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<title>BLAS Support - GNU Scientific Library -- Reference Manual</title>
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<h2 class="chapter">12 BLAS Support</h2>
<p><a name="index-linear-algebra_002c-BLAS-1071"></a><a name="index-matrix_002c-operations-1072"></a><a name="index-vector_002c-operations-1073"></a><a name="index-BLAS-1074"></a><a name="index-CBLAS-1075"></a><a name="index-Basic-Linear-Algebra-Subroutines-_0028BLAS_0029-1076"></a>
The Basic Linear Algebra Subprograms (<span class="sc">blas</span>) define a set of fundamental
operations on vectors and matrices which can be used to create optimized
higher-level linear algebra functionality.
<p>The library provides a low-level layer which corresponds directly to the
C-language <span class="sc">blas</span> standard, referred to here as “<span class="sc">cblas</span>”, and a
higher-level interface for operations on GSL vectors and matrices.
Users who are interested in simple operations on GSL vector and matrix
objects should use the high-level layer, which is declared in the file
<code>gsl_blas.h</code>. This should satisfy the needs of most users. Note
that GSL matrices are implemented using dense-storage so the interface
only includes the corresponding dense-storage <span class="sc">blas</span> functions. The full
<span class="sc">blas</span> functionality for band-format and packed-format matrices is
available through the low-level <span class="sc">cblas</span> interface.
<p>The interface for the <code>gsl_cblas</code> layer is specified in the file
<code>gsl_cblas.h</code>. This interface corresponds to the <span class="sc">blas</span> Technical
Forum's draft standard for the C interface to legacy <span class="sc">blas</span>
implementations. Users who have access to other conforming <span class="sc">cblas</span>
implementations can use these in place of the version provided by the
library. Note that users who have only a Fortran <span class="sc">blas</span> library can
use a <span class="sc">cblas</span> conformant wrapper to convert it into a <span class="sc">cblas</span>
library. A reference <span class="sc">cblas</span> wrapper for legacy Fortran
implementations exists as part of the draft <span class="sc">cblas</span> standard and can
be obtained from Netlib. The complete set of <span class="sc">cblas</span> functions is
listed in an appendix (see <a href="GSL-CBLAS-Library.html">GSL CBLAS Library</a>).
<p>There are three levels of <span class="sc">blas</span> operations,
<dl>
<dt><b>Level 1</b><dd>Vector operations, e.g. y = \alpha x + y
<br><dt><b>Level 2</b><dd>Matrix-vector operations, e.g. y = \alpha A x + \beta y
<br><dt><b>Level 3</b><dd>Matrix-matrix operations, e.g. C = \alpha A B + C
</dl>
<p class="noindent">Each routine has a name which specifies the operation, the type of
matrices involved and their precisions. Some of the most common
operations and their names are given below,
<dl>
<dt><b>DOT</b><dd>scalar product, x^T y
<br><dt><b>AXPY</b><dd>vector sum, \alpha x + y
<br><dt><b>MV</b><dd>matrix-vector product, A x
<br><dt><b>SV</b><dd>matrix-vector solve, inv(A) x
<br><dt><b>MM</b><dd>matrix-matrix product, A B
<br><dt><b>SM</b><dd>matrix-matrix solve, inv(A) B
</dl>
<p class="noindent">The types of matrices are,
<dl>
<dt><b>GE</b><dd>general
<br><dt><b>GB</b><dd>general band
<br><dt><b>SY</b><dd>symmetric
<br><dt><b>SB</b><dd>symmetric band
<br><dt><b>SP</b><dd>symmetric packed
<br><dt><b>HE</b><dd>hermitian
<br><dt><b>HB</b><dd>hermitian band
<br><dt><b>HP</b><dd>hermitian packed
<br><dt><b>TR</b><dd>triangular
<br><dt><b>TB</b><dd>triangular band
<br><dt><b>TP</b><dd>triangular packed
</dl>
<p class="noindent">Each operation is defined for four precisions,
<dl>
<dt><b>S</b><dd>single real
<br><dt><b>D</b><dd>double real
<br><dt><b>C</b><dd>single complex
<br><dt><b>Z</b><dd>double complex
</dl>
<p class="noindent">Thus, for example, the name <span class="sc">sgemm</span> stands for “single-precision
general matrix-matrix multiply” and <span class="sc">zgemm</span> stands for
“double-precision complex matrix-matrix multiply”.
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<li><a accesskey="2" href="BLAS-Examples.html">BLAS Examples</a>
<li><a accesskey="3" href="BLAS-References-and-Further-Reading.html">BLAS References and Further Reading</a>
</ul>
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