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lapack-3.6.0.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 3.6.0</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");
if (!noteholder) {
return;
}
var entriesToRemove = [];
for (i = 0; i < noteholder.childNodes.length; i++) {
var entry = noteholder.childNodes[i];
if (entry.nodeName.toLowerCase() == 'div' && entry.getAttribute("class") == "footnote")
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 3.6.0</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: 11/15.</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_thanks">2. Thanks</h2>
<div class="sectionbody">
<div class="paragraph"><p>Thanks for bug-report/patches/suggestions to:</p></div>
<div class="paragraph"><p>Forum users:</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_lapack_3_6_0_what_8217_s_new">3. LAPACK 3.6.0: What’s new</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
[Philippe Theveny, UC Denver] <strong>BLAS3 routines for generalised SVD</strong>
</p>
</li>
</ul></div>
<div class="paragraph"><p>xGGSVD3 and xGGSVP3. Use Level 3 BLAS algorithm. xGGSVD3 uses xGEQP3, xGGSVP3 uses xGGSVD3.
This replaces the deprecated subroutines xGGSVD and xGGSVP. xGGSVD3 was using xGEQPF, xGGSVP was using xGGSVD.</p></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/cggsvd3.f
SRC/cggsvp3.f
SRC/dggsvd3.f
SRC/dggsvp3.f
SRC/sggsvd3.f
SRC/sggsvp3.f
SRC/zggsvd3.f
SRC/zggsvp3.f</code></pre>
</div></div>
<div class="paragraph"><p>Modified:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/cgeqp3.f
SRC/cggsvd.f
SRC/cggsvp.f
SRC/dgeqp3.f
SRC/dggsvd.f
SRC/dggsvp.f
SRC/sgeqp3.f
SRC/sggsvd.f
SRC/sggsvp.f
SRC/zgeqp3.f
SRC/zggsvd.f
SRC/zggsvp.f</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
[Osni Marquez] <strong>Computing a Subset of the Singular Value Decomposition</strong>
full or partial (subset) SVD of a bidiagonal matrix through an associated eigenvalue problem
full or partial (subset) SVD of a general matrix by invoking bdsvdx
</p>
</li>
</ul></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/dbdsvdx.f
SRC/sbdsvdx.f:
SRC/dgesvdx.f
SRC/sgesvdx.f
SRC/zgesvdx.f
SRC/cgesvdx.f:</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
[Zlatko Drmac] <strong>Complex Jacobi SVD</strong>
</p>
</li>
</ul></div>
<div class="paragraph"><p>Inclusion of complex and double complex routines (real and double precision were included in LAPACK 3.2.0)</p></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/cgejsv.f
SRC/zgejsv.f
SRC/cgesvj.f
SRC/cgsvj0.f
SRC/cgsvj1.f
SRC/zgesvj.f
SRC/zgsvj0.f
SRC/zgsvj1.f</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
[Piotr Luszczek, Univ of TN and Yaohung Mike Tsai, Univ of TN] <strong>Recursive Cholesky</strong>
</p>
</li>
</ul></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>lapack/trunk/SRC/cpotrf2.f
lapack/trunk/SRC/dpotrf2.f
lapack/trunk/SRC/spotrf2.f
lapack/trunk/SRC/zpotrf2.f</code></pre>
</div></div>
<div class="paragraph"><p>Modified:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>lapack/trunk/SRC/cpotrf.f
lapack/trunk/SRC/dpotrf.f
lapack/trunk/SRC/spotrf.f
lapack/trunk/SRC/zpotrf.f</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
[Daniel Kressner and Meiyue Shao] <strong>Improvements to QR (NEP)</strong>
</p>
</li>
</ul></div>
<div class="paragraph"><p>Improvements to nonsymmetric generalized eigenvalue problems
xGGHD3: blocked Hessenberg-triangular reduction routines, xGGHD3, for nonsymmetric generalized eigenvalue problems. This replaces the current unblocked routines xGGHRD. CONTRIBUTION BY Daniel Kressner and Meiyue Shao</p></div>
<div class="ulist"><ul>
<li>
<p>
[Philippe Theveny, UC Denver] <strong>Deprecated routines</strong>
</p>
<div class="literalblock">
<div class="content">
<pre><code>CGEGS CGEGV CGELSX CGEQPF CGGSVD
CGGSVP CLAHRD CLATZM CTZRQF
DGEGS DGEGV DGELSX DGEQPF DGGSVD
DGGSVP DLAHRD DLATZM DTZRQF
SGEGS SGEGV SGELSX SGEQPF SGGSVD
SGGSVP SLAHRD SLATZM STZRQF
ZGEGS ZGEGV ZGELSX ZGEQPF ZGGSVD
ZGGSVP ZLAHRD ZLATZM ZTZRQF</code></pre>
</div></div>
</li>
<li>
<p>
matrix_order → matrix_layout in the LAPACKE C Interface.
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_external_contributors">3. External Contributors</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
Zlatko Drmac, University of Zagreb
</p>
</li>
<li>
<p>
Daniel Kressner, École Polytechnique Fédérale de Lausanne
</p>
</li>
<li>
<p>
Meiyue Shao, Lawrence Berkeley National Laboratory
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_4_thanks">4. Thanks</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
Aleksey Vorona
</p>
</li>
<li>
<p>
Alex Zotkevich
</p>
</li>
<li>
<p>
Alex Zotkevich (INTEL)
</p>
</li>
<li>
<p>
Alexander Kobotov (INTEL)
</p>
</li>
<li>
<p>
Allan Wollaber
</p>
</li>
<li>
<p>
Amran Illoul
</p>
</li>
<li>
<p>
Andreas Noack Jensen
</p>
</li>
<li>
<p>
Beresford Parlett
</p>
</li>
<li>
<p>
Bobby Chen (Mathworks)
</p>
</li>
<li>
<p>
btracey (GONUM)
</p>
</li>
<li>
<p>
Cezary Sliwa
</p>
</li>
<li>
<p>
Christoph Conrads
</p>
</li>
<li>
<p>
Dan Kortschak
</p>
</li>
<li>
<p>
David Hough (ORACLE)
</p>
</li>
<li>
<p>