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<html>
<head>
<title>
BLAS1_S - Basic Linear Algebra Subprograms - Level 1 -
Single Precision Real
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BLAS1_S <br>
Basic Linear Algebra Subprograms <br>
Level 1 <br>
Single Precision Real Arithmetic
</h1>
<hr>
<p>
<b>BLAS1_S</b>
is a MATLAB library which
implements the Level 1
BLAS, or Basic Linear Algebra Subprograms.
</p>
<p>
The BLAS are a small core library of linear algebra utilities,
which can be highly optimized for various architectures. Software
that relies on the BLAS is thus highly portable, and will typically
run very efficiently. The LINPACK
and LAPACK
linear algebra libraries make extensive use of the BLAS.
</p>
<p>
The Level 1 BLAS are primarily for use in vector operations.
In certain cases, they may also be used to operate on the rows
or columns of a two-dimensional array.
</p>
<p>
It is worth questioning whether one should try to implement the
Level 1 BLAS in MATLAB: for one thing, the MATLAB language makes
it very easy to carry out vector operations, even with nonunit
incrementing on the vector indices. Moreover, MATLAB actually
makes it more difficult to stick with the syntax of the BLAS, since
it is not so easy to make a two dimensional array "look like" a
vector.
</p>
<p>
In particular, if you want to work on a row of a matrix,
MATLAB essentially prefers you to make a temporary vector, as in
"A(3,1:N)"; in the standard BLAS, you would instead pass the location
of the first entry, A(3,1), and an increment, LDA, that will lead to
the next entry of the row. This is not easy or natural to do
in MATLAB. Still, for consistency, I have gone ahead and tried
to make a reasonable effort at implementing the Level 1 BLAS.
</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_S</b> is available in
<a href = "../../c_src/blas1_s/blas1_s.html">a C version</a> and
<a href = "../../cpp_src/blas1_s/blas1_s.html">a C++ version</a> and
<a href = "../../f77_src/blas1_s/blas1_s.html">a FORTRAN77 version</a> and
<a href = "../../f_src/blas1_s/blas1_s.html">a FORTRAN90 version</a> and
<a href = "../../m_src/blas1_s/blas1_s.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/blas0/blas0.html">
BLAS0</a>,
a MATLAB library which
contains auxilliary functions for the Basic Linear Algebra Subprograms
(BLAS).
</p>
<p>
<a href = "../../m_src/blas1_c/blas1_c.html">
BLAS1_C</a>,
a MATLAB library which
is the single precision complex arithmetic version of <b>BLAS1</b>.
</p>
<p>
<a href = "../../m_src/blas1_d/blas1_d.html">
BLAS1_D</a>,
a MATLAB library which
is the double precision real arithmetic version of <b>BLAS1</b>.
</p>
<p>
<a href = "../../m_src/blas1_z/blas1_z.html">
BLAS1_Z</a>,
a MATLAB library which
is the double precision complex arithmetic version of <b>BLAS1</b>.
</p>
<p>
<a href = "../../m_src/blas2/blas2.html">
BLAS2</a>,
a MATLAB library which
contains basic linear algebra subprograms (BLAS)
for matrix-vector operations;
</p>
<p>
<a href = "../../m_src/blas3/blas3.html">
BLAS3</a>,
a MATLAB library which
contains basic linear algebra subprograms (BLAS)
for matrix-matrix operations;
</p>
<p>
<a href = "../../m_src/linpack/linpack.html">
LINPACK</a>,
a MATLAB library which
is a linear algebra package that uses the <b>BLAS1</b> routines.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original FORTRAN77 version by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
MATLAB version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<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>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "isamax.m">isamax.m</a>,
returns the index of the vector entry of greatest magnitude;
</li>
<li>
<a href = "sasum.m">sasum.m</a>,
sums the absolute values of the entries of a vector;
</li>
<li>
<a href = "saxpy.m">saxpy.m</a>,
adds a constant times one vector to another.
</li>
<li>
<a href = "scopy.m">scopy.m</a>,
makes a copy of a vector;
</li>
<li>
<a href = "sdot.m">sdot.m</a>,
computes the scalar product of two vectors;
</li>
<li>
<a href = "snrm2.m">snrm2.m</a>,
computes the Euclidean norm of a vector.
</li>
<li>
<a href = "srot.m">srot.m</a>,
applies a plane rotation.
</li>
<li>
<a href = "srotg.m">srotg.m</a>,
constructs a Givens plane rotation.
</li>
<li>
<a href = "sscal.m">sscal.m</a>,
scales a vector by a constant.
</li>
<li>
<a href = "sswap.m">sswap.m</a>,
interchanges two vectors.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "blas1_s_test.m">blas1_s_test.m</a>,
calls all the tests;
</li>
<li>
<a href = "blas1_s_test.out">blas1_s_test.out</a>,
the output from the tests.
</li>
<li>
<a href = "blas1_s_test01.m">blas1_s_test01.m</a>,
tests ISAMAX;
</li>
<li>
<a href = "blas1_s_test02.m">blas1_s_test02.m</a>,
tests ISAMAX, SAXPY, SDOT, SSCAL;
</li>
<li>
<a href = "blas1_s_test03.m">blas1_s_test03.m</a>,
tests SASUM;
</li>
<li>
<a href = "blas1_s_test04.m">blas1_s_test04.m</a>,
tests SAXPY;
</li>
<li>
<a href = "blas1_s_test05.m">blas1_s_test05.m</a>,
tests SCOPY;
</li>
<li>
<a href = "blas1_s_test06.m">blas1_s_test06.m</a>,
tests SDOT;
</li>
<li>
<a href = "blas1_s_test07.m">blas1_s_test07.m</a>,
tests SMACH;
</li>
<li>
<a href = "blas1_s_test08.m">blas1_s_test08.m</a>,
tests SNRM2;
</li>
<li>
<a href = "blas1_s_test09.m">blas1_s_test09.m</a>,
tests SROT.
</li>
<li>
<a href = "blas1_s_test10.m">blas1_s_test10.m</a>,
tests SROTG;
</li>
<li>
<a href = "blas1_s_test11.m">blas1_s_test11.m</a>,
tests SSCAL;
</li>
<li>
<a href = "blas1_s_test12.m">blas1_s_test12.m</a>,
tests SSWAP;
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 24 June 2009.
</i>
<!-- John Burkardt -->
</body>
</html>