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<title>GNU Scientific Library &ndash; Reference Manual: Level 3 GSL BLAS Interface</title>

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<a name="Level-3-GSL-BLAS-Interface"></a>
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<p>
Previous: <a href="Level-2-GSL-BLAS-Interface.html#Level-2-GSL-BLAS-Interface" accesskey="p" rel="previous">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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<hr>
<a name="Level-3"></a>
<h4 class="subsection">13.1.3 Level 3</h4>


<dl>
<dt><a name="index-gsl_005fblas_005fsgemm"></a>Function: <em>int</em> <strong>gsl_blas_sgemm</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_TRANSPOSE_t <var>TransB</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, const gsl_matrix_float * <var>B</var>, float <var>beta</var>, gsl_matrix_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdgemm"></a>Function: <em>int</em> <strong>gsl_blas_dgemm</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_TRANSPOSE_t <var>TransB</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, const gsl_matrix * <var>B</var>, double <var>beta</var>, gsl_matrix * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcgemm"></a>Function: <em>int</em> <strong>gsl_blas_cgemm</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_TRANSPOSE_t <var>TransB</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_matrix_complex_float * <var>B</var>, const gsl_complex_float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzgemm"></a>Function: <em>int</em> <strong>gsl_blas_zgemm</strong> <em>(CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_TRANSPOSE_t <var>TransB</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_matrix_complex * <var>B</var>, const gsl_complex <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-GEMM_002c-Level_002d3-BLAS"></a>
<p>These functions compute the matrix-matrix product and sum <em>C =
\alpha op(A) op(B) + \beta C</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> and similarly for the parameter <var>TransB</var>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fblas_005fssymm"></a>Function: <em>int</em> <strong>gsl_blas_ssymm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, const gsl_matrix_float * <var>B</var>, float <var>beta</var>, gsl_matrix_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsymm"></a>Function: <em>int</em> <strong>gsl_blas_dsymm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, const gsl_matrix * <var>B</var>, double <var>beta</var>, gsl_matrix * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcsymm"></a>Function: <em>int</em> <strong>gsl_blas_csymm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_matrix_complex_float * <var>B</var>, const gsl_complex_float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzsymm"></a>Function: <em>int</em> <strong>gsl_blas_zsymm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_matrix_complex * <var>B</var>, const gsl_complex <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-SYMM_002c-Level_002d3-BLAS"></a>
<p>These functions compute the matrix-matrix product and sum <em>C =
\alpha A B + \beta C</em> for <var>Side</var> is <code>CblasLeft</code> and <em>C =
\alpha B A + \beta C</em> for <var>Side</var> is <code>CblasRight</code>, where the
matrix <var>A</var> is symmetric.  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_005fchemm"></a>Function: <em>int</em> <strong>gsl_blas_chemm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_matrix_complex_float * <var>B</var>, const gsl_complex_float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzhemm"></a>Function: <em>int</em> <strong>gsl_blas_zhemm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_matrix_complex * <var>B</var>, const gsl_complex <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-HEMM_002c-Level_002d3-BLAS"></a>
<p>These functions compute the matrix-matrix product and sum <em>C =
\alpha A B + \beta C</em> for <var>Side</var> is <code>CblasLeft</code> and <em>C =
\alpha B A + \beta C</em> for <var>Side</var> is <code>CblasRight</code>, where the
matrix <var>A</var> is hermitian.  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_005fstrmm"></a>Function: <em>int</em> <strong>gsl_blas_strmm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, gsl_matrix_float * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdtrmm"></a>Function: <em>int</em> <strong>gsl_blas_dtrmm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, gsl_matrix * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fctrmm"></a>Function: <em>int</em> <strong>gsl_blas_ctrmm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, gsl_matrix_complex_float * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fztrmm"></a>Function: <em>int</em> <strong>gsl_blas_ztrmm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, gsl_matrix_complex * <var>B</var>)</em></dt>
<dd><a name="index-TRMM_002c-Level_002d3-BLAS"></a>
<p>These functions compute the matrix-matrix product <em>B = \alpha op(A)
B</em> for <var>Side</var> is <code>CblasLeft</code> and <em>B = \alpha B op(A)</em> for
<var>Side</var> is <code>CblasRight</code>.  The matrix <var>A</var> is triangular and
<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 <var>A</var> 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_005fstrsm"></a>Function: <em>int</em> <strong>gsl_blas_strsm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, gsl_matrix_float * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdtrsm"></a>Function: <em>int</em> <strong>gsl_blas_dtrsm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, gsl_matrix * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fctrsm"></a>Function: <em>int</em> <strong>gsl_blas_ctrsm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, gsl_matrix_complex_float * <var>B</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fztrsm"></a>Function: <em>int</em> <strong>gsl_blas_ztrsm</strong> <em>(CBLAS_SIDE_t <var>Side</var>, CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>TransA</var>, CBLAS_DIAG_t <var>Diag</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, gsl_matrix_complex * <var>B</var>)</em></dt>
<dd><a name="index-TRSM_002c-Level_002d3-BLAS"></a>
<p>These functions compute the inverse-matrix matrix product 
<em>B = \alpha op(inv(A))B</em> for <var>Side</var> is 
<code>CblasLeft</code> and <em>B = \alpha B op(inv(A))</em> for
<var>Side</var> is <code>CblasRight</code>.  The matrix <var>A</var> is triangular and
<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 <var>A</var> 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_005fssyrk"></a>Function: <em>int</em> <strong>gsl_blas_ssyrk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, float <var>beta</var>, gsl_matrix_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsyrk"></a>Function: <em>int</em> <strong>gsl_blas_dsyrk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, double <var>beta</var>, gsl_matrix * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcsyrk"></a>Function: <em>int</em> <strong>gsl_blas_csyrk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_complex_float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzsyrk"></a>Function: <em>int</em> <strong>gsl_blas_zsyrk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_complex <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-SYRK_002c-Level_002d3-BLAS"></a>
<p>These functions compute a rank-k update of the symmetric matrix <var>C</var>,
<em>C = \alpha A A^T + \beta C</em> when <var>Trans</var> is
<code>CblasNoTrans</code> and <em>C = \alpha A^T A + \beta C</em> when
<var>Trans</var> is <code>CblasTrans</code>.  Since the matrix <var>C</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>C</var> are
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
and diagonal of <var>C</var> are used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcherk"></a>Function: <em>int</em> <strong>gsl_blas_cherk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzherk"></a>Function: <em>int</em> <strong>gsl_blas_zherk</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, double <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, double <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-HERK_002c-Level_002d3-BLAS"></a>
<p>These functions compute a rank-k update of the hermitian matrix <var>C</var>,
<em>C = \alpha A A^H + \beta C</em> when <var>Trans</var> is
<code>CblasNoTrans</code> and <em>C = \alpha A^H A + \beta C</em> when
<var>Trans</var> is <code>CblasConjTrans</code>.  Since the matrix <var>C</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>C</var> are
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
and diagonal of <var>C</var> are used.  The imaginary elements of the
diagonal are automatically set to zero.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fssyr2k"></a>Function: <em>int</em> <strong>gsl_blas_ssyr2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, float <var>alpha</var>, const gsl_matrix_float * <var>A</var>, const gsl_matrix_float * <var>B</var>, float <var>beta</var>, gsl_matrix_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fdsyr2k"></a>Function: <em>int</em> <strong>gsl_blas_dsyr2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, double <var>alpha</var>, const gsl_matrix * <var>A</var>, const gsl_matrix * <var>B</var>, double <var>beta</var>, gsl_matrix * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fcsyr2k"></a>Function: <em>int</em> <strong>gsl_blas_csyr2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_matrix_complex_float * <var>B</var>, const gsl_complex_float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzsyr2k"></a>Function: <em>int</em> <strong>gsl_blas_zsyr2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_matrix_complex * <var>B</var>, const gsl_complex <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-SYR2K_002c-Level_002d3-BLAS"></a>
<p>These functions compute a rank-2k update of the symmetric matrix <var>C</var>,
<em>C = \alpha A B^T + \alpha B A^T + \beta C</em> when <var>Trans</var> is
<code>CblasNoTrans</code> and <em>C = \alpha A^T B + \alpha B^T A + \beta C</em> when
<var>Trans</var> is <code>CblasTrans</code>.  Since the matrix <var>C</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>C</var> are
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
and diagonal of <var>C</var> are used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fblas_005fcher2k"></a>Function: <em>int</em> <strong>gsl_blas_cher2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex_float <var>alpha</var>, const gsl_matrix_complex_float * <var>A</var>, const gsl_matrix_complex_float * <var>B</var>, float <var>beta</var>, gsl_matrix_complex_float * <var>C</var>)</em></dt>
<dt><a name="index-gsl_005fblas_005fzher2k"></a>Function: <em>int</em> <strong>gsl_blas_zher2k</strong> <em>(CBLAS_UPLO_t <var>Uplo</var>, CBLAS_TRANSPOSE_t <var>Trans</var>, const gsl_complex <var>alpha</var>, const gsl_matrix_complex * <var>A</var>, const gsl_matrix_complex * <var>B</var>, double <var>beta</var>, gsl_matrix_complex * <var>C</var>)</em></dt>
<dd><a name="index-HER2K_002c-Level_002d3-BLAS"></a>
<p>These functions compute a rank-2k update of the hermitian matrix <var>C</var>,
<em>C = \alpha A B^H + \alpha^* B A^H + \beta C</em> when <var>Trans</var> is
<code>CblasNoTrans</code> and <em>C = \alpha A^H B + \alpha^* B^H A + \beta C</em> when
<var>Trans</var> is <code>CblasConjTrans</code>.  Since the matrix <var>C</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>C</var> are
used, and when <var>Uplo</var> is <code>CblasLower</code> then the lower triangle
and diagonal of <var>C</var> are used.  The imaginary elements of the
diagonal are automatically set to zero.
</p></dd></dl>

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