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<title>GNU Scientific Library &ndash; Reference Manual: Level 1 GSL BLAS Interface</title>

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<a name="Level-1-GSL-BLAS-Interface"></a>
<div class="header">
<p>
Next: <a href="Level-2-GSL-BLAS-Interface.html#Level-2-GSL-BLAS-Interface" accesskey="n" rel="next">Level 2 GSL BLAS Interface</a>, Up: <a href="GSL-BLAS-Interface.html#GSL-BLAS-Interface" accesskey="u" rel="up">GSL BLAS Interface</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Level-1"></a>
<h4 class="subsection">13.1.1 Level 1</h4>

<dl>
<dt><a name="index-gsl_005fblas_005fsdsdot"></a>Function: <em>int</em> <strong>gsl_blas_sdsdot</strong> <em>(float <var>alpha</var>, const gsl_vector_float * <var>x</var>, const gsl_vector_float * <var>y</var>, float * <var>result</var>)</em></dt>
<dd><a name="index-DOT_002c-Level_002d1-BLAS"></a>
<p>This function computes the sum <em>\alpha + x^T y</em> for the vectors
<var>x</var> and <var>y</var>, returning the result in <var>result</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsdot"></a>Function: <em>int</em> <strong>gsl_blas_sdot</strong> <em>(const gsl_vector_float * <var>x</var>, const gsl_vector_float * <var>y</var>, float * <var>result</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsdot"></a>Function: <em>int</em> <strong>gsl_blas_dsdot</strong> <em>(const gsl_vector_float * <var>x</var>, const gsl_vector_float * <var>y</var>, double * <var>result</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fddot"></a>Function: <em>int</em> <strong>gsl_blas_ddot</strong> <em>(const gsl_vector * <var>x</var>, const gsl_vector * <var>y</var>, double * <var>result</var>)</em></dt>
<dd><p>These functions compute the scalar product <em>x^T y</em> for the vectors
<var>x</var> and <var>y</var>, returning the result in <var>result</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcdotu"></a>Function: <em>int</em> <strong>gsl_blas_cdotu</strong> <em>(const gsl_vector_complex_float * <var>x</var>, const gsl_vector_complex_float * <var>y</var>, gsl_complex_float * <var>dotu</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzdotu"></a>Function: <em>int</em> <strong>gsl_blas_zdotu</strong> <em>(const gsl_vector_complex * <var>x</var>, const gsl_vector_complex * <var>y</var>, gsl_complex * <var>dotu</var>)</em></dt>
<dd><p>These functions compute the complex scalar product <em>x^T y</em> for the
vectors <var>x</var> and <var>y</var>, returning the result in <var>dotu</var>
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcdotc"></a>Function: <em>int</em> <strong>gsl_blas_cdotc</strong> <em>(const gsl_vector_complex_float * <var>x</var>, const gsl_vector_complex_float * <var>y</var>, gsl_complex_float * <var>dotc</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzdotc"></a>Function: <em>int</em> <strong>gsl_blas_zdotc</strong> <em>(const gsl_vector_complex * <var>x</var>, const gsl_vector_complex * <var>y</var>, gsl_complex * <var>dotc</var>)</em></dt>
<dd><p>These functions compute the complex conjugate scalar product <em>x^H
y</em> for the vectors <var>x</var> and <var>y</var>, returning the result in
<var>dotc</var>
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsnrm2"></a>Function: <em>float</em> <strong>gsl_blas_snrm2</strong> <em>(const gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdnrm2"></a>Function: <em>double</em> <strong>gsl_blas_dnrm2</strong> <em>(const gsl_vector * <var>x</var>)</em></dt>
<dd><a name="index-NRM2_002c-Level_002d1-BLAS"></a>
<p>These functions compute the Euclidean norm 
<em>||x||_2 = \sqrt {\sum x_i^2}</em> of the vector <var>x</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fscnrm2"></a>Function: <em>float</em> <strong>gsl_blas_scnrm2</strong> <em>(const gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdznrm2"></a>Function: <em>double</em> <strong>gsl_blas_dznrm2</strong> <em>(const gsl_vector_complex * <var>x</var>)</em></dt>
<dd><p>These functions compute the Euclidean norm of the complex vector <var>x</var>,
</p>
<div class="example">
<pre class="example">||x||_2 = \sqrt {\sum (\Re(x_i)^2 + \Im(x_i)^2)}.
</pre></div>
</dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsasum"></a>Function: <em>float</em> <strong>gsl_blas_sasum</strong> <em>(const gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdasum"></a>Function: <em>double</em> <strong>gsl_blas_dasum</strong> <em>(const gsl_vector * <var>x</var>)</em></dt>
<dd><a name="index-ASUM_002c-Level_002d1-BLAS"></a>
<p>These functions compute the absolute sum <em>\sum |x_i|</em> of the
elements of the vector <var>x</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fscasum"></a>Function: <em>float</em> <strong>gsl_blas_scasum</strong> <em>(const gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdzasum"></a>Function: <em>double</em> <strong>gsl_blas_dzasum</strong> <em>(const gsl_vector_complex * <var>x</var>)</em></dt>
<dd><p>These functions compute the sum of the magnitudes of the real and
imaginary parts of the complex vector <var>x</var>, 
<em>\sum |\Re(x_i)| + |\Im(x_i)|</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fisamax"></a>Function: <em>CBLAS_INDEX_t</em> <strong>gsl_blas_isamax</strong> <em>(const gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fidamax"></a>Function: <em>CBLAS_INDEX_t</em> <strong>gsl_blas_idamax</strong> <em>(const gsl_vector * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005ficamax"></a>Function: <em>CBLAS_INDEX_t</em> <strong>gsl_blas_icamax</strong> <em>(const gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fizamax"></a>Function: <em>CBLAS_INDEX_t</em> <strong>gsl_blas_izamax</strong> <em>(const gsl_vector_complex * <var>x</var>)</em></dt>
<dd><a name="index-AMAX_002c-Level_002d1-BLAS"></a>
<p>These functions return the index of the largest element of the vector
<var>x</var>. The largest element is determined by its absolute magnitude for
real vectors and by the sum of the magnitudes of the real and imaginary
parts <em>|\Re(x_i)| + |\Im(x_i)|</em> for complex vectors.  If the
largest value occurs several times then the index of the first
occurrence is returned.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsswap"></a>Function: <em>int</em> <strong>gsl_blas_sswap</strong> <em>(gsl_vector_float * <var>x</var>, gsl_vector_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdswap"></a>Function: <em>int</em> <strong>gsl_blas_dswap</strong> <em>(gsl_vector * <var>x</var>, gsl_vector * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcswap"></a>Function: <em>int</em> <strong>gsl_blas_cswap</strong> <em>(gsl_vector_complex_float * <var>x</var>, gsl_vector_complex_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzswap"></a>Function: <em>int</em> <strong>gsl_blas_zswap</strong> <em>(gsl_vector_complex * <var>x</var>, gsl_vector_complex * <var>y</var>)</em></dt>
<dd><a name="index-SWAP_002c-Level_002d1-BLAS"></a>
<p>These functions exchange the elements of the vectors <var>x</var> and <var>y</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fscopy"></a>Function: <em>int</em> <strong>gsl_blas_scopy</strong> <em>(const gsl_vector_float * <var>x</var>, gsl_vector_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdcopy"></a>Function: <em>int</em> <strong>gsl_blas_dcopy</strong> <em>(const gsl_vector * <var>x</var>, gsl_vector * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fccopy"></a>Function: <em>int</em> <strong>gsl_blas_ccopy</strong> <em>(const gsl_vector_complex_float * <var>x</var>, gsl_vector_complex_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzcopy"></a>Function: <em>int</em> <strong>gsl_blas_zcopy</strong> <em>(const gsl_vector_complex * <var>x</var>, gsl_vector_complex * <var>y</var>)</em></dt>
<dd><a name="index-COPY_002c-Level_002d1-BLAS"></a>
<p>These functions copy the elements of the vector <var>x</var> into the vector
<var>y</var>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fblas_005fsaxpy"></a>Function: <em>int</em> <strong>gsl_blas_saxpy</strong> <em>(float <var>alpha</var>, const gsl_vector_float * <var>x</var>, gsl_vector_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdaxpy"></a>Function: <em>int</em> <strong>gsl_blas_daxpy</strong> <em>(double <var>alpha</var>, const gsl_vector * <var>x</var>, gsl_vector * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcaxpy"></a>Function: <em>int</em> <strong>gsl_blas_caxpy</strong> <em>(const gsl_complex_float <var>alpha</var>, const gsl_vector_complex_float * <var>x</var>, gsl_vector_complex_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzaxpy"></a>Function: <em>int</em> <strong>gsl_blas_zaxpy</strong> <em>(const gsl_complex <var>alpha</var>, const gsl_vector_complex * <var>x</var>, gsl_vector_complex * <var>y</var>)</em></dt>
<dd><a name="index-AXPY_002c-Level_002d1-BLAS"></a>
<a name="index-DAXPY_002c-Level_002d1-BLAS"></a>
<a name="index-SAXPY_002c-Level_002d1-BLAS"></a>
<p>These functions compute the sum <em>y = \alpha x + y</em> for the vectors
<var>x</var> and <var>y</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsscal"></a>Function: <em>void</em> <strong>gsl_blas_sscal</strong> <em>(float <var>alpha</var>, gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdscal"></a>Function: <em>void</em> <strong>gsl_blas_dscal</strong> <em>(double <var>alpha</var>, gsl_vector * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcscal"></a>Function: <em>void</em> <strong>gsl_blas_cscal</strong> <em>(const gsl_complex_float <var>alpha</var>, gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzscal"></a>Function: <em>void</em> <strong>gsl_blas_zscal</strong> <em>(const gsl_complex <var>alpha</var>, gsl_vector_complex * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcsscal"></a>Function: <em>void</em> <strong>gsl_blas_csscal</strong> <em>(float <var>alpha</var>, gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzdscal"></a>Function: <em>void</em> <strong>gsl_blas_zdscal</strong> <em>(double <var>alpha</var>, gsl_vector_complex * <var>x</var>)</em></dt>
<dd><a name="index-SCAL_002c-Level_002d1-BLAS"></a>
<p>These functions rescale the vector <var>x</var> by the multiplicative factor
<var>alpha</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsrotg"></a>Function: <em>int</em> <strong>gsl_blas_srotg</strong> <em>(float <var>a</var>[], float <var>b</var>[], float <var>c</var>[], float <var>s</var>[])</em></dt>
<dt><a name="index-gsl_005fblas_005fdrotg"></a>Function: <em>int</em> <strong>gsl_blas_drotg</strong> <em>(double <var>a</var>[], double <var>b</var>[], double <var>c</var>[], double <var>s</var>[])</em></dt>
<dd><a name="index-ROTG_002c-Level_002d1-BLAS"></a>
<a name="index-Givens-Rotation_002c-BLAS"></a>
<p>These functions compute a Givens rotation <em>(c,s)</em> which zeroes the
vector <em>(a,b)</em>,
</p>
<div class="example">
<pre class="example">[  c  s ] [ a ] = [ r ]
[ -s  c ] [ b ]   [ 0 ]
</pre></div>

<p>The variables <var>a</var> and <var>b</var> are overwritten by the routine.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsrot"></a>Function: <em>int</em> <strong>gsl_blas_srot</strong> <em>(gsl_vector_float * <var>x</var>, gsl_vector_float * <var>y</var>, float <var>c</var>, float <var>s</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdrot"></a>Function: <em>int</em> <strong>gsl_blas_drot</strong> <em>(gsl_vector * <var>x</var>, gsl_vector * <var>y</var>, const double <var>c</var>, const double <var>s</var>)</em></dt>
<dd><p>These functions apply a Givens rotation <em>(x', y') = (c x + s y, -s
x + c y)</em> to the vectors <var>x</var>, <var>y</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsrotmg"></a>Function: <em>int</em> <strong>gsl_blas_srotmg</strong> <em>(float <var>d1</var>[], float <var>d2</var>[], float <var>b1</var>[], float <var>b2</var>, float <var>P</var>[])</em></dt>
<dt><a name="index-gsl_005fblas_005fdrotmg"></a>Function: <em>int</em> <strong>gsl_blas_drotmg</strong> <em>(double <var>d1</var>[], double <var>d2</var>[], double <var>b1</var>[], double <var>b2</var>, double <var>P</var>[])</em></dt>
<dd><a name="index-Modified-Givens-Rotation_002c-BLAS"></a>
<a name="index-Givens-Rotation_002c-Modified_002c-BLAS"></a>
<p>These functions compute a modified Givens transformation.  The modified
Givens transformation is defined in the original Level-1 <small>BLAS</small>
specification, given in the references.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsrotm"></a>Function: <em>int</em> <strong>gsl_blas_srotm</strong> <em>(gsl_vector_float * <var>x</var>, gsl_vector_float * <var>y</var>, const float <var>P</var>[])</em></dt>
<dt><a name="index-gsl_005fblas_005fdrotm"></a>Function: <em>int</em> <strong>gsl_blas_drotm</strong> <em>(gsl_vector * <var>x</var>, gsl_vector * <var>y</var>, const double <var>P</var>[])</em></dt>
<dd><p>These functions apply a modified Givens transformation.  
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Level-2-GSL-BLAS-Interface.html#Level-2-GSL-BLAS-Interface" accesskey="n" rel="next">Level 2 GSL BLAS Interface</a>, Up: <a href="GSL-BLAS-Interface.html#GSL-BLAS-Interface" accesskey="u" rel="up">GSL BLAS Interface</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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