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<html>
<head>
<title>
BLAS1 - The Basic Linear Algebra Subprograms - Level 1
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BLAS1 <br>
The Basic Linear Algebra Subprograms <br>
Level 1
</h1>
<hr>
<p>
<b>BLAS1</b>
is a FORTRAN90 library which
implements the Level 1 Basic Linear Algebra Subprograms (BLAS).
</p>
<p>
The <b>BLAS</b> are a small core library of linear algebra utilities,
which can be highly optimized for various architectures. Software
that relies on the <b>BLAS</b> is thus highly portable, and will typically
run very efficiently.
</p>
<p>
The Level 1 BLAS are primarily for use in vector operations, such
as vector norms, dot products, vector scaling, and the addition of a
scalar multiple of one vector to another.
</p>
<p>
While the entries of a typical vector are stored continguously in memory,
many BLAS1 routines allow the user to specify a vector by locating
its first element, and giving an increment to be used to locate the
successive elements. An increment of +1 corresponds to the typical vector;
however, by specifying other increments, a "logical" vector can be
selected that is actually a row, column, or even a diagonal of a two-dimensional
array.
</p>
<p>
The Level 1 BLAS are available in both real and complex arithmetic
versions, and using single precision or double precision. In most
cases, a given BLAS function has a root name, such as <b>AXPY</b>,
and prefix is used to identify the arithmetic and precision. Thus,
<ul>
<li>
<b>CAXPY</b> is the single precision complex version of AXPY;
</li>
<li>
<b>DAXPY</b> is the double precision real version of AXPY;
</li>
<li>
<b>SAXPY</b> is the single precision real version of AXPY;
</li>
<li>
<b>ZAXPY</b> is the double precision complex version of AXPY;
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>BLAS1</b> is available in
<a href = "../../c_src/blas1/blas1.html">a C version</a> and
<a href = "../../cpp_src/blas1/blas1.html">a C++ version</a> and
<a href = "../../f77_src/blas1/blas1.html">a FORTRAN77 version</a> and
<a href = "../../f_src/blas1/blas1.html">a FORTRAN90 version</a> and
<a href = "../../m_src/blas1/blas1.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/blas1_c/blas1_c.html">
BLAS1_C</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using single precision complex arithmetic;
</p>
<p>
<a href = "../../f_src/blas1_d/blas1_d.html">
BLAS1_D</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using double precision real arithmetic;
</p>
<p>
<a href = "../../f_src/blas1_s/blas1_s.html">
BLAS1_S</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using single precision real arithmetic;
</p>
<p>
<a href = "../../f_src/blas1_z/blas1_z.html">
BLAS1_Z</a>,
a FORTRAN90 library which
contains basic linear algebra routines for vector-vector operations,
using double precision complex arithmetic;
</p>
<p>
<a href = "../../f_src/blas2/blas2.html">
BLAS2</a>,
a FORTRAN90 library which
contains basic linear algebra routines for matrix-vector operations,
using single or precision real or complex arithmetic;
</p>
<p>
<a href = "../../f_src/blas3/blas3.html">
BLAS3</a>,
a FORTRAN90 library which
contains basic linear algebra routines for matrix-matrix operations,
using single or precision real or complex arithmetic;
</p>
<p>
<a href = "../../f_src/lapack_examples/lapack_examples.html">
LAPACK_EXAMPLES</a>,
a FORTRAN90 program which
demonstrates the use of the LAPACK linear algebra library.
</p>
<p>
<a href = "../../f_src/linpack/linpack.html">
LINPACK</a>,
a FORTRAN90 library which
is a linear algebra package that uses the <b>BLAS1</b> routines.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford,
James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum,
Sven Hammarling, Alan McKenney, Danny Sorensen,<br>
LAPACK User's Guide,<br>
Third Edition,<br>
SIAM, 1999,<br>
ISBN: 0898714478,<br>
LC: QA76.73.F25L36.
</li>
<li>
Thomas Coleman, Charles vanLoan,<br>
Handbook for Matrix Computations,<br>
SIAM, 1988,<br>
ISBN13: 978-0-898712-27-8,<br>
LC: QA188.C65.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
Algorithm 539:
Basic Linear Algebra Subprograms for Fortran Usage,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 3, September 1979, pages 308-323.
</li>
</ol>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 29 April 2012.
</i>
<!-- John Burkardt -->
</body>
</html>