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<html>
<head>
<title>
BLAS1_Z - Basic Linear Algebra Subprograms - Level 1 -
Double precision Complex Arithmetic
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BLAS1_Z <br>
Basic Linear Algebra Subprograms <br>
Level 1 <br>
Double Precision Complex Arithmetic
</h1>
<hr>
<p>
<b>BLAS1_Z</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_Z</b> is available in
<a href = "../../c_src/blas1_z/blas1_z.html">a C version</a> and
<a href = "../../cpp_src/blas1_z/blas1_z.html">a C++ version</a> and
<a href = "../../f77_src/blas1_z/blas1_z.html">a FORTRAN77 version</a> and
<a href = "../../f_src/blas1_z/blas1_z.html">a FORTRAN90 version</a> and
<a href = "../../m_src/blas1_z/blas1_z.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 a version of <b>BLAS1</b> for single precision complex arithmetic.
</p>
<p>
<a href = "../../m_src/blas1_d/blas1_d.html">
BLAS1_D</a>,
a MATLAB library which
is a version of <b>BLAS1</b> for double precision real arithmetic.
</p>
<p>
<a href = "../../m_src/blas1_s/blas1_s.html">
BLAS1_S</a>,
a MATLAB library which
is a version of <b>BLAS1</b> for single precision real arithmetic.
</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
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 = "dzasum.m">dzasum.m</a>,
sums the absolute values of the entries of a complex vector;
</li>
<li>
<a href = "dznrm2.m">dznrm2.m</a>,
computes the Euclidean norm of a complex vector.
</li>
<li>
<a href = "izamax.m">izamax.m</a>,
returns the index of the complex vector entry of greatest magnitude;
</li>
<li>
<a href = "zaxpy.m">zaxpy.m</a>,
adds a constant times one complex vector to another.
</li>
<li>
<a href = "zcopy.m">zcopy.m</a>,
makes a copy of a complex vector;
</li>
<li>
<a href = "zdotc.m">zdotc.m</a>,
computes the conjugated scalar product of two complex vectors;
</li>
<li>
<a href = "zdotu.m">zdotu.m</a>,
computes the unconjugated scalar product of two complex vectors;
</li>
<li>
<a href = "zdrot.m">zdrot.m</a>,
applies a plane rotation to complex vectors.
</li>
<li>
<a href = "zdscal.m">zdscal.m</a>,
scale a complex vector by a real constant.
</li>
<li>
<a href = "zrotg.m">zrotg.m</a>,
constructs a complex Givens plane rotation.
</li>
<li>
<a href = "zscal.m">zscal.m</a>,
scales a complex vector by a constant.
</li>
<li>
<a href = "zswap.m">zswap.m</a>,
interchanges two complex vectors.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "blas1_z_test.m">blas1_z_test.m</a>,
calls all the tests;
</li>
<li>
<a href = "blas1_z_test_output.txt">blas1_z_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "blas1_z_test01.m">blas1_z_test01.m</a>,
tests DZASUM;
</li>
<li>
<a href = "blas1_z_test02.m">blas1_z_test02.m</a>,
tests DZNRM2;
</li>
<li>
<a href = "blas1_z_test03.m">blas1_z_test03.m</a>,
tests IZAMAX;
</li>
<li>
<a href = "blas1_z_test04.m">blas1_z_test04.m</a>,
tests ZABS1;
</li>
<li>
<a href = "blas1_z_test05.m">blas1_z_test05.m</a>,
tests ZABS2;
</li>
<li>
<a href = "blas1_z_test06.m">blas1_z_test06.m</a>,
tests ZAXPY;
</li>
<li>
<a href = "blas1_z_test07.m">blas1_z_test07.m</a>,
tests ZCOPY;
</li>
<li>
<a href = "blas1_z_test08.m">blas1_z_test08.m</a>,
tests ZDOTC;
</li>
<li>
<a href = "blas1_z_test09.m">blas1_z_test09.m</a>,
tests ZDOTU;
</li>
<li>
<a href = "blas1_z_test10.m">blas1_z_test10.m</a>,
tests ZDROT;
</li>
<li>
<a href = "blas1_z_test11.m">blas1_z_test11.m</a>,
tests ZDSCAL;
</li>
<li>
<a href = "blas1_z_test12.m">blas1_z_test12.m</a>,
tests ZMACH.
</li>
<li>
<a href = "blas1_z_test13.m">blas1_z_test13.m</a>,
tests ZROTG;
</li>
<li>
<a href = "blas1_z_test14.m">blas1_z_test14.m</a>,
tests ZSCAL;
</li>
<li>
<a href = "blas1_z_test15.m">blas1_z_test15.m</a>,
tests ZSIGN1;
</li>
<li>
<a href = "blas1_z_test16.m">blas1_z_test16.m</a>,
tests ZSIGN2;
</li>
<li>
<a href = "blas1_z_test17.m">blas1_z_test17.m</a>,
tests ZSWAP;
</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>