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lapack-3.4.0.html
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lapack-3.4.0.html
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<!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 8.6.9" />
<title>LAPACK 3.4.0</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%;
}
a {
color: blue;
text-decoration: underline;
}
a:visited {
color: fuchsia;
}
em {
font-style: italic;
color: navy;
}
strong {
font-weight: bold;
color: #083194;
}
h1, h2, h3, h4, h5, h6 {
color: #527bbd;
margin-top: 1.2em;
margin-bottom: 0.5em;
line-height: 1.3;
}
h1, h2, h3 {
border-bottom: 2px solid silver;
}
h2 {
padding-top: 0.5em;
}
h3 {
float: left;
}
h3 + * {
clear: left;
}
h5 {
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;
}
ul > li { color: #aaa; }
ul > li > * { color: black; }
.monospaced, code, pre {
font-family: "Courier New", Courier, monospace;
font-size: inherit;
color: navy;
padding: 0;
margin: 0;
}
pre {
white-space: pre-wrap;
}
#author {
color: #527bbd;
font-weight: bold;
font-size: 1.1em;
}
#email {
}
#revnumber, #revdate, #revremark {
}
#footer {
font-size: small;
border-top: 2px solid silver;
padding-top: 0.5em;
margin-top: 4.0em;
}
#footer-text {
float: left;
padding-bottom: 0.5em;
}
#footer-badges {
float: right;
padding-bottom: 0.5em;
}
#preamble {
margin-top: 1.5em;
margin-bottom: 1.5em;
}
div.imageblock, div.exampleblock, div.verseblock,
div.quoteblock, div.literalblock, div.listingblock, div.sidebarblock,
div.admonitionblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
div.admonitionblock {
margin-top: 2.0em;
margin-bottom: 2.0em;
margin-right: 10%;
color: #606060;
}
div.content { /* Block element content. */
padding: 0;
}
/* Block element titles. */
div.title, caption.title {
color: #527bbd;
font-weight: bold;
text-align: left;
margin-top: 1.0em;
margin-bottom: 0.5em;
}
div.title + * {
margin-top: 0;
}
td div.title:first-child {
margin-top: 0.0em;
}
div.content div.title:first-child {
margin-top: 0.0em;
}
div.content + div.title {
margin-top: 0.0em;
}
div.sidebarblock > div.content {
background: #ffffee;
border: 1px solid #dddddd;
border-left: 4px solid #f0f0f0;
padding: 0.5em;
}
div.listingblock > div.content {
border: 1px solid #dddddd;
border-left: 5px solid #f0f0f0;
background: #f8f8f8;
padding: 0.5em;
}
div.quoteblock, div.verseblock {
padding-left: 1.0em;
margin-left: 1.0em;
margin-right: 10%;
border-left: 5px solid #f0f0f0;
color: #888;
}
div.quoteblock > div.attribution {
padding-top: 0.5em;
text-align: right;
}
div.verseblock > pre.content {
font-family: inherit;
font-size: inherit;
}
div.verseblock > div.attribution {
padding-top: 0.75em;
text-align: left;
}
/* DEPRECATED: Pre version 8.2.7 verse style literal block. */
div.verseblock + div.attribution {
text-align: left;
}
div.admonitionblock .icon {
vertical-align: top;
font-size: 1.1em;
font-weight: bold;
text-decoration: underline;
color: #527bbd;
padding-right: 0.5em;
}
div.admonitionblock td.content {
padding-left: 0.5em;
border-left: 3px solid #dddddd;
}
div.exampleblock > div.content {
border-left: 3px solid #dddddd;
padding-left: 0.5em;
}
div.imageblock div.content { padding-left: 0; }
span.image img { border-style: none; vertical-align: text-bottom; }
a.image:visited { color: white; }
dl {
margin-top: 0.8em;
margin-bottom: 0.8em;
}
dt {
margin-top: 0.5em;
margin-bottom: 0;
font-style: normal;
color: navy;
}
dd > *:first-child {
margin-top: 0.1em;
}
ul, ol {
list-style-position: outside;
}
ol.arabic {
list-style-type: decimal;
}
ol.loweralpha {
list-style-type: lower-alpha;
}
ol.upperalpha {
list-style-type: upper-alpha;
}
ol.lowerroman {
list-style-type: lower-roman;
}
ol.upperroman {
list-style-type: upper-roman;
}
div.compact ul, div.compact ol,
div.compact p, div.compact p,
div.compact div, div.compact div {
margin-top: 0.1em;
margin-bottom: 0.1em;
}
tfoot {
font-weight: bold;
}
td > div.verse {
white-space: pre;
}
div.hdlist {
margin-top: 0.8em;
margin-bottom: 0.8em;
}
div.hdlist tr {
padding-bottom: 15px;
}
dt.hdlist1.strong, td.hdlist1.strong {
font-weight: bold;
}
td.hdlist1 {
vertical-align: top;
font-style: normal;
padding-right: 0.8em;
color: navy;
}
td.hdlist2 {
vertical-align: top;
}
div.hdlist.compact tr {
margin: 0;
padding-bottom: 0;
}
.comment {
background: yellow;
}
.footnote, .footnoteref {
font-size: 0.8em;
}
span.footnote, span.footnoteref {
vertical-align: super;
}
#footnotes {
margin: 20px 0 20px 0;
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 {
padding-right: 0.5em;
padding-bottom: 0.3em;
vertical-align: top;
}
div.colist td img {
margin-top: 0.3em;
}
@media print {
#footer-badges { display: none; }
}
#toc {
margin-bottom: 2.5em;
}
#toctitle {
color: #527bbd;
font-size: 1.1em;
font-weight: bold;
margin-top: 1.0em;
margin-bottom: 0.1em;
}
div.toclevel0, div.toclevel1, div.toclevel2, div.toclevel3, div.toclevel4 {
margin-top: 0;
margin-bottom: 0;
}
div.toclevel2 {
margin-left: 2em;
font-size: 0.9em;
}
div.toclevel3 {
margin-left: 4em;
font-size: 0.9em;
}
div.toclevel4 {
margin-left: 6em;
font-size: 0.9em;
}
span.aqua { color: aqua; }
span.black { color: black; }
span.blue { color: blue; }
span.fuchsia { color: fuchsia; }
span.gray { color: gray; }
span.green { color: green; }
span.lime { color: lime; }
span.maroon { color: maroon; }
span.navy { color: navy; }
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; }
span.aqua-background { background: aqua; }
span.black-background { background: black; }
span.blue-background { background: blue; }
span.fuchsia-background { background: fuchsia; }
span.gray-background { background: gray; }
span.green-background { background: green; }
span.lime-background { background: lime; }
span.maroon-background { background: maroon; }
span.navy-background { background: navy; }
span.olive-background { background: olive; }
span.purple-background { background: purple; }
span.red-background { background: red; }
span.silver-background { background: silver; }
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 overriden by CSS in most browsers. */
div.tableblock > table[frame="void"] {
border-style: none;
}
div.tableblock > table[frame="hsides"] {
border-left-style: none;
border-right-style: none;
}
div.tableblock > table[frame="vsides"] {
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;
}
p.tableblock {
margin-top: 0;
}
table.tableblock {
border-width: 3px;
border-spacing: 0px;
border-style: solid;
border-color: #527bbd;
border-collapse: collapse;
}
th.tableblock, td.tableblock {
border-width: 1px;
padding: 4px;
border-style: solid;
border-color: #527bbd;
}
table.tableblock.frame-topbot {
border-left-style: hidden;
border-right-style: hidden;
}
table.tableblock.frame-sides {
border-top-style: hidden;
border-bottom-style: hidden;
}
table.tableblock.frame-none {
border-style: hidden;
}
th.tableblock.halign-left, td.tableblock.halign-left {
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);
for (var i = 0; i < entries.length; ++i) {
var entry = entries[i];
if (entry.element.id == "")
entry.element.id = "_toc_" + i;
var a = document.createElement("a");
a.href = "#" + entry.element.id;
a.appendChild(document.createTextNode(entry.text));
var div = document.createElement("div");
div.appendChild(a);
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.
var i;
var noteholder = document.getElementById("footnotes");
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entriesToRemove.push(entry);
}
for (i = 0; i < entriesToRemove.length; i++) {
noteholder.removeChild(entriesToRemove[i]);
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<body class="article">
<div id="header">
<h1>LAPACK 3.4.0</h1>
<div id="toc">
<div id="toctitle">Table of Contents</div>
<noscript><p><b>JavaScript must be enabled in your browser to display the table of contents.</b></p></noscript>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p>Release date: Fr 11/11/11.</p></div>
<div class="paragraph"><p>This material is based upon work supported by the National Science Foundation
and the Department of Energy under Grant No. NSF-OCI-1032861, NSF-CCF-00444486,
NSF-CNS 0325873, NSF-EIA 0122599, NSF-ACI-0090127, DOE-DE-FC02-01ER25478,
DOE-DE-FC02-06ER25768.</p></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="_1_support_and_questions">1. Support and questions:</h2>
<div class="sectionbody">
<div class="paragraph"><p><a href="http://icl.cs.utk.edu/lapack-forum/">http://icl.cs.utk.edu/lapack-forum/</a></p></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_lapack_3_4_0_what_8217_s_new">2. LAPACK 3.4.0: What’s new</h2>
<div class="sectionbody">
<div class="olist arabic"><ol class="arabic">
<li>
<p>
<strong>xGEQRT: QR factorization (improved interface).</strong> Contribution by Rodney
James (UC Denver). xGEQRT is analogous to xGEQRF with a modified interface which
enables better performance when the blocked reflectors need to be reused. The
companion subroutines xGEMQRT apply the reflectors.
</p>
</li>
<li>
<p>
<strong>xGEQRT3: recursive QR factorization.</strong> Contribution by Rodney James (UC
Denver). The recursive QR factorization enables cache-oblivious and enables high
performance on tall and skinny matrices.
See reference <a href="#1">[1]</a> below.
</p>
</li>
<li>
<p>
<strong>xTPQRT: Communication-Avoiding QR sequential kernels.</strong> Contribution by
Rodney James (UC Denver). These subroutines are useful for updating a QR
factorization and are used in sequential and parallel Communication Avoiding
QR. These subroutines support the general case Triangle on top of Pentagon
which includes as special cases so-called Triangle on top of Triangle and
Triangle on top of Square. This is the right-looking version of the subroutines
and the subroutines are blocked. The T matrices and the block size are part of
the interface. The companion subroutines xTPMQRT apply the reflectors.
</p>
</li>
<li>
<p>
<strong>CMAKE build system.</strong> We are striving to help our users install our
libraries seamlessly on their machines. The CMAKE team contributed to our
effort to port LAPACK and ScaLAPACK under the CMAKE build system. Building
under Windows has never been easier. This also allows us to release dll for
Windows, so users no longer need a Fortran compiler to use LAPACK under
Windows.
</p>
</li>
<li>
<p>
<strong>Doxygen documentation.</strong> LAPACK routine documentation has never been more
accessible. See <a href="http://www.netlib.org/lapack/explore-html/">http://www.netlib.org/lapack/explore-html/</a>.
</p>
</li>
<li>
<p>
<strong>New website allowing for easier navigation.</strong>
</p>
</li>
<li>
<p>
<strong>LAPACKE - Standard C language APIs for LAPACK.</strong> Since LAPACK 3.3.0, LAPACK
includes new C interfaces. With the LAPACK 3.4.0 release, LAPACKE is directly
integrated within the LAPACK library and has been enriched by the full set of
LAPACK subroutines. See <a href="lapacke.html">here</a>.
</p>
</li>
</ol></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_references">3. References</h2>
<div class="sectionbody">
<div class="dlist"><dl>
<dt class="hdlist1">
[1] <a id="1"></a>
</dt>
<dd>
<p>
E. Elmroth and F.G. Gustavson. “Applying recursion to serial and
parallel QR factorization leads to better performance.” IBM Journal of
Research and Development 44(4): 605-624 (2000)
</p>
</dd>
</dl></div>
</div>
</div>
<div class="sect1">
<h2 id="_4_external_contributors">4. External Contributors</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
CMAKE team
</p>
</li>
<li>
<p>
Intel MKL team
</p>
</li>
<li>
<p>
Craig Lucas (University of Manchester and NAG)
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_5_thanks">5. Thanks</h2>
<div class="sectionbody">
<div class="paragraph"><p>Thanks for bug-report/patches/suggestions to:
Ming Gu (UC Berkeley),
Hatem Ltaif (KAUST, Saudi Arabia),
omitrofa (intel team),
Tiago Requeijo,
Edward Smyth (NAG), and
Clint Whaley (University of Texas at San Antonio, USA).</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_6_developer_list">6. Developer list</h2>
<div class="sectionbody">
<div class="ulist"><div class="title">Principal Investigators</div><ul>
<li>
<p>
Jim Demmel (University of California, Berkeley, USA)
</p>
</li>
<li>
<p>
Jack Dongarra (University of Tennessee and ORNL, USA)
</p>
</li>
<li>
<p>
Julien Langou (University of Colorado Denver, USA)
</p>
</li>
</ul></div>
<div class="ulist"><div class="title">LAPACK developers involved in this release</div><ul>
<li>
<p>
Sven Hammarling (NAG Ltd. and University of Manchester, UK)
</p>
</li>
<li>
<p>
Igor Kozachenko (University of California, Berkeley, USA)
</p>
</li>
<li>
<p>
Julie Langou (University of Tennessee, USA)
</p>
</li>
<li>
<p>
Benjamin Lipshitz (University of California, Berkeley, USA)
</p>
</li>
<li>
<p>
Rodney James (University of Colorado Denver, USA)
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_7_more_details">7. More details</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_7_1_xgeqrt_qr_factorization_improved_interface">7.1. xGEQRT: QR factorization (improved interface)</h3>
<div class="paragraph"><div class="title">contributors</div><p>Rodney James (UC Denver)</p></div>
<div class="paragraph"><div class="title">contribution</div><p>xGEQRT is analogous to xGEQRF with a modified interface which enables better
performance when the blocked reflectors need to be reused. The companion
subroutines xGEMQRT apply the reflectors.</p></div>
<div class="literalblock">
<div class="title">public interfaces</div>
<div class="content">
<pre><code>A SRC/sgeqrt.f A SRC/sgemqrt.f A SRC/sgeqrt2.f
A SRC/cgeqrt.f A SRC/cgemqrt.f A SRC/cgeqrt2.f
A SRC/dgeqrt.f A SRC/dgemqrt.f A SRC/dgeqrt2.f
A SRC/zgeqrt.f A SRC/zgemqrt.f A SRC/zgeqrt2.f</code></pre>
</div></div>
</div>
<div class="sect2">
<h3 id="_7_2_xgeqrt3_recursive_qr_factorization">7.2. xGEQRT3: recursive QR factorization</h3>
<div class="paragraph"><div class="title">contributors</div><p>Rodney James (UC Denver)</p></div>
<div class="paragraph"><div class="title">reference</div><p>Elmroth, E., and Gustavson, F.G. “Applying recursion to serial and
parallel QR factorization leads to better performance.” IBM Journal of
Research and Development 44(4): 605-624 (2000)</p></div>
<div class="paragraph"><div class="title">contribution</div><p>The recursive QR factorization enables cache-oblivious and enables high
performance on tall and skinny matrices.</p></div>
<div class="literalblock">
<div class="title">public interfaces</div>
<div class="content">
<pre><code>A SRC/sgeqrt3.f
A SRC/cgeqrt3.f
A SRC/dgeqrt3.f
A SRC/zgeqrt3.f</code></pre>
</div></div>
</div>
<div class="sect2">
<h3 id="_7_3_xtpqrt_communication_avoiding_qr_sequential_kernels">7.3. xTPQRT: Communication-Avoiding QR sequential kernels</h3>
<div class="paragraph"><div class="title">contributors</div><p>Rodney James (UC Denver)</p></div>
<div class="paragraph"><div class="title">contribution</div><p>These subroutines are useful for updating a QR factorization and are used in
sequential and parallel Communication Avoiding QR. These subroutines support
the general case Triangle on top of Pentagon which includes as special cases
so-called Triangle on top of Triangle and Triangle on top of Square. This is
the right-looking version of the subroutines and the subroutines are blocked.
The T matrices and the block size are part of the interface. The companion
subroutines xTPMQRT apply the reflectors.</p></div>
<div class="literalblock">
<div class="title">public interfaces</div>
<div class="content">
<pre><code>A SRC/stpmqrt.f A SRC/stpqrt.f A SRC/stpqrt2.f A SRC/stprfb.f
A SRC/ctpmqrt.f A SRC/ctpqrt.f A SRC/ctpqrt2.f A SRC/ctprfb.f
A SRC/dtpmqrt.f A SRC/dtpqrt.f A SRC/dtpqrt2.f A SRC/dtprfb.f
A SRC/ztpmqrt.f A SRC/ztpqrt.f A SRC/ztpqrt2.f A SRC/ztprfb.f</code></pre>
</div></div>
</div>
<div class="sect2">
<h3 id="_7_4_cmake_build_system">7.4. CMAKE build system</h3>
<div class="paragraph"><div class="title">contributors</div><p>CMAKE team</p></div>
<div class="paragraph"><div class="title">lapacker</div><p>Julie Langou (University of Tennessee)</p></div>
<div class="paragraph"><div class="title">contribution</div><p>We are striving to help our users install our libraries seamlessly on their
machines. The CMAKE team contributed to our effort to port LAPACK and
ScaLAPACK under the CMAKE build system. Building under Windows has never been
easier. This also allows us to release dll for Windows, so users no longer need
a Fortran compiler to use LAPACK under Windows.</p></div>
</div>
<div class="sect2">
<h3 id="_7_5_doxygen_documentation">7.5. Doxygen documentation</h3>
<div class="paragraph"><div class="title">lapacker</div><p>Julie Langou (University of Tennessee)</p></div>
<div class="paragraph"><div class="title">contribution</div><p>LAPACK routine documentation has never been more
accessible. See <a href="http://www.netlib.org/lapack/explore-html/">http://www.netlib.org/lapack/explore-html/</a>.</p></div>
</div>
<div class="sect2">
<h3 id="_7_6_new_website_allowing_for_easier_navigation">7.6. New website allowing for easier navigation</h3>
<div class="paragraph"><div class="title">lapacker</div><p>Julie Langou (University of Tennessee)</p></div>
</div>
<div class="sect2">
<h3 id="_7_7_lapacke_standard_c_language_apis_for_lapack">7.7. LAPACKE - Standard C language APIs for LAPACK</h3>
<div class="paragraph"><div class="title">contributors</div><p>Intel MKL team</p></div>