- Basic Linear Algebra Subprograms
Basic Linear Algebra Subprograms (BLAS) is a de facto
application programming interfacestandard for publishing libraries to perform basic linear algebraoperations such as vector and matrix multiplication. They were first published in 1979, and are used to build larger packages such as LAPACK. Heavily used in high-performance computing, highly optimized implementations of the BLAS interface have been developed by hardware vendors such as by Intelas well as by other authors (e.g. ATLAS is a portable self-optimizing BLAS). The LINPACKbenchmark relies heavily on DGEMM, a BLAS subroutine, for its performance.
The BLAS functionality is divided into three levels: 1, 2 and 3.
This level contains "vector operations" of the form
as well as scalar
dot products and vector norms, among other things.
This level contains "matrix-vector operations" of the form
as well as solving for with being triangular, among other things.
This level contains "matrix-matrix operations" of the form
as well as solving for triangular matrices , among other things. This level contains the widely used
General Matrix Multiplyoperation.
;refblas: The official reference implementation from
netlib. C and Fortran 77 versions are available. [http://www.netlib.org/blas/] ;Accelerate: Apple Computer's framework for Mac OS X, which includes tuned versions of BLAS and LAPACK for both PowerPCand Intel Core processors. [http://developer.apple.com/releasenotes/Performance/RN-vecLib/] ;ACML: The AMDCore Math Library, supporting the AMD Athlonand OpteronCPUs under Linuxand Windows. [http://developer.amd.com/acml.aspx] ;ATLAS: Automatically Tuned Linear Algebra Software, an open sourceimplementation of BLAS APIs for C and Fortran 77. [http://math-atlas.sourceforge.net/] ;CUDA SDK: The NVIDIA CUDASDK includes BLAS functionality for writing C programs that runs on GeForce 8 Seriesgraphics cards.;ESSL: IBM's Engineering and Scientific Subroutine Library, supporting the PowerPCarchitecture under AIX and Linux. [http://publib.boulder.ibm.com/infocenter/clresctr/index.jsp?topic=/com.ibm.cluster.essl.doc/esslbooks.html] ;Goto BLAS: Kazushige Goto's implementation of BLAS. [http://www.tacc.utexas.edu/resources/software/#blas] ;HP MLIB: HP's Math library, supporting IA-64, PA-RISC, x86and Opteronarchitecture under HPUXand Linux.;Intel MKL: The IntelMath Kernel Library, supporting the Intel Pentiumand ItaniumCPUs under Linux, Windows and Mac OS X. [http://www.intel.com/cd/software/products/asmo-na/eng/perflib/mkl/] ;MathKeisan: NEC's math library, supporting NEC SX architectureunder SUPER-UX, and Itaniumunder Linux. [http://www.mathkeisan.com/] ;PDLIB/SX: NEC's Public Domain Mathematical Library for the NEC SX-4 system. [http://www.nec.co.jp/hpc/mediator/sxm_e/software/61.html] ;SCSL: SGI's Scientific Computing Software Library contains BLAS and LAPACK implementations for SGI's Irixworkstations. [http://www.sgi.com/products/software/scsl.html] ;Sun Performance Linaray: Optimized BLAS and LAPACK for SPARCand AMD64architectures under Solaris 8, 9, and 10. [http://developers.sun.com/prodtech/cc/perflib_index.html] ;uBLAS: A generic C++template class library providing BLAS functionality. Part of the Boost library. Note that, unlike other implementations, uBLAS focuses on correctness of the algorithms using advanced C++ features, rather than high performance. [http://www.boost.org/doc/libs/1_35_0/libs/numeric/ublas/doc/index.htm] ;GSL: The GNU Scientific LibraryContains a multi-platform implementation in C which is distributed under the GNU General Public License.
The Sparse BLAS
Sparse extensions to the previously dense BLAS exist such as in ACML
Numerical linear algebra, the type of problem BLAS solves
LAPACK, the Linear Algebra Package
* [http://www.netlib.org/blas/ BLAS homepage] on Netlib.org
* [http://www.netlib.org/blas/faq.html BLAS FAQ]
* [http://www.gnu.org/software/gsl/manual/html_node/BLAS-Support.html BLAS operations] from the GNU Scientific Library reference manual
* [http://www.netlib.org/lapack/lug/node145.html BLAS Quick Reference Guide] from LAPACK Users' Guide
* [http://history.siam.org/oralhistories/lawson.htm Lawson Oral History] One of the original authors of the BLAS discusses its creation in an oral history interview. Charles L. Lawson Oral history interview by Thomas Haigh, 6 and 7 November, 2004, San Clemente, California. Society for Industrial and Applied Mathematics, Philadelphia, PA.
* [http://history.siam.org/oralhistories/dongarra.htm Dongarra Oral History] In an oral history interview, Jack Dongarra explores the early relationship of BLAS to LINPACK, the creation of higher level BLAS versions for new architectures, and his later work on the ATLAS system to automatically optimize BLAS for particular machines. Jack Dongarra, Oral history interview by Thomas Haigh, 26 April, 2005, University of Tennessee, Knoxville TN. Society for Industrial and Applied Mathematics, Philadelphia, PA
* An Overview of the Sparse Basic Linear Algebra Subprograms: The New Standard from the BLAS Technical Forum doi-inline|10.1145/567806.567810
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