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<html>
<head>
<title>LAPACK FAQ</title>
</head>
<body>
<center>
<h1> LAPACK Frequently Asked Questions (FAQ) </h1>
<h2>
<i>
<a href="mailto:lapack@cs.utk.edu"><address>lapack@cs.utk.edu</address></a>
</i>
</h2>
</center>
<p>
<IMG SRC="http://www.netlib.org/scalapack/html/gif/blue.gif"></p>
<p>
<i>
Many thanks to the <a href="http://www.netlib.org/utk/icl/maintainers.html">
netlib_maintainers@netlib.org</a> from whose FAQ list I have patterned
this list for LAPACK.
</i>
</p>

<p>
<IMG SRC="http://www.netlib.org/scalapack/html/gif/blue.gif"></p>

<h2>
Table of Contents
</h2>

<dl>
<dd>LAPACK
   <dl>
    <a href="#1.1"> <dd>1.1)  What is LAPACK?</a>
    <a href="#1.2"> <dd>1.2)  Are there legal restrictions on the use of LAPACK software?</a>
    <a href="#1.3"> <dd>1.3)  How do I reference LAPACK in a scientific publication?</a>
    <a href="#1.4"> <dd>1.4)  What revisions have been made since the last release?</a>
    <a href="#1.5"> <dd>1.5)  When is the next scheduled release of LAPACK?</a>
    <a href="#1.6"> <dd>1.6)  Where can I find out more information about LAPACK?</a>
    <a href="#1.7"> <dd>1.7)  Where can I find Java LAPACK?</a>
    <a href="#1.8"> <dd>1.8)  How do I obtain a copy of the LAPACK Users' Guide?</a>
    <a href="#1.9"> <dd>1.9)  Why aren't BLAS routines included when I download an LAPACK routine?</a>
    <a href="#1.10"> <dd>1.10)  Are prebuilt LAPACK libraries available?</a>
    <a href="#1.11"> <dd>1.11)  Are prebuilt LAPACK libraries (lib and dll) available for Windows?</a>
    <a href="#1.12"> <dd>1.12)  Is there an LAPACK rpm available for RedHat Linux?</a>
    <a href="#1.13"> <dd>1.13)  Is there an LAPACK deb file available for Debian Linux?</a>
    <a href="#1.14"> <dd>1.14)  How do I install LAPACK under Windows 98/NT?</a>
    <a href="#1.15"> <dd>1.15)  What is the naming scheme for LAPACK routines?</a>
    <a href="#1.16"> <dd>1.16)  How do I find a particular routine?</a>
    <a href="#1.17"> <dd>1.17)  Are there routines in LAPACK to compute determinants?</a>
    <a href="#1.18"> <dd>1.18)  Are there routines in LAPACK for the complex symmetric eigenproblem?</a>
    <a href="#1.19"> <dd>1.19)  Why aren't auxiliary routines listed on the index?</a>
    <a href="#1.20"> <dd>1.20)  I can't get a program to work.  What should I do?</a>
    <a href="#1.21"> <dd>1.21)  How can I unpack lapack.tgz?</a>
    <a href="#1.22"> <dd>1.22)  Where do I find details of the LAPACK Test Suite?</a>
    <a href="#1.23"> <dd>1.23) What technical support for LAPACK is available?</a>
    <a href="#1.24"> <dd>1.24) How do I interpret LAPACK testing failures?</a>
    <a href="#1.25"> <dd>1.25) Problems running the BLAS test suite with an optimized BLAS library?</a>
    <a href="#1.26"> <dd>1.26) Problems compiling dlamch.f?</a>
   </dl>
<p>
<p>
<dd>BLAS
   <dl>
    <a href="#2.1"> <dd>2.1)  What and where are the BLAS?</a>
    <a href="#2.2"> <dd>2.2)  Publications/references for the BLAS?</a>
    <a href="#2.3"> <dd>2.3)  Is there a Quick Reference Guide to the BLAS available?</a>
    <a href="#2.4"> <dd>2.4)  Are optimized BLAS libraries available?</a>
    <a href="#2.5"> <dd>2.5)  What is ATLAS?</a>
    <a href="#2.6"> <dd>2.6)  Where can I find vendor supplied BLAS?</a>
    <a href="#2.7"> <dd>2.7)  Where can I find the Intel BLAS for Windows NT?</a>
    <a href="#2.8"> <dd>2.8)  Where can I find Java BLAS?</a>
    <a href="#2.9"> <dd>2.9)  Is there a C interface to the BLAS?</a>
    <a href="#2.10"> <dd>2.10)  Are prebuilt Fortran77 ref implementation BLAS lib
raries available from Netlib?</a>
   </dl>
</dl>

<p>
<IMG SRC="http://www.netlib.org/scalapack/html/gif/blue.gif"></p>
<h2>
1)  LAPACK 
</h2>

<p>
<strong>
<a name="1.1">
    1.1) What is LAPACK?  <br>
</a>
</strong>

<p>
<B>LAPACK</B> 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>
 
<B>Release 3.0 of LAPACK</B> introduces new routines, as well as extending
the functionality of existing routines.  For detailed information
on the revisions, please refer to <a href="http://www.netlib.org/lapack/revisions.info">revisions.info</a>.
<p>
<ul>
<li>
<a href="http://www.netlib.org/lapack/lug/lapack_lug.html">LAPACK Users' Guide, Third Edition</a>
</ul>
<p>
 
The original goal of the <B>LAPACK</B> project was to make the widely
used <a href="http://www.netlib.org/eispack/">EISPACK</a> and
<a href="http://www.netlib.org/linpack/">LINPACK</a> 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>
LAPACK routines are written so that as much as possible of the computation
is performed by calls to the <a href="http://www.netlib.org/blas/">Basic Linear Algebra Subprograms (BLAS)</a>.
While LINPACK and EISPACK are based on the vector operation kernels
of the Level 1 BLAS, LAPACK was 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>
Highly efficient machine-specific implementations of the BLAS are
available for many modern high-performance computers. The BLAS
enable LAPACK routines to achieve high performance with transportable
software.
Although a model Fortran implementation of the BLAS in available
from netlib in the <a href="http://www.netlib.org/blas/">BLAS library</a>,
it is not expected to perform as well as a specially
tuned implementation on most high-performance computers -- on some
machines
it may give much worse performance -- but it allows users to run LAPACK
software on machines that do not offer any other implementation of the
BLAS.
<p>
<strong>
<a name="1.2">
    1.2)  Are there legal restrictions on the use of LAPACK software?<br>
</a>
</strong>

<p>
LAPACK is a freely-available
software package.  It is available from netlib via anonymous ftp and
the World Wide Web.  Thus, it can be included in commercial
software packages (and has been).
We only ask that proper credit be given to the authors.</p>
<p> 
Like all software, it is copyrighted.  It is not trademarked, but we do
ask the following:</p>
<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>
<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>

<p>
<strong>
    <a name="1.3">
        1.3) How do I reference LAPACK in a scientific publication?<br>
</a>
</strong>
<p>
We ask that you cite the LAPACK Users' Guide, Third Edition.
</p>
<pre>
@BOOK{laug,
      AUTHOR = {Anderson, E. and Bai, Z. and Bischof, C. and
                Blackford, S. and Demmel, J. and Dongarra, J. and
                Du Croz, J. and Greenbaum, A. and Hammarling, S. and
                McKenney, A. and Sorensen, D.},
      TITLE = {{LAPACK} Users' Guide},
      EDITION = {Third},
      PUBLISHER = {Society for Industrial and Applied Mathematics},
      YEAR = {1999},
      ADDRESS = {Philadelphia, PA},
      ISBN = {0-89871-447-8 (paperback)} }
</pre>

<p>
<strong>
<a name="1.4">
    1.4)  What revisions have been made since the last release? <br>
</a>
</strong>

<p>
For detailed information on the revisions since the previous public
release, please refer to
<a href="http://www.netlib.org/lapack/release_notes.html">release_notes.html</a>.

<p>
<strong>
<a name="1.5">
    1.5)  When is the next scheduled release of LAPACK? <br>
</a>
</strong>

<p>
<B>LAPACK, version 3.0</B> was announced June 30, 1999.  The
update to this release <a href="http://www.netlib.org/lapack/update.tgz">update.tgz</a> was posted to netlib in November, 1999.<br> 
The most significant new routines are:</p>
<ol>

 <li> a faster singular value decomposition (SVD),
    computed by divide-and-conquer (xGESDD)
 <li> faster routines for solving rank-deficient least squares problems:
     <ul>
     <li>  using QR with column pivoting (xGELSY, based on xGEQP3)
     <li>  using the SVD based on divide-and-conquer (xGELSD)
     </ul>
 <li> new routines for the generalized symmetric eigenproblem:
     <ul>
     <li> xHEGVD/xSYGVD, xHPGVD/xSPGVD, xHBGVD/xSBGVD: faster routines
          based on divide-and-conquer
     <li> xHEGVX/xSYGVX, xHPGVX/xSPGVX, xHBGVX/xSBGVX: routines based on
          bisection/inverse iteration, for computing part of the spectrum
     </ul>
 <li> faster routine for the symmetric eigenproblem using "relatively robust
    eigenvector algorithm" (xSTEGR, xSYEVR/xHEEVR, SSTEVR)
 <li> new simple and expert drivers for the generalized nonsymmetric
    eigenproblem (xGGES,xGGEV,xGGESX,xGGEVX), including error bounds
 <li> solver for generalized Sylvester equation (xTGSYL), used in 5)
 <li> computational routines (xTGEXC, xTGSEN, xTGSNA) used in 5))
 <li> a blocked version of xTZRQF (xTZRZF), and associated xORMRZ/xUNMRZ
</ol>
<p>
The <B>LAPACK Users' Guide, Third Edition</B> is available from SIAM,
as well as in HTML form, <a href="http://www.netlib.org/lapack/lug/lapack_lug.html">LAPACK Users' Guide, Third Edition</a>.

<p>
<strong>
<a name="1.6">
    1.6)  Where can I find more information about LAPACK?<br>
</a>
</strong>

<p>
A variety of working notes related to the development of the
LAPACK library were published as LAPACK Working Notes and are
available in postscript or pdf format at:
<dl>
<dd><a href="http://www.netlib.org/lapack/lawns/index.html"><address>http://www.netlib.org/lapack/lawns/</address></a>
<dd><a href="http://www.netlib.org/lapack/lawnspdf/index.html"><address>http://www.netlib.org/lapack/lawnspdf/</address></a>
</dl>

<p>
<strong>
<a name="1.7">
    1.7)  Where can I find Java LAPACK?<br>
</a>
</strong>

<p>
The first public release of the Java LAPACK (version 0.3 beta) is available
for download at the following URL:

<dl>
<dd><a href="http://www.netlib.org/java/f2j/"><address>http://www.netlib.org/java/f2j/</address></a>
</dl>
The <a href="http://math.nist.gov/javanumerics/">JavaNumerics</a>
webpage provides a focal point for information
on numerical computing in Java!

</p>

<p>
<strong>
<a name="1.8">
    1.8)  How do I obtain a copy of the LAPACK Users' Guide?<br>
</a>
</strong>

<p>
An html version of the <a href="http://www.netlib.org/lapack/lug/lapack_lug.html"><B>LAPACK Users' Guide</B></a> is available for viewing on netlib.</p>
<p>
The printed version of the <b>LAPACK Users' Guide, Third Edition</b> is
available from SIAM (Society for Industrial and Applied Mathematics).
The list price is $39.00 and the SIAM
Member Price is $31.20.  The order code for the book is <b>SE09</b>.
Contact SIAM for additional information.</p>
<p>
<ul>
<li><a href="http://www.siam.org/"><address>http://www.siam.org/</address></a>.
<li><a href="mailto:service@siam.org"><address>service@siam.org</address></a>
<li>fax: 215-386-7999
<li>phone: (USA) 800-447-SIAM
<li>(outside USA) 215-382-9800
<li>mail: SIAM, Customer Service, P. O. Box 7260, Philadelphia, PA 19104.
</ul>
<P>
 
<P>
The royalties from the sales of this book are being placed in a fund
to help students attend SIAM meetings and other SIAM related activities.
This fund is administered by SIAM and qualified individuals are encouraged to
write directly to SIAM for guidelines.
<p>

<p>
<strong>
<a name="1.9">
    1.9) Why aren't BLAS routines included when I download an LAPACK routine?<br>
</a>
</strong>

<p>
It is assumed that you have a machine-specific optimized <b>BLAS</b> library
already available on the architecture to which you are installing
<b>LAPACK</b>.  If this is not the case, you can download a
<a href="http://www.netlib.org/blas/blas.shar">Fortran77 reference implementation of the BLAS</a> from netlib.
<p>
Although a model implementation of the BLAS in available
from netlib in the <a href="http://www.netlib.org/blas/">blas directory</a>,
it is not expected to perform as well as a specially
tuned implementation on most high-performance computers -- on some machines
it may give much worse performance -- but it allows users to run LAPACK
software on machines that do not offer any other implementation of the
BLAS.</p>
<p>
Alternatively, you can automatically generate an optimized BLAS library for
your machine, using ATLAS <a href="http://www.netlib.org/atlas/"><address>http://www.netlib.org/atlas/</address></a>.

<p>
<strong>
<a name="1.10">
    1.10)  Are prebuilt LAPACK libraries available?<br>
</a>
</strong>

<p>
Yes, prebuilt LAPACK libraries are available for a variety
of architectures.  Refer to
<dl>
<dd><a href="http://www.netlib.org/lapack/archives/">
<address>http://www.netlib.org/lapack/archives/</address></a>
</dl>
for a complete list of available prebuilt libraries.

<p>
<strong>
<a name="1.11">
    1.11)  Are prebuilt LAPACK libraries (lib and dll) available for Windows?<br>
</a>
</strong>

<p>
Yes, refer to the
<a href="http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/matlisp/matlisp/lib/"><address>http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/matlisp/matlisp/lib/</address></a> 
webpage for details.

<p>
<strong>
<a name="1.12">
    1.12)  Is there an LAPACK rpm available for RedHat Linux?<br>
</a>
</strong>

<p>
Yes!  Refer to the <a href="http://www.netlib.org/lapack/rpms/"><address>http://www.netlib.org/lapack/rpms</address></a> directory on netlib for the
LAPACK rpms for RedHat Linux.
</p>

<p>
<strong>
<a name="1.13">
    1.13)  Is there an LAPACK deb file available for Debian Linux?<br>
</a>
</strong>

<p>
Yes!  Refer to <a href="http://www.debian.org/Packages/frozen/libs/lapack.html">LAPACK deb file for Debian Linux</a>.
</p>
<p>
<strong>
<a name="1.14">
    1.14)  How do I install LAPACK under Windows 98/NT?<br>
</a>
</strong>

<p>
Separate zip files are available for installation using Digital Fortran
or Watcom Fortran 77/32 compiler version 11.0.  Both zip files use
Microsoft <i>nmake</i>.
Refer to the <a href="http://www.netlib.org/lapack/lapack-pc-df.zip">lapack-pc-df.zip</a> or
<a href="http://www.netlib.org/lapack/lapack-pc-wfc.zip">lapack-pc-wfc.zip</a>
files on the lapack index.
<p>
Otherwise,
the lapack.tgz distribution file requires unix-style make and /bin/sh commands in order to install on a 
Windows system.  A fairly complete unix-style environment is available free of
charge at the cygnus website,<br>
   <a href="http://sourceware.cygnus.com/cygwin/"><address>http://sourceware.cygnus.com/cygwin/</address></a>
</p>
<p>
From this website, you can download the package, get installation instructions,
etc.  You will want to download the "full" version of cygwin, which includes
compilers, shells, make, etc.  You will need to download the fortran compiler
separately.
</P>
<P>
The installation is quite simple, involving downloading an executable and
installing with Windows' usual install procedure (you can remove it from
your machine with Windows' ADD/REMOVE if you later decide you don't want it).
</P>
<P>
<CENTER>
IMPORTANT: 
</CENTER>
<P>
Windows 95/98 does a poor job of process load balance.  If you change
the focus from the cygnus window, performance will immediately drop by
at least 1/3, and the timings will be inaccurate.  When doing timings, it is
recommended that you leave the focus on the window throughout the entire
timing suite.
This is not necessary for Windows NT.
</P>
<P>
Because people often miss them in the install instructions, I repeat two
very important pieces of information about the cygnus install here:
</P>
<P>
<OL>
<LI>
<PRE>
If, after installing cygnus, you get the message:
    Out of environment space
add the line 
    shell=C:\command.com /e:4096 /p
to your c:\config.sys
</PRE>
<LI>
<PRE>
For installation, LAPACK needs to find /bin/sh, so you should (assuming you
don't already have this directory made):
   mkdir -p /bin
Then, you should copy sh.exe from the cygwin bin directory to this one.
The location of the cygwin bin directory changes depending on where you
did the install, what type of machine you have, and the version of cygnus.
Here is an example:
    /cygnus/cygwin-b20/H-i586-cygwin32/bin
the cygwin-b20 is a version number, so you might see cygwin-b21, if you have
a newer release, for instance.  The i586 refers to your processor, you might
expect to see i386, i486, i586 or i686, for instance.
</PRE>
</OL>
<UL>
<LI> <b>NOTE:</b>
Gnu g77 and gcc provide better performance than MSVC++ (Digital Fortran) 
(or Watcom F77 or C), so we recommend that you use g77 and gcc.
<LI> <b>NOTE:</b>
Be careful.  Many PC compilers often perform optimization by default at
compile time!  Thus, for routines such as LAPACK/SRC/slamch.f and
LAPACK/SRC/dlamch.f, you will need to explicitly set a compile flag to
turn OFF optimization.
<LI> <b>NOTE:</b>
Be aware that Microsoft <i>nmake</i> and Watcom <i>wmake</i> contain only
a subset of the functionality of unix-style make.  Therefore, if you choose
to use this form of <i>make</i>, you will need to simply the makefiles.  In
the future, these makefiles may be made available.
<LI> <b>NOTE:</b>
Timing functions and Windows 98/NT...  You will need to modify the
LAPACK/INSTALL/second.f and dsecnd.f to call <b>clock()</b>, as there
are no sophisticate timing functions available.  Many users have written
their own timing functions for Windows 98/NT applications.
<LI> <b>NOTE:</b>
An optimized BLAS library for Windows on an Intel Pentium is available.
Refer to the <a href="http://www.netlib.org/blas/faq.html">BLAS FAQ</a>
for further details.
</UL>
<p>
<strong>
<a name="1.15">
    1.15)  What is the naming scheme for LAPACK routines?<br>
</a>
</strong>

<p>
The name of each LAPACK routine is a coded specification of
its function (within the very tight limits of standard Fortran 77
6-character names).</p>
<p>
All driver and computational routines have names of the form <b>XYYZZZ</b>,
where for some driver routines the 6th character is blank.
<p> 
The first letter, <b>X</b>, indicates the data type as follows:
</p>
<pre> 
    S  REAL
    D  DOUBLE PRECISION
    C  COMPLEX
    Z  COMPLEX*16  or DOUBLE COMPLEX
</pre> 
<p>
The next two letters, <b>YY</b>, indicate the type of matrix (or of the most
significant matrix).  Most of these two-letter codes apply to both real
and complex matrices; a few apply specifically to one or the other.
<p> 
The last three letters <b>ZZZ</b> indicate the computation performed.
For example, SGEBRD is a single precision routine that performs a
bidiagonal reduction (BRD) of a real general matrix.</p>

<p>
<strong>
<a name="1.16">
    1.16)  How do I find a particular routine?<br>
</a>
</strong>

<p>
Indexes of individual LAPACK driver and computational routines
are available.  These indexes contain brief descriptions of each
routine.

<p>
<B>LAPACK</B> routines are available in four types:  <B>single precision
real</B>, <B>double precision real</B>, <B>single precision complex</B>, and
<B>double precision complex</B>.</P>
<UL>
<LI><a href="http://www.netlib.org/lapack/single/index.html">Index of LAPACK Single Precision REAL Routines</a>.
<LI><a href="http://www.netlib.org/lapack/double/index.html">Index of LAPACK Double Precision REAL Routines</a>.
<LI><a href="http://www.netlib.org/lapack/complex/index.html">Index of LAPACK Single Precision COMPLEX Routines</a>.
<LI><a href="http://www.netlib.org/lapack/complex16/index.html">Index of LAPACK Double Precision COMPLEX Routines</a>.
</UL>
<p>
<i>NOTE:  For brevity, LAPACK auxiliary routines are NOT listed on
these indexes of routines. </i></p>

<p>
<strong>
<a name="1.17">
    1.17)  Are there routines in LAPACK to compute determinants?<br>
</a>
</strong>

<p>
No.  There are no routines in LAPACK to compute determinants.  This
is discussed in the "Accuracy and Stability" chapter in the
<a href="http://www.netlib.org/lapack/lug/lapack_lug.html">LAPACK Users'
Guide</a>.

<p>
<strong>
<a name="1.18">
    1.18)  Are there routines in LAPACK for the complex symmetric eigenproblem?<br>
</a>
</strong>

<p>
About your question on the eigenvalue problem
of a pair of complex symmetric matrices, there
is no public domain software I know of for
solving this problem directly. Three closest references are:<br>
<ol>
<li> in QMRpack (your can access it from www.netlib.org)
     there is a Lanczos method for finding
     a few eigenvalues/eigenvectors by exploring
     the complex symmetric structure. 
<li> Back to few years ago, J. Cullum and ... published
    a paper on using QR iteration to find all eigenvalues
    and eigenvectors of a complex symmtric tridiagonal 
    matrix. The paper was published in SIAM J. Matrix Analysis 
    and Applications. 
<li> A couple of years ago, Bar-on published a paper in 
    SIAM J. of Sci. Comp. for full dense complex symmetric
    eigenvalue problems. He discussed how to use a variant of
     Householder reduction for tridiagonalization. 
</ol>
<p>    
All these approaches try to explore the symmetric structure
for saving in CPU time and storage. However, since there is
no particular mathematical properties we can explore in a complex
symmetric system, all above mentioned approaches are potentially
numerical unstable! This also reflects why there is no 
high quality (black-box) math. software available. 


<p>
<strong>
<a name="1.19">
    1.19)  Why aren't auxiliary routines listed on the index?<br>
</a>
</strong>

<p>
<i>For brevity, LAPACK auxiliary routines are not listed on
the indexes of routines. </i></p>
<p>
However, the routines are contained in the
respective directories on netlib.  If you download a routine with
dependencies, these auxiliary routines should be included with your
request.  Or, if for some reason you wish to obtain an individual
auxiliary routine, and you already know the name of the routine,
you can request that routine.  For example, if I would like to 
obtain <i>dlacpy.f</i>, I would connect to the URL:</p>
<pre>
   http://www.netlib.org/lapack/double/dlacpy.f
</pre>


<p>
<strong>
<a name="1.20">
    1.20) I can't get a program to work.  What should I do?<br>
</a>
</strong>

<p>
Technical questions should be directed to the authors at
<a href="mailto:lapack@cs.utk.edu"><address>lapack@cs.utk.edu.</address></a></p>
<p>
Please tell us the type of machine on
which the tests were run, the compiler and compiler options that
were used, details of the BLAS library that was used, and a copy of
the input file if appropriate.</p>
<p>
Be prepared to answer the following questions:</p>
<ol>
<li> Have you run the BLAS and LAPACK test suites?
<li> Have you checked the errata list on netlib?
     <ul>
     <li> <a href="http://www.netlib.org/lapack/release_notes.html">release_notes.html</a>
     </ul>
<li> If you are using an optimized BLAS library, have you tried
     using the reference implementation from netlib?
</ol>
Machine-specific installation hints can be found in <a href="http://www.netlib.org/lapack/release_notes.html">release_notes.html</a>, as well as the <a href="http://www.netlib.org/lapack/lawns/lawn81.ps">Quick Installation Guide</a>.  

<p>
<strong>
<a name="1.21">
    1.21) How can I unpack lapack.tgz?<br>
</a>
</strong>

<p>
<pre>
   gunzip -c lapack.tgz | tar xvf -
</pre>

<p>
The compression program <i>gzip (and gunzip)</i> is Gnu software.  If
it is not already available on your machine, you can download it 
via <i>anonymous ftp</i>:</p>
<pre>
   ncftp prep.ai.mit.edu
   cd pub/gnu/
   get gzip-1.2.4.tar
</pre>

<p>
<strong>
<a name="1.22">
    1.22) Where do I find details of the LAPACK Test Suite and Timing Suite?<br>
</a>
</strong>

<p>
Full details of the LAPACK Test Suite and Timing Suite can be found in
LAPACK Working Note 41:  "Installation Guide to LAPACK" available via the
URL:
<ul>
<li><a href="http://www.netlib.org/lapack/lawns/lawn41.ps">LAPACK Working Note 41</a>.
</ul>

<p>
<strong>
<a name="1.23">
    1.23) What technical support for LAPACK is available?<br>
</a>
</strong>

<p>
Technical questions and comments should be directed to the authors at
<a href="mailto:lapack@cs.utk.edu"><address>lapack@cs.utk.edu.</address></a>
<p>
See <a href="#1.20">Question 1.20</a>

<p>
<strong>
<a name="1.24">
    1.24) How do I interpret LAPACK testing failures?<br>
</a>
</strong>

<p>
Installation hints for various architectures are maintained in
the <a href="http://www.netlib.org/lapack/release_notes.html">http://www.netlib.org/lapack/release_notes.html</a> file on netlib.  Click on "Machine-Specific
Installation Hints".</p>
<p>
The only known testing failures are in condition number estimation
routines in the generalized nonsymmetric eigenproblem testing.  
Specifically in <b>sgd.out</b>, <b>dgd.out</b>, <b>cgd.out</b> and
<b>zgd.out</b>. The cause for 
the failures of some test cases is that the mathematical algorithm 
used for estimating the condition numbers could over- or under-estimate
the true values in a certain factor in some rare cases.  Further
details can be found in <a href="http://www.netlib.org/lapack/lawns/lawn87.ps">LAPACK Working Note 87</a>. </p>
<p>
In addition, LAPACK, version 3.0, introduced new routines which
rely on IEEE-754 compliance.  Refer to the <a href="http://www.netlib.org/lapack/lawns/lawn41.ps">Installation Guide</a> for complete details.  As
a result, two settings were added to LAPACK/SRC/ilaenv.f to denote
IEEE-754 compliance for NaN and infinity arithmetic, respectively.
By default, ILAENV assumes an IEEE machine and does a test for
IEEE-754 compliance.  If you are installing LAPACK on a non-IEEE
machine, you MUST modify ILAENV, as this test inside ILAENV will
crash!  Note that there are also specialized testing/timing versions
of ILAENV located in LAPACK/TESTING/LIN/, LAPACK/TESTING/EIG/, 
LAPACK/TIMING/LIN/, and LAPACK/TIMING/EIG/, that must also be
modified.  Be aware that some compilers have IEEE-754 compliance
by default, and some compilers require a separate compiler flag.
</p> 
Testing failures can be divided into two categories.  <i>Minor</i> testing
failures, and <i>major</i> testing failures.  
</p>
<p>
A <i>minor</i> testing failure is one in which the test ratio reported
in the LAPACK/TESTING/*.out file slightly exceeds the threshold (specified 
in the associated LAPACK/TESTING/*.in file).  The cause of such failures
can mainly be attributed to differences in the implementation of math
libraries (square root, absolute value, complex division, complex absolute
value, etc).  These failures are negligible, and do not affect the
proper functioning of the library.
</p>
<p>
A <i>major</i> testing failures is one in which the test ratio reported
in the LAPACK/TESTING/*.out file is on the order of E+06.  This type
of testing failure should be investigated.  For a complete discussion
of the comprehensive LAPACK testing suite, please refer to
<a href="http://www.netlib.org/lapack/lawns/lawn41.ps">LAPACK Working Note 41</a>.  When a
testing failure occurs, the output in the LAPACK/TESTING/*.out file will
tell the user which test criterion failed and for which type of matrix.
It is important to note if the error only occurs with a specific
matrix type, a specific precision, a specific test criterion, and 
the number of tests failed.
There can be several possible causes of such failures:</p>
<ul>
<li>compiler optimization bug
<li>bug in the optimized BLAS library
<li>bug in an LAPACK routine
</ul>
<p>
The first question/suggestion is, if you are using an optimized BLAS library,
did you run the BLAS test suite?  Also, have you tried linking to the
reference implementation BLAS library to see if the error disappears?
There is a reference implementation BLAS library included with the
LAPACK distribution.  This type of problem will typically cause a lot
of test failures for only a specific matrix type.</p>
<p>
A compiler optimization bug will typically also cause a lot of 
test failures for only a specific matrix type.  If a compiler 
optimization problem is suspected, the user should recompile 
the entire library with no optimization and see if the error
disappears.  If the error disappears, then the user will need to pinpoint
which routine causes the optimization problem.  This search can
be narrowed by noticing which precision caused the error and for
which matrix type.
</p>
<p> In some rare cases, naive implementations
of functions such as complex absolute value and complex division can
result in <i>major</i> testing failures.  Refer to the discussion of
the LAPACK/SRC/slabad.f and dlabad.f routines to restrict the range
of representable numbers to be used in testing (<a href="http://www.netlib.org/lapack/lawns/lawn41.ps">LAPACK Working Note 41</a>).
</p>
<p>
An isolated test failure that is not affected by the level of optimization
or the BLAS library used, should be reported to the authors
<a href="mailto:lapack@cs.utk.edu"><address>lapack@cs.utk.edu.</address></a>.
</p>

<p>
Installation hints for various architectures are maintained in
the <a href="http://www.netlib.org/lapack/release_notes.html">http://www.netlib.org/lapack/release_notes.html</a> file on netlib.  Click on "Machine-Specific
Installation Hints".</p>

<p>
<strong>
<a name="1.25">
    1.25) Problems running the BLAS test suite with an optimized BLAS library?<br>
</a>
</strong>
<p>
If you encounter difficulties running the BLAS Test Suite with an
optimized BLAS library, it may be that you need to disable "input
error checking" in the BLAS Test Suite.  Most optimized BLAS 
libraries do NOT perform input error checking.  To disable
"input error checking" in the BLAS testers, you need to modify
line 7 of the data files LAPACK/BLAS/*blat2.in and LAPACK/BLAS/*blat3.in by
setting the "T" to "F".
<pre>
F        LOGICAL FLAG, T TO TEST ERROR EXITS.
</pre>
</p>

<p>
<strong>
<a name="1.26">
    1.26) Problems compiling dlamch.f?<br>
</a>
</strong>
<p>
The routine dlamch.f (and its dependent subroutines dlamc1, dlamc2,
dlamc3, dlamc4, dlamc5) MUST be compiled without optimization.
If you downloaded the entire lapack distribution this will be
taken care of by the LAPACK/SRC/Makefile.  However, if you downloaded
a specific LAPACK routine plus dependencies, you need to take care
that slamch.f (if you downloaded a single precision real or 
single precision complex routine) or dlamch.f (if you downloaded
a double precision real or double precision complex routine) has
been included.
</p>

<p>
<IMG SRC="http://www.netlib.org/scalapack/html/gif/blue.gif"></p>
<h2>
2)  BLAS 
</h2>

<p>
<strong>
<a name="2.1">
    2.1) What and where are the BLAS?<br>
</a>
</strong>

<p>
The BLAS (Basic Linear Algebra Subprograms) are high quality
"building block" routines for performing basic vector and matrix
operations.  Level 1 BLAS do vector-vector operations, Level 2
BLAS do matrix-vector operations, and Level 3 BLAS do
matrix-matrix operations.  Because the BLAS are efficient,
portable, and widely available, they're commonly used in the
development of high quality linear algebra software,
<a href="http://www.netlib.org/linpack/">LINPACK</a> and
<a href="http://www.netlib.org/lapack/">LAPACK</a> for example.  
<p>
A Fortran77 reference implementation of the BLAS is located in the
<a href="http://www.netlib.org/blas/">blas directory</a> of Netlib.

<p>
<strong>
<a name="2.2">
    2.2) Publications/references for the BLAS?<br>
</a>
</strong>

<p>
<ol>
<li>
C. L. Lawson, R. J. Hanson, D. Kincaid, and F. T. Krogh, <i>Basic
Linear Algebra Subprograms for FORTRAN usage</i>, <a href="http://www.acm.org/toms/V5.html#v5n3">ACM Trans. Math.
Soft., 5 (1979)</a>, pp. 308--323.<p>

<li>
J. J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson, <i>An
extended set of FORTRAN Basic Linear Algebra Subprograms</i>, <a href="http://www.acm.org/toms/V14.html">ACM Trans.
Math. Soft., 14 (1988)</a>, pp. 1--17.<p>

<li>
J. J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson,
<i>Algorithm 656: An extended set of FORTRAN Basic Linear Algebra
Subprograms</i>, <a href="http://www.acm.org/toms/V14.html">ACM Trans. Math. Soft., 14 (1988)</a>, pp. 18--32.<p>

<li>
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, <i>A set of
Level 3 Basic Linear Algebra Subprograms</i>, <a href="http://www.acm.org/toms/V16.html">ACM Trans. Math. Soft.,
16 (1990)</a>, pp. 1--17.<p>

<li>
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, <i>Algorithm
679: A set of Level 3 Basic Linear Algebra Subprograms</i>, <a href="http://www.acm.org/toms/V16.html">ACM Trans.
Math. Soft., 16 (1990)</a>, pp. 18--28.<p>
</ol>

<p>
<strong>
<a name="2.3">
    2.3)  Is there a Quick Reference Guide to the BLAS available?<br>
</a>
</strong>
 
<p>
Yes, there is a postscript version of the <a href="http://www.netlib.org/blas/blasqr.ps">Quick Reference Guide to the BLAS</a> available.

<p>
<strong>
<a name="2.4">
    2.4)  Are optimized BLAS libraries available?<br>
</a>
</strong>

<p>
YES!  Machine-specific optimized BLAS libraries are available for
a variety of computer architectures.  These optimized BLAS libraries
are provided by the computer vendor or by an independent software
vendor (ISV).  For further details, please contact your local vendor
representative.  </p>
<p>
Alternatively, the user can download <a href="http://www.netlib.org/atlas/">ATLA
S</a> to automatically generate an optimized BLAS library for his
architecture.
</p>
<p>
If all else fails, the user can
download a <a href="http://www.netlib.org/blas/blas.tgz">Fortran77
reference implementation of the BLAS</a> from netlib.  However,
keep in mind that this is a reference implementation and is not
optimized.</p>
 

<p>
<strong>
<a name="2.5">
    2.5)  What is ATLAS?<br>
</a>
</strong>

<p>
ATLAS is an approach for the automatic generation and optimization of
numerical software for processors with deep memory hierarchies and pipelined
functional units. The production of such software for machines ranging from
desktop workstations to embedded processors can be a tedious and time
consuming task. ATLAS has been designed to automate much of this process.
We concentrate our efforts on the widely used linear algebra kernels
called the Basic Linear Algebra Subroutines (BLAS). </p>
<p>
For further information, refer to the <a href="http://www.netlib.org/atlas/">ATL
AS webpage</a>.</p>


<p>
<strong>
<a name="2.6">
    2.6)  Where can I find vendor supplied BLAS?<br>
</a>
</strong>
<p>
BLAS Vendor List <BR>
Last updated: March 14, 2001 <BR>
<HR><TABLE BORDER="1" CELLPADDING="3">
  <TR><TD ALIGN=LEFT><BOLD><H3> Vendor </H3></TD>
  <TD ALIGN=LEFT><BOLD><H3> URL </H3></BOLD></TD></TR>


  <TR><TD ALIGN=LEFT> Compaq </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://www.compaq.com/hpc/software/dxml.html">
  http://www.compaq.com/hpc/software/dxml.html
  </A></TD></TR>

  <TR><TD ALIGN=LEFT> HP </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://www.hp.com/rsn/mlib/mlibhome.html">
  http://www.hp.com/rsn/mlib/mlibhome.html
  </A></TD></TR>

  <TR><TD ALIGN=LEFT> IBM </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://www.rs6000.ibm.com/software/Apps/essl.html">
  http://www.rs6000.ibm.com/software/Apps/essl.html
  <BR>
  <A HREF="http://www.rs6000.ibm.com/software/sp_products/esslpara.html">
  http://www.rs6000.ibm.com/software/sp_products/esslpara.html
  </A></TD></TR>

  <TR><TD ALIGN=LEFT> Intel </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://developer.intel.com/software/products/mkl/index.htm">
  http://developer.intel.com/software/products/mkl/index.htm 
  </A></TD></TR>

  <TR><TD ALIGN=LEFT> SGI </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://www.sgi.com/software/scsl.html">
  http://www.sgi.com/software/scsl.html
  </A></TD></TR>

  <TR><TD ALIGN=LEFT> SUN </TD>
  <TD ALIGN=LEFT>
  <A HREF="http://docs.sun.com/htmlcoll/coll.118.3/iso-8859-1/PERFLIBUG/plug_bookTOC.html
">
http://docs.sun.com/htmlcoll/coll.118.3/iso-8859-1/PERFLIBUG/plug_bookTOC.html
  </A></TD></TR>

</TABLE>
</p>

<p>
<strong>
<a name="2.7">
    2.7)  Where can I find the Intel BLAS for Linux?<br>
</a>
</strong>
<p>
Yes, the Intel BLAS for Linux are available!  Refer to the following
URL:</p>
<a href="http://www.cs.utk.edu/~ghenry/distrib">Intel BLAS for Linux</a>.
</p>

<p>
<strong>
<a name="2.8">
    2.8)  Where can I find Java BLAS?<br>
</a>
</strong>
<p>
Yes, Java BLAS are available.  Refer to the following
URLs:
<a href="http://www.cs.utk.edu/f2j/download.html/">Java LAPACK</a>
and
<a href="http://math.nist.gov/javanumerics/">JavaNumerics</a>.
The <b>JavaNumerics</b> webpage provides a focal point for information
on numerical computing in Java.
</p>

<p>
<strong>
<a name="2.9">
    2.9)  Is there a C interface to the BLAS?<br>
</a>
</strong>
<p>
Yes, a C interface to the BLAS was defined in the <a href="http://www.netlib.org
/blas/blast-forum/">BLAS Technical Forum Standard</a>.  The <a href="http://www.
netlib.org/blas/blast-forum/cblas.tgz">source code</a> is
also available.
</p>



<p>
<strong>
<a name="2.10">
    2.10)  Are prebuilt Fortran77 ref implementation BLAS libraries available?<br>
</a>
</strong>
 
<p>
Yes.  HOWEVER, it is assumed that you have a machine-specific optimized <b>BLAS</b>
library already available on the architecture to which you are installing
<b>LAPACK</b>.  If this is not the case, you can download a
<a href="http://www.netlib.org/blas/archives/">prebuilt Fortran77 reference
implementation BLAS library</a> or compile the
<a href="http://www.netlib.org/blas/blas.tgz">Fortran77 reference implementation
source code of the BLAS</a> from netlib.
<p>
Although a model implementation of the BLAS in available
from netlib in the <a href="http://www.netlib.org/blas/">blas directory</a>,
it is not expected to perform as well as a specially
tuned implementation on most high-performance computers -- on some machines
it may give much worse performance -- but it allows users to run LAPACK
software on machines that do not offer any other implementation of the
BLAS.
<p>
Alternatively, you can automatically generate an optimized BLAS library
for your machine using ATLAS, <a href="http://www.netlib.org/atlas/"><address>http://www.netlib.org/atlas/</address></a>.

<p>
<IMG SRC="http://www.netlib.org/scalapack/html/gif/blue.gif"></p>
<a href="mailto:lapack@cs.utk.edu"><address>lapack@cs.utk.edu</address></a>

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