==================
BLAS Level 1: axpy                                                       [TOC]
==================

*axpy* (defined in namespace `flens::blas`) computes $y \leftarrow y +\alpha x$
where $x, y$ are vectors and $\alpha$ is a constant scalar. *axpy* is short
for *a*lpha times *x* *p*lus *y*.

We also provide a variant that does the computation for matrices instead of
vectors.


Vector Variant
==============
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename VX, typename VY>                      |
|      typename RestrictTo<IsDenseVector<VX>::value                         |
|                       && IsDenseVector<VY>::value,                        |
|               void>::Type                                                 |
|      axpy(const ALPHA &alpha, const VX &x, VY &&y);                       |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#&1t0.0#&1t0.1#&t]
                         [0.2#templatetypenameALPHA,typenameVX,typenameVYtyp]
                         [enameRestrictToIsDenseVectorVXvalueandIsDenseVecto]
                         [rVYvalue,voidType                                 ]

    alpha    `(input) real scalar`                                             +
             Scaling factor for the values in $x$.
    x        `(input) real or complex valued DenseVector`                      +
             Vector $x$.
    y        `(input/output) real or complex valued DenseVector`               +
             Vector $y$.


Matrix Variant (Level 1 Extension)
==================================
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsGeMatrix<MA>::value                            |
|                       && IsGeMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsGeMatrixM]
                         [AvalueandIsGeMatrixMBvalue,voidType               ]

    trans    `(input)`                                                         +
             Specifiy the operation, i.e.
              NoTrans      $B \leftarrow B + \alpha\, A$
              Trans        $B \leftarrow B + \alpha\, A^T$
              ConjTrans    $B \leftarrow B + \alpha\, A^H$
    alpha    `(input) real scalar`                                             +
             Scaling factor for the values in $x$.
    A        `(input) real or complex valued GeMatrix`                         +
             Matrix $A$.
    B        `(input/output) real or complex valued GeMatrix`                  +
             Matrix $B$.

################################################################################
#
#  The following CODEREFs are automatically created stubs.
#
################################################################################


*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename VX, typename VY>                      |
|      typename RestrictTo<IsTinyVector<VX>::value                          |
|                       && IsTinyVector<VY>::value,                         |
|               void>::Type                                                 |
|      axpy(const ALPHA &alpha, const VX &x, VY &&y);                       |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#&1t0.0#&1t0.1#&t]
                         [0.2#templatetypenameALPHA,typenameVX,typenameVYtyp]
                         [enameRestrictToIsTinyVectorVXvalueandIsTinyVectorV]
                         [Yvalue,voidType                                   ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsGbMatrix<MA>::value                            |
|                       && IsGbMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsGbMatrixM]
                         [AvalueandIsGbMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsGeTinyMatrix<MA>::value                        |
|                       && IsGeTinyMatrix<MB>::value,                       |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsGeTinyMat]
                         [rixMAvalueandIsGeTinyMatrixMBvalue,voidType       ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsHbMatrix<MA>::value                            |
|                       && IsHbMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsHbMatrixM]
                         [AvalueandIsHbMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsHpMatrix<MA>::value                            |
|                       && IsHpMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsHpMatrixM]
                         [AvalueandIsHpMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsSbMatrix<MA>::value                            |
|                       && IsSbMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsSbMatrixM]
                         [AvalueandIsSbMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsSpMatrix<MA>::value                            |
|                       && IsSpMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsSpMatrixM]
                         [AvalueandIsSpMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsTbMatrix<MA>::value                            |
|                       && IsTbMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsTbMatrixM]
                         [AvalueandIsTbMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsTpMatrix<MA>::value                            |
|                       && IsTpMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Taxpy#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&t0.2#templatetypenameALPHA,]
                         [typenameMA,typenameMBtypenameRestrictToIsTpMatrixM]
                         [AvalueandIsTpMatrixMBvalue,voidType               ]

    Defined in namespace `flens::blas`.
    Function `axpy` with 3 template parameters.