. For details of known vendor- or
ISV-provided BLAS, consult the BLAS FAQ. Alternatively, the user can download
ATLAS to automatically generate an optimized BLAS library for the architecture.
A Fortran 77 reference implementation of the BLAS is available from netlib;
however, its use is discouraged as it will not perform as well as a specifically
tuned implementation.</p></div>
<div class="paragraph"><div class="title">Acknowledgments:</div><p>This material is based upon work supported by the
National Science Foundation and the Department of Energy (DOE). Any opinions,
findings and conclusions or recommendations expressed in this material are
those of the author(s) and do not necessarily reflect the views of the National
Science Foundation (NSF) or the Department of Energy (DOE).</p></div>
<div class="paragraph"><p>The LAPACK project is also sponsored in part by <a href="http://www.mathworks.com/">MathWorks</a> and <a href="https://software.intel.com/en-us/intel-mkl">Intel</a> since many years.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_software">Software</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_licensing">Licensing</h3>
<div class="paragraph"><p>LAPACK is a freely-available software package. It is available from netlib via
anonymous ftp and the World Wide Web at <a href="http://www.netlib.org/lapack">http://www.netlib.org/lapack</a> . Thus, it
can be included in commercial software packages (and has been). We only ask
that proper credit be given to the authors.</p></div>
<div class="paragraph"><p>The license used for the software is the modified BSD license, see:</p></div>
<div class="ulist"><ul>
<li>
<p>
<a href="LICENSE.txt">LICENSE</a>
</p>
</li>
</ul></div>
<div class="paragraph"><p>Like all software, it is copyrighted. It is not trademarked, but we do ask the
following:</p></div>
<div class="ulist"><ul>
<li>
<p>
If you modify the source for these routines we ask that you change the name of
the routine and comment the changes made to the original.
</p>
</li>
<li>
<p>
We will gladly answer any questions regarding the software. If a modification
is done, however, it is the responsibility of the person who modified the
routine to provide support.
</p>
</li>
</ul></div>
</div>
<div class="sect2">
<h3 id="_lapack_version_3_12_0">LAPACK, version 3.12.0</h3>
<div class="exampleblock">
<div class="content">
<div class="ulist"><ul>
<li>
<p>
Download: <a href="https://github.com/Reference-LAPACK/lapack/archive/refs/tags/v3.12.0.tar.gz">lapack-3.12.0.tar.gz</a>
</p>
</li>
<li>
<p>
<a href="lapack-3.12.0.html">LAPACK 3.12.0 Release Notes</a>
</p>
</li>
<li>
<p>
Updated: November 24 2023
</p>
</li>
<li>
<p>
<a href="https://github.com/Reference-LAPACK/lapack/issues?q=is%3Aissue+is%3Aopen+label%3A%22Type%3A+Bug%22">LAPACK GitHub Open Bug</a> (Current known bugs)
</p>
</li>
</ul></div>
</div></div>
</div>
<div class="sect2">
<h3 id="_standard_c_language_apis_for_lapack">Standard C language APIs for LAPACK</h3>
<div class="paragraph"><p>collaboration LAPACK and INTEL Math Kernel Library Team</p></div>
<div class="exampleblock">
<div class="content">
<div class="ulist"><ul>
<li>
<p>
LAPACK C INTERFACE is now included in the LAPACK package (in the lapacke directory)
</p>
</li>
<li>
<p>
<a href="lapacke.html">LAPACKE User Guide</a>
</p>
</li>
<li>
<p>
Updated: November 16, 2013
</p>
</li>
<li>
<p>
header files: <a href="lapacke.h">lapacke.h</a>, <a href="lapacke_config.h">lapacke_config.h</a>, <a href="lapacke_mangling.h">lapacke_mangling.h</a>, <a href="lapacke_utils.h">lapacke_utils.h</a>
</p>
</li>
</ul></div>
</div></div>
</div>
<div class="sect2">
<h3 id="_lapack_for_windows">LAPACK for Windows</h3>
<div class="paragraph"><p>LAPACK is built under Windows using <a href="http://www.cmake.org">Cmake</a> the cross-platform, open-source build system.
The new build system was developed in collaboration with Kitware Inc.</p></div>
<div class="paragraph"><p>A dedicated website (<a href="http://icl.cs.utk.edu/lapack-for-windows/lapack">http://icl.cs.utk.edu/lapack-for-windows/lapack</a>) is available for Windows users.</p></div>
<div class="ulist"><ul>
<li>
<p>
You will find information about your configuration need.
</p>
</li>
<li>
<p>
You will be able to download BLAS, LAPACK, LAPACKE pre-built libraries.
</p>
</li>
<li>
<p>
You will learn how you can directly run LAPACKE from VS Studio (just C code, no Fortran!!!). LAPACK now offers Windows users the ability to code in C using Microsoft Visual Studio
and link to LAPACK Fortran libraries without the need of a vendor-supplied Fortran compiler add-on. To get more information, please refer to <a href="http://www.netlib.org/lapack/lawnspdf/lawn270.pdf">lawn 270</a>.
</p>
</li>
<li>
<p>
You will get step by steps procedures Easy Windows Build.
</p>
</li>
</ul></div>
</div>
<div class="sect2">
<h3 id="_git_access">GIT Access</h3>
<div class="paragraph"><p>The LAPACK GIT (<a href="http://github.com/Reference-LAPACK/lapack">http://github.com/Reference-LAPACK/lapack</a>) repository is open for read-only for our users.</p></div>
<div class="literalblock">
<div class="content">
<pre><code>Please use our link:http://github.com/Reference-LAPACK/lapack[*LAPACK development repository*] to get the latest bug fixed, submit issues or pull requests.</code></pre>
</div></div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_support">Support</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
<a href="https://github.com/Reference-LAPACK/lapack"><strong>LAPACK on GitHub</strong></a>
</p>
</li>
<li>
<p>
<a href="http://icl.cs.utk.edu/lapack-forum">Browse the LAPACK/ScaLAPACK User Forum</a>
</p>
</li>
<li>
<p>
<a href="mailto:[email protected]">Contact the LAPACK team</a>
</p>
</li>
<li>
<p>
<a href="http://icl.cs.utk.edu/lapack-forum/archives/">Archives of LAPACK mailing list</a>
</p>
</li>
</ul></div>
<div class="paragraph"><p>Do not forget to check our GitHub repository for Current and Fixed issues and Improvements</p></div>
<div class="ulist"><ul>
<li>
<p>
<a href="https://github.com/Reference-LAPACK/lapack/issues">Current Issues</a>
</p>
</li>
<li>
<p>
<a href="https://github.com/Reference-LAPACK/lapack/milestone/2?closed=1">Fixed issues and Improvements since last release</a>
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_contributors">Contributors</h2>
<div class="sectionbody">