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

*axpy* (defined in namespace `cxxblas`) computes $y \leftarrow y +\alpha x$
where $x, y$ are vectors and $\alpha$ is a constant scalar.


Generic Implementation
======================
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename IndexType, typename ALPHA, typename X, typename Y>    |
|      void                                                                 |
|      axpy(IndexType n, const ALPHA &alpha, const X *x, IndexType incX,    |
|           Y *y, IndexType incY);                                          |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@cxxblas@FT@>4#T#T#T#Taxpy#t0.0#&1t0.1#*1t0.2#]
                         [S0_#*t0.3#S0_#templatetypenameIndexType,typenameAL]
                         [PHA,typenameX,typenameYvoid                       ]

    n         `(input)`                                                        +
              Specifies the number of elements in vector $x$ and $y$.
    alpha     `(input)`                                                        +
              Scaling factor for the values in $x$.
    x         `(input)`                                                        +
              Pointer to the first element of vector $x$.
    incX      `(input)`                                                        +
              Specifies the increment for indexing vector $x$.
    y         `(input/output)`                                                 +
              Pointer to the first element of vector $y$.
    incY      `(input)`                                                        +
              Specifies the increment for indexing vector $y$.


CBLAS Implementation
====================
If a __CBLAS__ implementations like __ATLAS__, __GotoBLAS__, ... is available
then the following *optimized variants* are provided.


Single Precision
----------------
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename IndexType>                                            |
|      typename If<IndexType>::isBlasCompatibleInteger                      |
|      axpy(IndexType n, const float &alpha,                                |
|           const float *x, IndexType incX,                                 |
|           float *y, IndexType incY);                                      |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@cxxblas@FT@>1#Taxpy#t0.0#&1f#*1f#S0_#*f#S0_#t]
                         [emplatetypenameIndexTypetypenameIfIndexTypeisBlasC]
                         [ompatibleInteger                                  ]



Double Precision
----------------
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename IndexType>                                            |
|      typename If<IndexType>::isBlasCompatibleInteger                      |
|      axpy(IndexType n, const double &alpha,                               |
|           const double *x, IndexType incX,                                |
|           double *y, IndexType incY);                                     |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@cxxblas@FT@>1#Taxpy#t0.0#&1d#*1d#S0_#*d#S0_#t]
                         [emplatetypenameIndexTypetypenameIfIndexTypeisBlasC]
                         [ompatibleInteger                                  ]


Complex Single Precision
------------------------
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename IndexType>                                            |
|      typename If<IndexType>::isBlasCompatibleInteger                      |
|      axpy(IndexType n, const ComplexFloat &alpha,                         |
|           const ComplexFloat *x, IndexType incX,                          |
|           ComplexFloat *y, IndexType incY);                               |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@cxxblas@FT@>1#Taxpy#t0.0#&1$@N@std@N@__1@C@co]
                         [mplex>#f#*1S2_#S0_#*S2_#S0_#templatetypenameIndexT]
                         [ypetypenameIfIndexTypeisBlasCompatibleInteger     ]


Complex Double Precision
------------------------
*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename IndexType>                                            |
|      typename If<IndexType>::isBlasCompatibleInteger                      |
|      axpy(IndexType n, const ComplexDouble &alpha,                        |
|           const ComplexDouble *x, IndexType incX,                         |
|           ComplexDouble *y, IndexType incY);                              |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@cxxblas@FT@>1#Taxpy#t0.0#&1$@N@std@N@__1@C@co]
                         [mplex>#d#*1S2_#S0_#*S2_#S0_#templatetypenameIndexT]
                         [ypetypenameIfIndexTypeisBlasCompatibleInteger     ]

:links: __CBLAS__    -> http://www.netlib.org/blas/
        __ATLAS__    -> http://math-atlas.sourceforge.net
        __GotoBLAS__ -> http://www.tacc.utexas.edu/tacc-projects/gotoblas2