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lapack-3.7.0.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 3.7.0</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 3.7.0</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: 12/24/16.</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 ACI 1339797, 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 class="paragraph"><p><a href="https://github.com/Reference-LAPACK/lapack/">https://github.com/Reference-LAPACK/lapack/</a></p></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_lapack_3_7_0_what_8217_s_new">2. LAPACK 3.7.0: What’s new</h2>
<div class="sectionbody">
</div>
</div>
<div class="sect1">
<h2 id="_2_1_linear_least_squares_minimum_norm_solution">2.1. Linear Least Squares / Minimum Norm solution</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Syd Hashemi Ghermezi (UC Berkeley), Jim Demmel (UC Berkeley),
with some help from Eugene Chereshnev (Intel) and Konstantin Arturov (Intel).</p></div>
<div class="ulist"><ul>
<li>
<p>
New TP (triangle on top of trapezoid kernels for LQ factorization
</p>
</li>
<li>
<p>
Short and Wide LQ (SWLQ) and Tall and Skinny QR (TSQR) factorization
</p>
</li>
<li>
<p>
New interface for QR and LQ factorization is GEQR and GELQ
</p>
</li>
<li>
<p>
Corresponding Linear Least Squares / Minimum Norm solution driver (GETSLS)
</p>
</li>
</ul></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/cgelq.f SRC/dgelq.f SRC/sgelq.f SRC/zgelq.f
SRC/cgelqt.f SRC/dgelqt.f SRC/sgelqt.f SRC/zgelqt.f
SRC/cgelqt3.f SRC/dgelqt3.f SRC/sgelqt3.f SRC/zgelqt3.f
SRC/cgemlq.f SRC/dgemlq.f SRC/sgemlq.f SRC/zgemlq.f
SRC/cgemlqt.f SRC/dgemlqt.f SRC/sgemlqt.f SRC/zgemlqt.f
SRC/cgemqr.f SRC/dgemqr.f SRC/sgemqr.f SRC/zgemqr.f
SRC/cgeqr.f SRC/dgeqr.f SRC/sgeqr.f SRC/zgeqr.f
SRC/cgetsls.f SRC/dgetsls.f SRC/sgetsls.f SRC/zgetsls.f
SRC/clamswlq.f SRC/dlamswlq.f SRC/slamswlq.f SRC/zlamswlq.f
SRC/clamtsqr.f SRC/dlamtsqr.f SRC/slamtsqr.f SRC/zlamtsqr.f
SRC/claswlq.f SRC/dlaswlq.f SRC/slaswlq.f SRC/zlaswlq.f
SRC/clatsqr.f SRC/dlatsqr.f SRC/slatsqr.f SRC/zlatsqr.f
SRC/ctplqt.f SRC/dtplqt.f SRC/stplqt.f SRC/ztplqt.f
SRC/ctplqt2.f SRC/dtplqt2.f SRC/stplqt2.f SRC/ztplqt2.f
SRC/ctpmlqt.f SRC/dtpmlqt.f SRC/stpmlqt.f SRC/ztpmlqt.f</code></pre>
</div></div>
<div class="paragraph"><p>References:</p></div>
<div class="ulist"><ul>
<li>
<p>
Brian C. Gunter and Robert A. Van De Geijn, Parallel out-of-core computation
and updating of the QR factorization, ACM Transactions on Mathematical
Software, 31(1):60-78, 2005.
</p>
</li>
<li>
<p>
James Demmel, Laura Grigori, Mark Hoemmen, and Julien Langou.
Communication-Optimal Parallel and Sequential QR and LU Factorizations. SIAM J.
Scientific Computing, 34(1):A206—A239, 2012.
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_2_symmetric_indefinite_factorization_aasen_8217_s_tridiagonalization">2.2. Symmetric-indefinite Factorization: Aasen’s tridiagonalization</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Ichitaro Yamazaki (University of Tennessee).</p></div>
<div class="paragraph"><p>This is Aasen’s factorization for symmetric-indefinite factorization.</p></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/chesv_aa.f SRC/dsysv_aa.f SRC/ssysv_aa.f SRC/zhesv_aa.f
SRC/chetrf_aa.f SRC/dsytrf_aa.f SRC/ssytrf_aa.f SRC/zhetrf_aa.f
SRC/chetrs_aa.f SRC/dsytrs_aa.f SRC/ssytrs_aa.f SRC/zhetrs_aa.f
SRC/clahef_aa.f SRC/dlasyf_aa.f SRC/slasyf_aa.f SRC/zlahef_aa.f</code></pre>
</div></div>
<div class="paragraph"><p>References:</p></div>
<div class="ulist"><ul>
<li>
<p>
Miroslav Rozloznik, Gil Shklarski, and Sivan Toledo, Partitioned triangular
tridiagonalization, ACM Transactions on Mathematical Software,
37(4), article 38, 16 pages, 2011
</p>
</li>
<li>
<p>
Jan Ole Aasen, On the reduction of a symmetric matrix to tridiagonal form,
BIT, 11 (1971), pp. 233–242.
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_3_symmetric_indefinite_factorization_new_storage_format_for_l_factor_in_rook_pivoting_and_bunch_kaufman_of_ldlt">2.3. Symmetric-indefinite Factorization: New storage format for L factor in Rook Pivoting and Bunch Kaufman of LDLT</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Igor Kozachenko and Jim Demmel (UC Berkeley).</p></div>
<div class="paragraph"><p>This storage format is akin to LU and enables Level 3 BLAS TRS and TRI. Added
routines for new factorization code for symmetric indefinite ( or Hermitian
indefinite ) matrices with bounded Bunch-Kaufman ( rook ) pivoting algorithm.
New more efficient storage format for factors U (or L), block-diagonal matrix
D, and pivoting information stored in IPIV: factor L is stored explicitly in
lower triangle of A; diagonal of D is stored on the diagonal of A; subdiagonal
elements of D are stored in array E; IPIV format is the same as in *_ROOK
routines, but differs from SY Bunch-Kaufman routines (e.g. *SYTRF). The
factorization output of these new rook _RK routines is not compatible with the
existing _ROOK routines and vice versa. This new factorization format is
designed in such a way, that there is a possibility in the future to write new
Bunch-Kaufman routines that conform to this new factorization format. Then the
future Bunch-Kaufman routines could share solver *TRS_3,inversion *TRI_3 and
condition estimator *CON_3.</p></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/dsytf2_rk.f SRC/ssytf2_rk.f SRC/zsytf2_rk.f SRC/zhetf2_rk.f SRC/csytf2_rk.f SRC/chetf2_rk.f
SRC/dlasyf_rk.f SRC/slasyf_rk.f SRC/zlasyf_rk.f SRC/zlahef_rk.f SRC/clasyf_rk.f SRC/clahef_rk.f
SRC/dsytrf_rk.f SRC/ssytrf_rk.f SRC/zsytrf_rk.f SRC/zhetrf_rk.f SRC/csytrf_rk.f SRC/chetrf_rk.f
SRC/dsytrs_3.f SRC/ssytrs_3.f SRC/zsytrs_3.f SRC/zhetrs_3.f SRC/csytrs_3.f SRC/chetrs_3.f
SRC/dsycon_3.f SRC/ssycon_3.f SRC/zsycon_3.f SRC/zhecon_3.f SRC/csycon_3.f SRC/checon_3.f
SRC/dsytri_3.f SRC/ssytri_3.f SRC/zsytri_3.f SRC/zhetri_3.f SRC/csytri_3.f SRC/chetri_3.f
SRC/dsytri_3x.f SRC/ssytri_3x.f SRC/zsytri_3x.f SRC/zhetri_3x.f SRC/csytri_3x.f SRC/chetri_3x.f
SRC/dsysv_rk.f SRC/ssysv_rk.f SRC/zsysv_rk.f SRC/zhesv_rk.f SRC/csysv_rk.f SRC/chesv_rk.f</code></pre>
</div></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_4_symmetric_eigenvalue_problem_two_stage_algorithm_for_reduction_to_tridiagonal_form">2.4. Symmetric eigenvalue problem: Two-stage algorithm for reduction to tridiagonal form</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Azzam Haidar (University of Tennessee).</p></div>
<div class="paragraph"><p>This is the two-stage algorithm for reduction to tridiagonal form. Based on an algorithm from Lang.</p></div>
<div class="paragraph"><p>Added:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/chb2st_kernels.f SRC/dsb2st_kernels.f SRC/ssb2st_kernels.f SRC/zhb2st_kernels.f
SRC/chbev_2stage.f SRC/dsbev_2stage.f SRC/ssbev_2stage.f SRC/zhbev_2stage.f
SRC/chbevd_2stage.f SRC/dsbevd_2stage.f SRC/ssbevd_2stage.f SRC/zhbevd_2stage.f
SRC/chbevx_2stage.f SRC/dsbevx_2stage.f SRC/ssbevx_2stage.f SRC/zhbevx_2stage.f
SRC/cheev_2stage.f SRC/dsyev_2stage.f SRC/ssyev_2stage.f SRC/zheev_2stage.f
SRC/cheevd_2stage.f SRC/dsyevd_2stage.f SRC/ssyevd_2stage.f SRC/zheevd_2stage.f
SRC/cheevr_2stage.f SRC/dsyevr_2stage.f SRC/ssyevr_2stage.f SRC/zheevr_2stage.f
SRC/cheevx_2stage.f SRC/dsyevx_2stage.f SRC/ssyevx_2stage.f SRC/zheevx_2stage.f
SRC/chegv_2stage.f SRC/dsygv_2stage.f SRC/ssygv_2stage.f SRC/zhegv_2stage.f
SRC/chetrd_2stage.f SRC/dsytrd_2stage.f SRC/ssytrd_2stage.f SRC/zhetrd_2stage.f
SRC/chetrd_hb2st.F SRC/dsytrd_sb2st.F SRC/ssytrd_sb2st.F SRC/zhetrd_hb2st.F
SRC/chetrd_he2hb.f SRC/dsytrd_sy2sb.f SRC/ssytrd_sy2sb.f SRC/zhetrd_he2hb.f
SRC/clarfy.f SRC/dlarfy.f SRC/slarfy.f SRC/zlarfy.f</code></pre>
</div></div>
<div class="paragraph"><p>References:</p></div>
<div class="ulist"><ul>
<li>
<p>
Christian H. Bischof, Bruno Lang, and Xiaobai Sun, A framework for symmetric
band reduction, ACM Transactions on Mathematical Software, 26(4): 581-601,
2000.
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_5_improved_complex_jacobi_svd">2.5. Improved Complex Jacobi SVD</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Zlatko Drmac (University of Zagreb).</p></div>
<div class="paragraph"><p>(1) LWORK query added; (2) few modifications in pure one sided Jacobi (XGESVJ)
to remove possible error in the really extreme cases (sigma_max close to
overflow and sigma_min close to underflow) - note that XGESVJ is designed to
compute the singular values in the full range; it was used (double complex) to
compute SVD of certain factored Hankel matrices with the condition number
1.0e616; (3) <code>same</code> modifications in the preconditioned Jacobi SVD (XGEJSV),
the idea is also to extend the computational range, this brings assumptions on
how other lapack routines behave under those extreme conditions.</p></div>
<div class="paragraph"><p>Modified:</p></div>
<div class="literalblock">
<div class="content">
<pre><code>SRC/cgejsv.f SRC/zgejsv.f
SRC/cgesvj.f SRC/zgesvj.f
SRC/cgsvj0.f SRC/zgsvj0.f
SRC/cgsvj1.f SRC/zgsvj1.f</code></pre>
</div></div>
</div>
</div>
<div class="sect1">
<h2 id="_2_6_lapacke_interfaces">2.6. LAPACKE interfaces</h2>
<div class="sectionbody">
<div class="paragraph"><p>A contribution from Julie Langou (University of Tennessee).</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_3_developer_list">3. Developer list</h2>
<div class="sectionbody">
<div class="ulist"><div class="title">External Contributors</div><ul>
<li>
<p>
Konstantin Arturov, Intel
</p>
</li>
<li>
<p>
Eugene Chereshnev, Intel
</p>
</li>
<li>
<p>
Zlatko Drmac, University of Zagreb
</p>
</li>
</ul></div>
<div class="ulist"><div class="title">LAPACK developers involved in this release</div><ul>
<li>
<p>
Mark Gates (University of Tennessee)
</p>
</li>
<li>
<p>
Syd Hashemi Ghermezi (UC Berkeley)
</p>
</li>
<li>
<p>
Azzam Haidar (University of Tennessee)
</p>
</li>
<li>
<p>
Igor Kozachenko (University of California, Berkeley, USA)
</p>
</li>
<li>
<p>
Julie Langou (University of Tennessee, USA)
</p>