Basic Linear Algebra Subprograms

Basic Linear Algebra Subprograms (BLAS) are routines which perform basic linear algebra operations such as vector and matrix multiplication. They are used to build larger packages such as LAPACK. BLAS routines are tuned by high performance computing, supercomputer hardware, and software vendors to run extremely fast under a variety of problem sizes. The LINPACK benchmark relies heavily on DGEMM, a BLAS subroutine, for its performance.

Functionality

The BLAS functionality is divided into three levels: 1, 2 and 3.

Level 1

This level contains vector operations of the form

${\displaystyle \mathbf {y} \leftarrow \alpha \mathbf {x} +\mathbf {y} \!}$ 

as well as scalar dot products and vector norms, among other things.

Level 2

This level contains matrix-vector operations of the form

${\displaystyle \mathbf {y} \leftarrow \alpha A\mathbf {x} +\beta \mathbf {y} \!}$ 

as well as solving ${\displaystyle T\mathbf {x} =\mathbf {y} }$  for x with ${\displaystyle T}$  being triangular, among other things.

Level 3

This level contains matrix-matrix operations of the form

${\displaystyle C\leftarrow \alpha AB+\beta C\!}$ 

as well as solving ${\displaystyle B\leftarrow \alpha T^{-1}B}$  for triangular matrices ${\displaystyle T}$ , among other things. This level contains the widely used General Matrix Multiply operation.

Implementations

refblas

The official reference implementation from netlib. C and Fortran 77 versions are available.[1]

ACML

The AMD Core Math Library, supporting the AMD Athlon and Opteron CPUs under Linux and Windows.[2]

ATLAS

Automatically Tuned Linear Algebra Software, an open source implementation of BLAS APIs for C and Fortran 77.[3]

ESSL

IBM's Engineering and Scientific Subroutine Library, supporting the PowerPC architecture under AIX and Linux.[4]

Goto BLAS

Kazushige Goto's implementation of BLAS.[5]

HP MLIB

HP's Math library, supporting Itanium, PA-RISC, x86 and Opteron architecture under HPUX and Linux.

IMKL

The Intel Math Kernel Library, supporting the Intel Pentium and Itanium CPUs under Linux and Windows.[6]

uBLAS

A generic C++ template class library providing BLAS functionality. Part of the Boost library.[7]

External links

• BLAS homepage on Netlib.org
• BLAS FAQ
• BLAS operations from the GNU Scientific Library reference manual
• BLAS Quick Reference Guide from LAPACK Users' Guide
• BLAS-Implementation Automatically Tuned Linear Algebra Software (ATLAS)