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<html>
<head>
<title>
BLAS2 - Level 2 Basic Linear Algebra Subprograms
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BLAS2 <br> Level 2 Basic Linear Algebra Subprograms
</h1>
<hr>
<p>
<b>BLAS2</b>
is a FORTRAN90 library which
implements the Level 2
<b>BLAS</b>, or Basic Linear Algebra Subprograms.
</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 2 BLAS are designed to handle a variety of matrix-vector
operations.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>BLAS2</b> is available in
<a href = "../../f_src/blas2/blas2.html">a FORTRAN90 version</a> and
<a href = "../../f77_src/blas2/blas2.html">a FORTRAN77 version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/blas1/blas1.html">
BLAS1</a>,
a FORTRAN90 library which
handles vector-vector operations.
</p>
<p>
<a href = "../../f_src/blas3/blas3.html">
BLAS3</a>,
a FORTRAN90 library which
handles matrix-matrix operations.
</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>
<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>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "blas2.f90">blas2.f90</a>, the vector code;
</li>
<li>
<a href = "blas2.sh">blas2.sh</a>, commands to compile
the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "blas2_prb.f90">blas2_prb.f90</a>, a calling program;
</li>
<li>
<a href = "blas2_prb.sh">blas2_prb.sh</a>, commands to
compile, link, load and run the calling program;
</li>
<li>
<a href = "blas2_prb_output.txt">blas2_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>DGBMV</b> SY:=alpha*A*SX+beta*SY, A a band matrix.
</li>
<li>
<b>DGEMV</b> SY:=alpha*A*SX+beta*SY, A a rectangular matrix.
</li>
<li>
<b>DGER</b> A:=A+alpha*SX*TRANSPOSE(SY), rank 1 update, A a rectangular matrix.
</li>
<li>
<b>DMXPY</b> SY:=SY+A*SX
</li>
<li>
<b>DSBMV</b> SY:=alpha*A*SX+beta*SY, A a symmetric band matrix.
</li>
<li>
<b>DSPMV</b> SY:=alpha*A*SX+beta*SY, A a packed symmetric matrix.
</li>
<li>
<b>DSPR</b> A:=A+alpha*SX*TRANSPOSE(SX), A a packed symmetric matrix.
</li>
<li>
<b>DSPR2</b> A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A packed symmetric.
</li>
<li>
<b>DSYMV</b> SY:=alpha*A*SX+beta*SY, A a symmetric matrix.
</li>
<li>
<b>DSYR</b> A:=A+alpha*SX*TRANSPOSE(SX), A a symmetric matrix.
</li>
<li>
<b>DSYR2</b> A:=A+alpha*SX*TRANSPOSE(SY)+alpha*SY*TRANSPOSE(SX), A a symmetric matrix.
</li>
<li>
<b>DTBMV</b> SX:=A*SX, A a triangular band matrix.
</li>
<li>
<b>DTBSV</b> SX:=INVERSE(A)*SX, A a triangular band matrix.
</li>
<li>
<b>DTPMV</b> SX:=A*SX, A a packed symmetric matrix.
</li>
<li>
<b>DTPSV</b> SX:=INVERSE(A)*SX, A a packed symmetric matrix.
</li>
<li>
<b>DTRMV</b> SX:=A*SX, A a triangular matrix.
</li>
<li>
<b>DTRSV</b> SX:=INVERSE(A)*SX, A a triangular matrix.
</li>
<li>
<b>DXMPY</b> SY:=SY+SX*A
</li>
</ul>
</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 30 August 2005.
</i>
<!-- John Burkardt -->
</body>
</html>