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BLAS

The Basic Linear Algebra Subprograms (BLAS) is a common library including high-quality routines for performing basic operations on vectors and matrices. The first FORTRAN version was released in 1979. As the routines are efficient and portable, they are often used in linear algebra software, like LAPACK. Most implementations are written in C, C++, or FORTRAN 77.

ATLAS

High-performance implementation of the BLAS API, for C and FORTRAN 77 (BSD licence).

BLAS

The official reference implementation by Netlib (C and FORTRAN 77). Also known as refblas (public domain).

IMKL

The Intel Math Kernel Library includes BLAS for Intel processors. Professional and community editions for C, C++, and Fortran are distributed (proprietary).

Please see Wikipedia for a more comprehensive overview of BLAS libraries.

Operations

The functionality of BLAS is divided into three sets of routines, called levels. Below, A, B, C, and T are matrices, x and y are vectors, and α and β are scalars.

Level 1: Scalar-Vector and Vector-Vector Operations

The level provides low-level operations, like dot product of vectors and vector additions, such as

y ← αx + y.

Level 2: Matrix-Vector Operations

The level contains basic matrix-vector operations, such as

y ← αAx + βy.

It also includes a solver for x in the triangular equation

Tx = y,

with triangular matrix T.

Level 3: Matrix-Matrix Operations

The level includes matrix-matrix operations, such as

C ← αAB + βC,

and routines for solving

B ← αT⁻¹B,

with triangular matrix T.

Installation

On FreeBSD, the LAPACK implementation of BLAS is available as a port:

# pkg install math/blas

But BLAS can be build also from source. Download version 3.8.0 from Netlib, unpack the archive, and compile the Fortran code manually. In order to create a shared library libblas.so, run:

$ gfortran9 -O2 -shared -fPIC -o libblas.so *.f

Or, if the static library libblas.a is prefered, run:

$ gfortran9 -O2 -c *.f
$ ar cr libblas.a *.o

Example

The following example program scales a vector by a constant using BLAS.

! example.f90
program main
    ! Example program that scales a vector by a constant using BLAS.
    implicit none
    external :: sscal

    integer, parameter :: N = 3
    integer            :: i
    real               :: x(N) = [ 5., 6., 7. ]
    real               :: a    = 5.

    print '(a, f0.1)', 'a = ', a
    print '(a)',       'X ='

    do i = 1, N
        print '(f0.1)', x(i)
    end do

    call sscal(N, a, x, 1)

    print '(/, a)', 'X = a * X'
    print '(a)',    'X ='

    do i = 1, N
        print '(f0.1)', x(i)
    end do
end program main

Compile and link the example with:

$ gfortran9 -L/usr/local/lib/ -o example example.f90 -lblas

If you link against the static library libblas.a, point the library search path -L to the correct location. The program outputs:

$ ./example
a = 5.0
X =
5.0
6.0
7.0

X = a * X
X =
25.0
30.0
35.0

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