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|
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE guide SYSTEM "/dtd/guide.dtd">
# $Id$
<guide link="/proj/en/science/linalg.xml">
<title>Linear Algebra on Gentoo</title>
<author title="Author">
<mail link="bicatali@gentoo.org">Sébastien Fabbro</mail>
</author>
<abstract>
This guide explains the use of linear algebra libraries and focus on
how to use the different implementations of BLAS and LAPACK available on Gentoo.
</abstract>
<!-- The content of this document is licensed under the CC-BY-SA license -->
<!-- See http://creativecommons.org/licenses/by-sa/2.5 -->
<license/>
<version>1.0</version>
<date>2010-12-22</date>
<chapter>
<title>Introduction</title>
<section>
<body>
<p>
There are <uri link="http://en.wikipedia.org/wiki/List_of_numerical_libraries">many</uri>
performant numerical libraries available.
The Basic Linear Algebra Subprograms (BLAS) and the Linear Algebra PACKage (LAPACK)
are well designed linear algebra libraries developed by the
High Performance Computing (HPC) community. BLAS is an API of dense
matrix and vectors products, while LAPACK provides routines for
solving systems of linear equations. Both are widely used in
many scientific applications and it is, therefore, important to
have efficient implementations available.
</p>
<p>
BLAS and LAPACK were originally written in FORTRAN 77. Since then, a
number of additional language wrappers have been developed for
languages like C, C++, FORTRAN 95, Java, Python, etc...
Netlib offers exact implementations of the APIs and they are called
"reference" libraries.
</p>
<ul>
<li>
<uri link="http://www.netlib.org/blas/">BLAS</uri>: FORTRAN 77 and C
(CBLAS) implementations of BLAS
</li>
<li>
<uri link="http://www.netlib.org/lapack/">LAPACK</uri>: FORTRAN 77 and
C (LAPACKE) implementations of LAPACK
</li>
</ul>
<p>
</p>
<ul>
<li>
<uri link="http://www.netlib.org/blacs/">BLACS</uri>: FORTRAN 77 and C
implementations of BLACS
</li>
<li>
<uri link="http://www.netlib.org/scalapack/">ScaLAPACK</uri>: FORTRAN 77 and
C implementations of PBLAS and ScaLAPACK
</li>
</ul>
<p>
In addition, Gentoo provides a number of optimized implementations
of the above linear algebra libraries that will be described
below. You can switch between implementations with the
Gentoo's <c>eselect</c> system and the widely used <c>pkg-config</c>
tool.
</p>
<p>
It is important to note that if you require, e.g., a well performing
BLAS implementation, simply emerging X over Y often is not enough. Rather, you will have
to carefully benchmark your applications since performance may depend
on many factors,
such as hardware or network.
If you are simply looking for a well performing and well tested
implementation, the reference ebuilds will likely be your best choice.
</p>
</body>
</section>
</chapter>
<chapter>
<title>For Users</title>
<section>
<title>Installing</title>
<body>
<p>
If best possible performance is not of paramount importance for you
and you simply need BLAS and/or LAPACK, just emerge the virtual
package:
</p>
<pre caption="Installing">
# <i>emerge lapack</i>
</pre>
<p>
This will install both <><> and <><> the reference packages from
<uri>http://www.netlib.org/</uri> . They are well tested, easy to debug
implementations. They should satisfy most users; if they're all you need, you're
done reading.
</p>
<p>
However, if:
</p>
<ul>
<li>linear algebra libraries are critical for the speed of your applications</li>
<li>you absolutely need to build the fastest computer</li>
<li>you want to help Gentoo sci project to improve their packages</li>
</ul>
<p>
... then read on, and be sure to file bugs both to Gentoo and upstream.
</p>
<p>
There is a number of optimized implementations of these libraries in the Portage
tree:
</p>
<ul>
<li>
<uri link="http://math-atlas.sourceforge.net">ATLAS</uri>: Automatically
Tuned Linear Algebra Software is an open-source package that empirically
tunes the library to the machine it is being compiled on. It provides BLAS
(FORTRAN 77 and C), and LAPACK implementations on various architectures.
</li>
<li>
<uri
link="http://www.tacc.utexas.edu/tacc-projects/gotoblas2/">GotoBLAS</uri>:
Goto BLAS provides open-source, free for academic use, hand-coded
machine language, processor optimized versions of the FORTRAN 77
and C BLAS routines. Still claims to be the fastest BLAS.
</li>
<li>
<uri link="http://developer.amd.com/cpu/libraries/acml/Pages/default.aspx">ACML</uri>:
AMD Core Math Library is a closed-source but free package containing BLAS (FORTRAN 77
only) and LAPACK for x86 and x86_64 architectures, but also other math tools
such as statistical libraries and FFTs.
</li>
<li>
<uri link="http://software.intel.com/en-us/articles/intel-mkl/">MKL</uri>:
Intel® Math Kernel Library is a closed-source but free package for
non-commercial use on Linux systems containing implementations of all the linear
algebra libraries mentioned here.
</li>
</ul>
<p>
Usually performance gain is noticeable mainly with BLAS, since LAPACK routines
depend on BLAS kernels.
</p>
</body>
</section>
<section>
<title>Developping with the installed linear algebra libraries</title>
<body>
<p>
We took great care to make sure that each package provides
consistent pkg-config files generated by us.
Compiling and linking becomes straightforward:
</p>
<pre caption="Compiling and linking linear algebra libraries">
# <i>pkg-config --libs blas</i> <comment>(To link with FORTRAN 77 BLAS library)</comment>
# <i>pkg-config --cflags cblas</i> <comment>(To compile against C BLAS library)</comment>
# <i>pkg-config --libs cblas</i> <comment>(To link with C BLAS library)</comment>
# <i>pkg-config --libs scalapack</i> <comment>(To link with the ScaLAPACK library)</comment>
</pre>
<p>
<c>pkg-config</c> files are available for all implementations and
various alternatives within implementations. The default names of
the implementations are: blas, cblas, lapack, lapacke, blacs and
scalapack, and they can be chosen with <c>eselect</c>. You can also always compile or link
with an library not selected for the
More information on using <c>pkg-config</c> can be obtained with <c>man pkg-config</c>.
</p>
</body>
</section>
<section>
<title>Selecting libraries</title>
<body>
<p>
You can switch BLAS, CBLAS and LAPACK implementations with
<c>eselect</c>. you can view which implementations of CBLAS
are available.
</p>
<pre caption="Viewing available implementations of CBLAS">
# <i>eselect cblas list</i>
Installed CBLAS for library directory lib64
[1] atlas
[2] atlas-threads
[3] gsl
[4] mkl-threads *
[5] reference
</pre>
<p>
The implementation marked with an asterisk (*) is the currently
selected implementation. To switch implementations, run:
</p>
<pre caption="Switching to the threaded ATLAS implementation of BLAS">
# <i>eselect blas set atlas-threads</i>
</pre>
<p>
To learn more about the <c>eselect</c> tool, visit the
<uri link="http://www.gentoo.org/proj/en/eselect/user-guide.xml">eselect guide</uri>
</p>
<p>
When selecting your linear algebra profiles try to avoid mixing
different implementations since we don't have any mechanism to enforce
reasonable profiles. However, here is a list of well performing
profile combinations that have been used successfully in the past:
</p>
<ul>
<li> performant on most CPUs:
<ul>
<li>blas, cblas: atlas (or atlas-threads with multi-processor)</li>
<li>lapack, lapacke: atlas</li>
</ul>
</li>
<li> performant on most CPUs:
<ul>
<li>blas, cblas: goto2 </li>
<li>lapack, lapacke: reference</li>
</ul>
</li>
<li> performant on AMD based CPUs:
<ul>
<li>blas, lapack: acml-gfortran (or acml-gfortran-openmp with
multi-processors) </li>
<li>cblas: reference</li>
</ul>
</li>
<li> performant on Intel based CPUs:
<ul>
<li>blas,cblas,lapack: mkl-threads</li>
</ul>
</li>
</ul>
</body>
</section>
<section>
<title>Choosing a compiler</title>
<body>
<p>
All the above libraries have been tested with the GNU compiler
collections (gcc, gfortran).
There are many available C compilers and a few FORTRAN (ifort,
Open64) compilers on Gentoo and many other FORTRAN compilers outside
of Gentoo ().
</p>
<pre caption="Installing BLAS with the Intel FORTRAN compiler">
# <i>F77=ifort FFLAGS="-O2 -mp1" emerge blas-reference</i>
</pre>
<p>
Depending on your hardware, a small performance gain can be noticed thanks to
vectorization. The <c>-mp</c> flag maintains floating-point precision, since by
default ifort is pretty aggressive on floating point arithmetic, and we are
actually compiling a math package. Try <c>man ifort</c> to see additional flags
to fit your hardware.
</p>
<p>
Some of the implementations let you specify the Intel® C compiler as
well. Please beware that not all libraries compile with all
combinations. You should receive an error during the emerge in case you have
chosen an incompatible combination.
</p>
<p>
As usual for Gentoo, there are many combinations of USE flags and
compilers with which you could compile a package. Unfortunately
switching compilers between BLAS and LAPACK might not be always
compatible. For example:
</p>
<pre caption="Looking for trouble combinations">
# <i>USE=ifort emerge acml</i>
# <i>eselect blas set acml-ifort-openmp</i>
# <i>FC=gfortran FFLAGS="-O2" emerge lapack-reference</i>
</pre>
<p>
This will most likely break things or not even compile.
</p>
<p>
Try to be consistent in your choice. Stay with the GCC most of the time will
avoid you some trouble, unless you want to use the MKL, in which case the Intel
compilers make a good combination.
</p>
</body>
</section>
<section>
<title>Documentation</title>
<body>
<p>
If you need BLAS or LAPACK to develop your own programs, the documentation
becomes pretty handy. Setting the USE="doc" flag for the corresponding BLAS or
LAPACK package will install man pages and quick reference sheets from the
<c>app-doc/blas-docs</c> and <c>app-doc/lapack-docs</c> packages. They are
standard and valid for all implementations. For optimized packages, the
USE="doc" flags will usually install extra doc in PDF or HTML format.
</p>
</body>
</section>
</chapter>
<chapter>
<title>For ebuild developers</title>
<section>
<section>
<title>Packages with BLAS/LAPACK dependencies</title>
<body>
<p>
You need two things:
set [R]DEPEND to <c>virtual/<imp></c>. To build some
packages, you m need to use the pkg-config tool. If you are lucky, the
package uses autotools together with the autoconf <>AX_BLAS and <>AX_LAPACK M4
macros. In this case, the configuration step becomes simple. For example:
</p>
<pre caption="Sample package configuration with autotools">
<keyword>econf</keyword> --with-blas="<var>$(pkg-config --libs blas)</var>"
</pre>
</body>
</section>
<title>Providing new implementations</title>
<body>
<p>
The Portage tree contains many ebuilds that depend on the
BLAS/CBLAS/LAPACK/BLACS/ScaLAPACK libraries. As there is more than
one possible implementation, the Gentoo Science Project
reorganized all the packages to provide <c>virtual</c>. All ebuilds using
should depend on this virtual package, unless it is explicitly
known to break with a specific implementation.
</p>
<p>
To work with Gentoo's configuration tools
<c>app-admin/eselect-{blas,cblas,lapack}</c>, and the virtual, every ebuild that
installs a BLAS implementation must fulfill following requirements:
</p>
<ol>
<li>
The ebuild must install an eselect file for each profile it provides. The
libraries should link to the ones in <path>/usr/$(get_libdir)</path>
directories and the include files in <path>/usr/include</path>:
<ul>
<li>
<path>libblas.so[.0]</path> - Shared object for FORTRAN BLAS
applications
</li>
<li>
<path>libblas.a</path> - Static library for FORTRAN BLAS applications
</li>
<li>
<path>libcblas.so[.0]</path> - Shared object for C/C++ CBLAS applications
</li>
<li>
<path>libcblas.a</path> - Static library for C/C++ CBLAS applications
</li>
<li><path>cblas.h</path> - Include header for C/C++ applications</li>
<li>
<path>liblapack.so[.0]</path> - Shared object for FORTRAN LAPACK
applications
</li>
<li>
<path>liblapack.a</path> - Static library for FORTRAN LAPACK applications
</li>
</ul>
</li>
<li>
The ebuild must install a <path>blas.pc</path>, <path>cblas.pc</path> and/or
<path>lapack.pc</path> pkg-config file and therefore RDEPEND on
<c>dev-util/pkgconfig</c>. They should also be included in the eselect
files, and link to the <path>/usr/$(get_libdir)/pkgconfig</path> directory:
<ul>
<li><path>blas.pc</path> - BLAS pkg-config file</li>
<li><path>cblas.pc</path> - CBLAS pkg-config file</li>
<li><path>lapack.pc</path> - LAPACK pkg-config file</li>
</ul>
</li>
<li>Be included in the virtual package as a possible provider:
<ul>
<li><c>virtual/blas</c> - BLAS virtual package</li>
<li><c>virtual/cblas</c> - CBLAS virtual package</li>
<li><c>virtual/lapack</c> - LAPACK virtual package</li>
</ul>
</li>
</ol>
<p>
The easiest way of understanding all this is probably getting inspiration from
one of the available packages. Currently the Portage tree provide the following
virtual packages:
</p>
<table>
<tr>
<th>Package name</th>
<th>virtual/blas</th>
<th>virtual/cblas</th>
<th>virtual/lapack</th>
<th>virtual/lapacke</th>
<th>virtual/blacs</th>
<th>virtual/scalapack</th>
</tr>
<tr>
<ti><c>sci-libs/acml</c></ti>
<ti>*</ti>
<ti></ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/atlas</c></ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/gotoblas2</c></ti>
<ti>*</ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/blas-reference</c></ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/cblas-reference</c></ti>
<ti></ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/gsl</c></ti>
<ti></ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/lapack-reference</c></ti>
<ti></ti>
<ti></ti>
<ti>*</ti>
<ti></ti>
<ti></ti>
<ti></ti>
</tr>
<tr>
<ti><c>sci-libs/mkl</c></ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
<ti>*</ti>
</tr>
</table>
</body>
</section>
</chapter>
<chapter>
<title>Benchmarks</title>
<section>
<body>
<p>
If you feel inclined to write an ebuild for these, you
are more than welcomed to file it on our <uri
link="http://bugs.gentoo.org">Bugzilla</uri>.
</p>
</body>
</section>
</chapter>
</guide>
|
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