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lapack-3.5.0.html
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lapack-3.5.0.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 3.5.0</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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return;
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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 3.5.0</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: 11/13.</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="ulist"><ul>
<li>
<p>
Alexander Kobotov (INTEL) - r1350
</p>
</li>
<li>
<p>
Bo Kagstrom
</p>
</li>
<li>
<p>
Brian Sutton (Randolph-Macon College) - r1414
</p>
</li>
<li>
<p>
Duncan Po (Mathworks) - r1349
</p>
</li>
<li>
<p>
Elena Ivanov (ORACLE) - r1416
</p>
</li>
<li>
<p>
Hong Bo Peng (IBM) - r1425
</p>
</li>
<li>
<p>
Lawrence Mulholland (NAG) - r1439
</p>
</li>
<li>
<p>
Mathieu Faverge (INRIA) - r1447 and r1449
</p>
</li>
<li>
<p>
Michael Baudin (SciLAB)
</p>
</li>
<li>
<p>
Sergey Kuznetsov (INTEL) - r1384
</p>
</li>
<li>
<p>
Tyrone Rees (STFC Rutherford Appleton Laboratory, UK) - r1385
</p>
</li>
<li>
<p>
Victor Liu (Stanford University) - r1372
</p>
</li>
</ul></div>
<div class="paragraph"><p>Forum users:
* bmoloney (OHSU)
* eem2314</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_lapack_3_5_0_what_8217_s_new">3. LAPACK 3.5.0: What’s new</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
[Igor Kozachenko] added <strong>Symmetric/Hermitian LDLT factorization routines with rook pivoting algorithm</strong>
</p>
<div class="literalblock">
<div class="content">
<pre><code>A ./SRC/checon_rook.f A ./SRC/csytrf_rook.f A ./SRC/ssycon_rook.f A ./SRC/zhetrs_rook.f
A ./SRC/chesv_rook.f A ./SRC/csytri_rook.f A ./SRC/ssysv_rook.f A ./SRC/zlahef_rook.f
A ./SRC/chetf2_rook.f A ./SRC/csytrs_rook.f A ./SRC/ssytf2_rook.f A ./SRC/zlasyf_rook.f
A ./SRC/chetrf_rook.f A ./SRC/dlasyf_rook.f A ./SRC/ssytrf_rook.f A ./SRC/zsycon_rook.f
A ./SRC/chetri_rook.f A ./SRC/dsycon_rook.f A ./SRC/ssytri_rook.f A ./SRC/zsysv_rook.f
A ./SRC/chetrs_rook.f A ./SRC/dsysv_rook.f A ./SRC/ssytrs_rook.f A ./SRC/zsytf2_rook.f
A ./SRC/clahef_rook.f A ./SRC/dsytf2_rook.f A ./SRC/zhecon_rook.f A ./SRC/zsytrf_rook.f
A ./SRC/clasyf_rook.f A ./SRC/dsytrf_rook.f A ./SRC/zhesv_rook.f A ./SRC/zsytri_rook.f
A ./SRC/csycon_rook.f A ./SRC/dsytri_rook.f A ./SRC/zhetf2_rook.f A ./SRC/zsytrs_rook.f
A ./SRC/csysv_rook.f A ./SRC/dsytrs_rook.f A ./SRC/zhetrf_rook.f
A ./SRC/csytf2_rook.f A ./SRC/slasyf_rook.f A ./SRC/zhetri_rook.f</code></pre>
</div></div>
<div class="literalblock">
<div class="content">
<pre><code>A ./lapacke/src/lapacke_csysv_rook.c
A ./lapacke/src/lapacke_csysv_rook_work.c
A ./lapacke/src/lapacke_dsysv_rook.c
A ./lapacke/src/lapacke_dsysv_rook_work.c
A ./lapacke/src/lapacke_ssysv_rook.c
A ./lapacke/src/lapacke_ssysv_rook_work.c
A ./lapacke/src/lapacke_zsysv_rook.c
A ./lapacke/src/lapacke_zsysv_rook_work.c</code></pre>
</div></div>
<div class="literalblock">
<div class="content">
<pre><code>A ./TESTING/LIN/cchkhe_rook.f A ./TESTING/LIN/schksy_rook.f
A ./TESTING/LIN/cchksy_rook.f A ./TESTING/LIN/sdrvsy_rook.f
A ./TESTING/LIN/cdrvhe_rook.f A ./TESTING/LIN/slavsy_rook.f
A ./TESTING/LIN/cdrvsy_rook.f A ./TESTING/LIN/ssyt01_rook.f
A ./TESTING/LIN/chet01_rook.f A ./TESTING/LIN/zchkhe_rook.f
A ./TESTING/LIN/clavhe_rook.f A ./TESTING/LIN/zchksy_rook.f
A ./TESTING/LIN/clavsy_rook.f A ./TESTING/LIN/zdrvhe_rook.f
A ./TESTING/LIN/csyt01_rook.f A ./TESTING/LIN/zdrvsy_rook.f
A ./TESTING/LIN/dchksy_rook.f A ./TESTING/LIN/zhet01_rook.f
A ./TESTING/LIN/ddrvsy_rook.f A ./TESTING/LIN/zlavhe_rook.f
A ./TESTING/LIN/dlavsy_rook.f A ./TESTING/LIN/zlavsy_rook.f
A ./TESTING/LIN/dsyt01_rook.f A ./TESTING/LIN/zsyt01_rook.f</code></pre>
</div></div>
</li>
<li>
<p>
[Brian Sutton] <strong>2-by-1 CSD to be used for tall and skinny matrix with orthonormal columns</strong>
</p>
</li>
</ul></div>
<div class="paragraph"><p>(in LAPCK 3.4.0, we already integrated CSD of a full square orthogonal matrix)</p></div>
<div class="paragraph"><p>More info here:</p></div>
<div class="ulist"><ul>
<li>
<p>
<a href="http://faculty.rmc.edu/bsutton/simultaneousbidiagonalization.htmlStable computation of the CS decomposition: simultaneous bidiagonalization">Stable computation of the CS decomposition: simultaneous bidiagonalization</a>
</p>
</li>
<li>
<p>
<a href="http://faculty.rmc.edu/bsutton/csd-software.html">The fundamental CS decomposition</a>
</p>
</li>
<li>
<p>
<a href="http://faculty.rmc.edu/bsutton/csd.html">Computing the complete CS decomposition</a>
</p>
</li>
<li>
<p>
[Bradley Lowery, Julien Langou and Rodney James, r1413] <strong>New stopping criteria for balancing</strong>.
</p>
</li>
</ul></div>
<div class="paragraph"><p>Fix from Bradley Lowery, Julien Langou and Rodney James: <a href="http://arxiv.org/abs/1401.5766">http://arxiv.org/abs/1401.5766</a></p></div>
<div class="paragraph"><p>This fix the problem described in: <a href="http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=13&t=4270">http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=13&t=4270</a></p></div>
<div class="literalblock">
<div class="content">
<pre><code>M ./SRC/cgebal.f M ./SRC/dgebal.f M ./SRC/sgebal.f M ./SRC/zgebal.f</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
[Victor Liu, r1372] New complex division algorithm.
</p>
</li>
</ul></div>
<div class="paragraph"><p>Following the algorithm of Michael Baudin, Robert L. Smith (see arxiv.1210.4539 )</p></div>
<div class="literalblock">
<div class="content">
<pre><code>M ./SRC/dladiv.f M ./SRC/sladiv.f</code></pre>
</div></div>
<div class="paragraph"><p>improvements:
* slasyf.f, clasyf.f, clahef.f, dlasyf.f, zlahef.f, zlasyf.f :: various improvements by Igor Kozachenko
* dhgeqz.f, shgeqz.f :: improvements by Duncan Po (MathWorks), committed by Rodney James
* dlasd4.f, slasd4.f :: improvements by Sergey Kuznetsov (Intel), committed by Rodney James
* clarfb.f, dlarfb.f, slarfb.f, zlarfb.f :: improvements by Rodney James</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_external_contributors">3. External Contributors</h2>
<div class="sectionbody">
</div>
</div>
<div class="sect1">
<h2 id="_5_developer_list">5. 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>
Igor Kozachenko (University of California, Berkeley, USA)
</p>
</li>
<li>
<p>
Julie Langou (University of Tennessee, USA)
</p>
</li>
<li>
<p>
Rodney James (University of Colorado Denver, USA)
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_6_more_details">6. More details</h2>
<div class="sectionbody">
<div class="literalblock">
<div class="content">
<pre><code> *xSYSV_ROOK: LDL^T^ with rook pivoting.* Contribution by Craig Lucas (University
of Manchester and NAG) and Sven Hammarling (NAG). These subroutines enable
better stability than the Bunch-Kaufman pivoting scheme currently used in
LAPACK xSYSV solvers; also, the elements of L are bounded, which is important
in some applications. The computational time of xSYSV_ROOK is slightly higher than
the one of xSYSV.</code></pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
New stopping criteria for balancing.
</p>
</li>
<li>
<p>
more robust complex division routine [DLADIV]- suggested by Victor Liu <<a href="mailto:vkl@stanford.edu">vkl@stanford.edu</a>>
contributed by Michael Baudin, Robert L. Smith