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<title>Level 2 GSL BLAS Interface - GNU Scientific Library -- Reference Manual</title>
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Previous: <a rel="previous" accesskey="p" href="Level-1-GSL-BLAS-Interface.html">Level 1 GSL BLAS Interface</a>,
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<h4 class="subsection">13.1.2 Level 2</h4>
<div class="defun">
— Function: int <b>gsl_blas_sgemv</b> (<var>CBLAS_TRANSPOSE_t TransA, float alpha, const gsl_matrix_float * A, const gsl_vector_float * x, float beta, gsl_vector_float * y</var>)<var><a name="index-gsl_005fblas_005fsgemv-1200"></a></var><br>
— Function: int <b>gsl_blas_dgemv</b> (<var>CBLAS_TRANSPOSE_t TransA, double alpha, const gsl_matrix * A, const gsl_vector * x, double beta, gsl_vector * y</var>)<var><a name="index-gsl_005fblas_005fdgemv-1201"></a></var><br>
— Function: int <b>gsl_blas_cgemv</b> (<var>CBLAS_TRANSPOSE_t TransA, const gsl_complex_float alpha, const gsl_matrix_complex_float * A, const gsl_vector_complex_float * x, const gsl_complex_float beta, gsl_vector_complex_float * y</var>)<var><a name="index-gsl_005fblas_005fcgemv-1202"></a></var><br>
— Function: int <b>gsl_blas_zgemv</b> (<var>CBLAS_TRANSPOSE_t TransA, const gsl_complex alpha, const gsl_matrix_complex * A, const gsl_vector_complex * x, const gsl_complex beta, gsl_vector_complex * y</var>)<var><a name="index-gsl_005fblas_005fzgemv-1203"></a></var><br>
<blockquote><p><a name="index-GEMV_002c-Level_002d2-BLAS-1204"></a>These functions compute the matrix-vector product and sum y =
\alpha op(A) x + \beta y, where op(A) = A,
A^T, A^H for <var>TransA</var> = <code>CblasNoTrans</code>,
<code>CblasTrans</code>, <code>CblasConjTrans</code>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_strmv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_float * A, gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fstrmv-1205"></a></var><br>
— Function: int <b>gsl_blas_dtrmv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix * A, gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fdtrmv-1206"></a></var><br>
— Function: int <b>gsl_blas_ctrmv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_complex_float * A, gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fctrmv-1207"></a></var><br>
— Function: int <b>gsl_blas_ztrmv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_complex * A, gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fztrmv-1208"></a></var><br>
<blockquote><p><a name="index-TRMV_002c-Level_002d2-BLAS-1209"></a>These functions compute the matrix-vector product
x = op(A) x for the triangular matrix <var>A</var>, where
op(A) = A, A^T, A^H 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_strsv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_float * A, gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fstrsv-1210"></a></var><br>
— Function: int <b>gsl_blas_dtrsv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix * A, gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fdtrsv-1211"></a></var><br>
— Function: int <b>gsl_blas_ctrsv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_complex_float * A, gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fctrsv-1212"></a></var><br>
— Function: int <b>gsl_blas_ztrsv</b> (<var>CBLAS_UPLO_t Uplo, CBLAS_TRANSPOSE_t TransA, CBLAS_DIAG_t Diag, const gsl_matrix_complex * A, gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fztrsv-1213"></a></var><br>
<blockquote><p><a name="index-TRSV_002c-Level_002d2-BLAS-1214"></a>These functions compute inv(op(A)) x for <var>x</var>, where
op(A) = A, A^T, A^H 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_ssymv</b> (<var>CBLAS_UPLO_t Uplo, float alpha, const gsl_matrix_float * A, const gsl_vector_float * x, float beta, gsl_vector_float * y</var>)<var><a name="index-gsl_005fblas_005fssymv-1215"></a></var><br>
— Function: int <b>gsl_blas_dsymv</b> (<var>CBLAS_UPLO_t Uplo, double alpha, const gsl_matrix * A, const gsl_vector * x, double beta, gsl_vector * y</var>)<var><a name="index-gsl_005fblas_005fdsymv-1216"></a></var><br>
<blockquote><p><a name="index-SYMV_002c-Level_002d2-BLAS-1217"></a>These functions compute the matrix-vector product and sum y =
\alpha A x + \beta y 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_chemv</b> (<var>CBLAS_UPLO_t Uplo, const gsl_complex_float alpha, const gsl_matrix_complex_float * A, const gsl_vector_complex_float * x, const gsl_complex_float beta, gsl_vector_complex_float * y</var>)<var><a name="index-gsl_005fblas_005fchemv-1218"></a></var><br>
— Function: int <b>gsl_blas_zhemv</b> (<var>CBLAS_UPLO_t Uplo, const gsl_complex alpha, const gsl_matrix_complex * A, const gsl_vector_complex * x, const gsl_complex beta, gsl_vector_complex * y</var>)<var><a name="index-gsl_005fblas_005fzhemv-1219"></a></var><br>
<blockquote><p><a name="index-HEMV_002c-Level_002d2-BLAS-1220"></a>These functions compute the matrix-vector product and sum y =
\alpha A x + \beta y 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_sger</b> (<var>float alpha, const gsl_vector_float * x, const gsl_vector_float * y, gsl_matrix_float * A</var>)<var><a name="index-gsl_005fblas_005fsger-1221"></a></var><br>
— Function: int <b>gsl_blas_dger</b> (<var>double alpha, const gsl_vector * x, const gsl_vector * y, gsl_matrix * A</var>)<var><a name="index-gsl_005fblas_005fdger-1222"></a></var><br>
— Function: int <b>gsl_blas_cgeru</b> (<var>const gsl_complex_float alpha, const gsl_vector_complex_float * x, const gsl_vector_complex_float * y, gsl_matrix_complex_float * A</var>)<var><a name="index-gsl_005fblas_005fcgeru-1223"></a></var><br>
— Function: int <b>gsl_blas_zgeru</b> (<var>const gsl_complex alpha, const gsl_vector_complex * x, const gsl_vector_complex * y, gsl_matrix_complex * A</var>)<var><a name="index-gsl_005fblas_005fzgeru-1224"></a></var><br>
<blockquote><p><a name="index-GER_002c-Level_002d2-BLAS-1225"></a><a name="index-GERU_002c-Level_002d2-BLAS-1226"></a>These functions compute the rank-1 update A = \alpha x y^T + A of
the matrix <var>A</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_cgerc</b> (<var>const gsl_complex_float alpha, const gsl_vector_complex_float * x, const gsl_vector_complex_float * y, gsl_matrix_complex_float * A</var>)<var><a name="index-gsl_005fblas_005fcgerc-1227"></a></var><br>
— Function: int <b>gsl_blas_zgerc</b> (<var>const gsl_complex alpha, const gsl_vector_complex * x, const gsl_vector_complex * y, gsl_matrix_complex * A</var>)<var><a name="index-gsl_005fblas_005fzgerc-1228"></a></var><br>
<blockquote><p><a name="index-GERC_002c-Level_002d2-BLAS-1229"></a>These functions compute the conjugate rank-1 update A = \alpha x
y^H + A of the matrix <var>A</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_ssyr</b> (<var>CBLAS_UPLO_t Uplo, float alpha, const gsl_vector_float * x, gsl_matrix_float * A</var>)<var><a name="index-gsl_005fblas_005fssyr-1230"></a></var><br>
— Function: int <b>gsl_blas_dsyr</b> (<var>CBLAS_UPLO_t Uplo, double alpha, const gsl_vector * x, gsl_matrix * A</var>)<var><a name="index-gsl_005fblas_005fdsyr-1231"></a></var><br>
<blockquote><p><a name="index-SYR_002c-Level_002d2-BLAS-1232"></a>These functions compute the symmetric rank-1 update A = \alpha x
x^T + A 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_cher</b> (<var>CBLAS_UPLO_t Uplo, float alpha, const gsl_vector_complex_float * x, gsl_matrix_complex_float * A</var>)<var><a name="index-gsl_005fblas_005fcher-1233"></a></var><br>
— Function: int <b>gsl_blas_zher</b> (<var>CBLAS_UPLO_t Uplo, double alpha, const gsl_vector_complex * x, gsl_matrix_complex * A</var>)<var><a name="index-gsl_005fblas_005fzher-1234"></a></var><br>
<blockquote><p><a name="index-HER_002c-Level_002d2-BLAS-1235"></a>These functions compute the hermitian rank-1 update A = \alpha x
x^H + A 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_ssyr2</b> (<var>CBLAS_UPLO_t Uplo, float alpha, const gsl_vector_float * x, const gsl_vector_float * y, gsl_matrix_float * A</var>)<var><a name="index-gsl_005fblas_005fssyr2-1236"></a></var><br>
— Function: int <b>gsl_blas_dsyr2</b> (<var>CBLAS_UPLO_t Uplo, double alpha, const gsl_vector * x, const gsl_vector * y, gsl_matrix * A</var>)<var><a name="index-gsl_005fblas_005fdsyr2-1237"></a></var><br>
<blockquote><p><a name="index-SYR2_002c-Level_002d2-BLAS-1238"></a>These functions compute the symmetric rank-2 update A = \alpha x
y^T + \alpha y x^T + A 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_cher2</b> (<var>CBLAS_UPLO_t Uplo, const gsl_complex_float alpha, const gsl_vector_complex_float * x, const gsl_vector_complex_float * y, gsl_matrix_complex_float * A</var>)<var><a name="index-gsl_005fblas_005fcher2-1239"></a></var><br>
— Function: int <b>gsl_blas_zher2</b> (<var>CBLAS_UPLO_t Uplo, const gsl_complex alpha, const gsl_vector_complex * x, const gsl_vector_complex * y, gsl_matrix_complex * A</var>)<var><a name="index-gsl_005fblas_005fzher2-1240"></a></var><br>
<blockquote><p><a name="index-HER2_002c-Level_002d2-BLAS-1241"></a>These functions compute the hermitian rank-2 update A = \alpha x
y^H + \alpha^* y x^H + A 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></blockquote></div>
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