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<title>GNU Scientific Library &ndash; Reference Manual: Level 2 GSL BLAS Interface</title>

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<a name="Level-2-GSL-BLAS-Interface"></a>
<div class="header">
<p>
Next: <a href="Level-3-GSL-BLAS-Interface.html#Level-3-GSL-BLAS-Interface" accesskey="n" rel="next">Level 3 GSL BLAS Interface</a>, Previous: <a href="Level-1-GSL-BLAS-Interface.html#Level-1-GSL-BLAS-Interface" accesskey="p" rel="previous">Level 1 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-2"></a>
<h4 class="subsection">13.1.2 Level 2</h4>

<dl>
<dt><a name="index-gsl_005fblas_005fsgemv"></a>Function: <em>int</em> <strong>gsl_blas_sgemv</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, const gsl_vector_float * <var>x</var>, float <var>beta</var>, gsl_vector_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdgemv"></a>Function: <em>int</em> <strong>gsl_blas_dgemv</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, const gsl_vector * <var>x</var>, double <var>beta</var>, gsl_vector * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcgemv"></a>Function: <em>int</em> <strong>gsl_blas_cgemv</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_vector_complex_float * <var>x</var>, const gsl_complex_float <var>beta</var>, gsl_vector_complex_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzgemv"></a>Function: <em>int</em> <strong>gsl_blas_zgemv</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_vector_complex * <var>x</var>, const gsl_complex <var>beta</var>, gsl_vector_complex * <var>y</var>)</em></dt>
<dd><a name="index-GEMV_002c-Level_002d2-BLAS"></a>
<p>These functions compute the matrix-vector product and sum <em>y =
\alpha op(A) x + \beta y</em>, where <em>op(A) = A</em>,
<em>A^T</em>, <em>A^H</em> for <var>TransA</var> = <code>CblasNoTrans</code>,
<code>CblasTrans</code>, <code>CblasConjTrans</code>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fblas_005fstrmv"></a>Function: <em>int</em> <strong>gsl_blas_strmv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_float * <var>A</var>, gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdtrmv"></a>Function: <em>int</em> <strong>gsl_blas_dtrmv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix * <var>A</var>, gsl_vector * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fctrmv"></a>Function: <em>int</em> <strong>gsl_blas_ctrmv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_complex_float * <var>A</var>, gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fztrmv"></a>Function: <em>int</em> <strong>gsl_blas_ztrmv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_complex * <var>A</var>, gsl_vector_complex * <var>x</var>)</em></dt>
<dd><a name="index-TRMV_002c-Level_002d2-BLAS"></a>
<p>These functions compute the matrix-vector product 
<em>x = op(A) x</em> for the triangular matrix <var>A</var>, where
<em>op(A) = A</em>, <em>A^T</em>, <em>A^H</em> for <var>TransA</var> =
<code>CblasNoTrans</code>, <code>CblasTrans</code>, <code>CblasConjTrans</code>.  When
<var>Uplo</var> is <code>CblasUpper</code> then the upper triangle of <var>A</var> is
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
of <var>A</var> is used.  If <var>Diag</var> is <code>CblasNonUnit</code> then the
diagonal of the matrix is used, but if <var>Diag</var> is <code>CblasUnit</code>
then the diagonal elements of the matrix <var>A</var> are taken as unity and
are not referenced.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fblas_005fstrsv"></a>Function: <em>int</em> <strong>gsl_blas_strsv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_float * <var>A</var>, gsl_vector_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdtrsv"></a>Function: <em>int</em> <strong>gsl_blas_dtrsv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix * <var>A</var>, gsl_vector * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fctrsv"></a>Function: <em>int</em> <strong>gsl_blas_ctrsv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_complex_float * <var>A</var>, gsl_vector_complex_float * <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fztrsv"></a>Function: <em>int</em> <strong>gsl_blas_ztrsv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_matrix_complex * <var>A</var>, gsl_vector_complex * <var>x</var>)</em></dt>
<dd><a name="index-TRSV_002c-Level_002d2-BLAS"></a>
<p>These functions compute <em>inv(op(A)) x</em> for <var>x</var>, where
<em>op(A) = A</em>, <em>A^T</em>, <em>A^H</em> for <var>TransA</var> =
<code>CblasNoTrans</code>, <code>CblasTrans</code>, <code>CblasConjTrans</code>.  When
<var>Uplo</var> is <code>CblasUpper</code> then the upper triangle of <var>A</var> is
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
of <var>A</var> is used.  If <var>Diag</var> is <code>CblasNonUnit</code> then the
diagonal of the matrix is used, but if <var>Diag</var> is <code>CblasUnit</code>
then the diagonal elements of the matrix <var>A</var> are taken as unity and
are not referenced.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fblas_005fssymv"></a>Function: <em>int</em> <strong>gsl_blas_ssymv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, const gsl_vector_float * <var>x</var>, float <var>beta</var>, gsl_vector_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsymv"></a>Function: <em>int</em> <strong>gsl_blas_dsymv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, const gsl_vector * <var>x</var>, double <var>beta</var>, gsl_vector * <var>y</var>)</em></dt>
<dd><a name="index-SYMV_002c-Level_002d2-BLAS"></a>
<p>These functions compute the matrix-vector product and sum <em>y =
\alpha A x + \beta y</em> for the symmetric matrix <var>A</var>.  Since the
matrix <var>A</var> is symmetric only its upper half or lower half need to be
stored.  When <var>Uplo</var> is <code>CblasUpper</code> then the upper triangle
and diagonal of <var>A</var> are used, and when <var>Uplo</var> is
<code>CblasLower</code> then the lower triangle and diagonal of <var>A</var> are
used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fchemv"></a>Function: <em>int</em> <strong>gsl_blas_chemv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_vector_complex_float * <var>x</var>, const gsl_complex_float <var>beta</var>, gsl_vector_complex_float * <var>y</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzhemv"></a>Function: <em>int</em> <strong>gsl_blas_zhemv</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_vector_complex * <var>x</var>, const gsl_complex <var>beta</var>, gsl_vector_complex * <var>y</var>)</em></dt>
<dd><a name="index-HEMV_002c-Level_002d2-BLAS"></a>
<p>These functions compute the matrix-vector product and sum <em>y =
\alpha A x + \beta y</em> for the hermitian matrix <var>A</var>.  Since the
matrix <var>A</var> is hermitian only its upper half or lower half need to be
stored.  When <var>Uplo</var> is <code>CblasUpper</code> then the upper triangle
and diagonal of <var>A</var> are used, and when <var>Uplo</var> is
<code>CblasLower</code> then the lower triangle and diagonal of <var>A</var> are
used.  The imaginary elements of the diagonal are automatically assumed
to be zero and are not referenced.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fsger"></a>Function: <em>int</em> <strong>gsl_blas_sger</strong> <em>(float <var>alpha</var>, const gsl_vector_float * <var>x</var>, const gsl_vector_float * <var>y</var>, gsl_matrix_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdger"></a>Function: <em>int</em> <strong>gsl_blas_dger</strong> <em>(double <var>alpha</var>, const gsl_vector * <var>x</var>, const gsl_vector * <var>y</var>, gsl_matrix * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcgeru"></a>Function: <em>int</em> <strong>gsl_blas_cgeru</strong> <em>(const gsl_complex_float <var>alpha</var>, const gsl_vector_complex_float * <var>x</var>, const gsl_vector_complex_float * <var>y</var>, gsl_matrix_complex_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzgeru"></a>Function: <em>int</em> <strong>gsl_blas_zgeru</strong> <em>(const gsl_complex <var>alpha</var>, const gsl_vector_complex * <var>x</var>, const gsl_vector_complex * <var>y</var>, gsl_matrix_complex * <var>A</var>)</em></dt>
<dd><a name="index-GER_002c-Level_002d2-BLAS"></a>
<a name="index-GERU_002c-Level_002d2-BLAS"></a>
<p>These functions compute the rank-1 update <em>A = \alpha x y^T + A</em> of
the matrix <var>A</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcgerc"></a>Function: <em>int</em> <strong>gsl_blas_cgerc</strong> <em>(const gsl_complex_float <var>alpha</var>, const gsl_vector_complex_float * <var>x</var>, const gsl_vector_complex_float * <var>y</var>, gsl_matrix_complex_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzgerc"></a>Function: <em>int</em> <strong>gsl_blas_zgerc</strong> <em>(const gsl_complex <var>alpha</var>, const gsl_vector_complex * <var>x</var>, const gsl_vector_complex * <var>y</var>, gsl_matrix_complex * <var>A</var>)</em></dt>
<dd><a name="index-GERC_002c-Level_002d2-BLAS"></a>
<p>These functions compute the conjugate rank-1 update <em>A = \alpha x
y^H + A</em> of the matrix <var>A</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fssyr"></a>Function: <em>int</em> <strong>gsl_blas_ssyr</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, float <var>alpha</var>, const gsl_vector_float * <var>x</var>, gsl_matrix_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsyr"></a>Function: <em>int</em> <strong>gsl_blas_dsyr</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, double <var>alpha</var>, const gsl_vector * <var>x</var>, gsl_matrix * <var>A</var>)</em></dt>
<dd><a name="index-SYR_002c-Level_002d2-BLAS"></a>
<p>These functions compute the symmetric rank-1 update <em>A = \alpha x
x^T + A</em> of the symmetric matrix <var>A</var>.  Since the matrix <var>A</var> is
symmetric only its upper half or lower half need to be stored.  When
<var>Uplo</var> is <code>CblasUpper</code> then the upper triangle and diagonal of
<var>A</var> are used, and when <var>Uplo</var> is <code>CblasLower</code> then the
lower triangle and diagonal of <var>A</var> are used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcher"></a>Function: <em>int</em> <strong>gsl_blas_cher</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, float <var>alpha</var>, const gsl_vector_complex_float * <var>x</var>, gsl_matrix_complex_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzher"></a>Function: <em>int</em> <strong>gsl_blas_zher</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, double <var>alpha</var>, const gsl_vector_complex * <var>x</var>, gsl_matrix_complex * <var>A</var>)</em></dt>
<dd><a name="index-HER_002c-Level_002d2-BLAS"></a>
<p>These functions compute the hermitian rank-1 update <em>A = \alpha x
x^H + A</em> of the hermitian matrix <var>A</var>.  Since the matrix <var>A</var> is
hermitian only its upper half or lower half need to be stored.  When
<var>Uplo</var> is <code>CblasUpper</code> then the upper triangle and diagonal of
<var>A</var> are used, and when <var>Uplo</var> is <code>CblasLower</code> then the
lower triangle and diagonal of <var>A</var> are used.  The imaginary elements
of the diagonal are automatically set to zero.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fssyr2"></a>Function: <em>int</em> <strong>gsl_blas_ssyr2</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, float <var>alpha</var>, const gsl_vector_float * <var>x</var>, const gsl_vector_float * <var>y</var>, gsl_matrix_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsyr2"></a>Function: <em>int</em> <strong>gsl_blas_dsyr2</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, double <var>alpha</var>, const gsl_vector * <var>x</var>, const gsl_vector * <var>y</var>, gsl_matrix * <var>A</var>)</em></dt>
<dd><a name="index-SYR2_002c-Level_002d2-BLAS"></a>
<p>These functions compute the symmetric rank-2 update <em>A = \alpha x
y^T + \alpha y x^T + A</em> of the symmetric matrix <var>A</var>.  Since the
matrix <var>A</var> is symmetric only its upper half or lower half need to be
stored.  When <var>Uplo</var> is <code>CblasUpper</code> then the upper triangle
and diagonal of <var>A</var> are used, and when <var>Uplo</var> is
<code>CblasLower</code> then the lower triangle and diagonal of <var>A</var> are
used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcher2"></a>Function: <em>int</em> <strong>gsl_blas_cher2</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex_float <var>alpha</var>, const gsl_vector_complex_float * <var>x</var>, const gsl_vector_complex_float * <var>y</var>, gsl_matrix_complex_float * <var>A</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzher2"></a>Function: <em>int</em> <strong>gsl_blas_zher2</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex <var>alpha</var>, const gsl_vector_complex * <var>x</var>, const gsl_vector_complex * <var>y</var>, gsl_matrix_complex * <var>A</var>)</em></dt>
<dd><a name="index-HER2_002c-Level_002d2-BLAS"></a>
<p>These functions compute the hermitian rank-2 update <em>A = \alpha x
y^H + \alpha^* y x^H + A</em> of the hermitian matrix <var>A</var>.  Since the
matrix <var>A</var> is hermitian only its upper half or lower half need to be
stored.  When <var>Uplo</var> is <code>CblasUpper</code> then the upper triangle
and diagonal of <var>A</var> are used, and when <var>Uplo</var> is
<code>CblasLower</code> then the lower triangle and diagonal of <var>A</var> are
used.  The imaginary elements of the diagonal are automatically set to zero.
</p></dd></dl>

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