KokkosBlas::axpy
################

Defined in header: :code:`KokkosBlas1_axpby.hpp`

.. code:: c++

  template <class execution_space, class AV, class XMV, class YMV>
  void axpy(const execution_space& space, const AV& a, const XMV& X, const YMV& Y)

  template <class AV, class XMV, class YMV>
  void axpy(const AV& a, const XMV& X, const YMV& Y)

Add entries of :code:`X` scaled by coefficient :code:`a` to entries of :code:`Y`: ``Y += a*X``

1. iterate over the entries of ``Y`` and add the corresponding entries of ``X`` scaled by ``a`` using the resources of ``space``
2. iterate over the entries of ``Y`` and add the corresponding entries of ``X`` scaled by ``a`` using the resources of the default instance of ``typename XMV::execution_space``

``a`` may each be any of the following:
  - a scalar value
  - a rank-0 host-accessible ``Kokkos::View``
  - a rank-0 device-accessible ``Kokkos::View``
  - a rank-1 device-accessible ``Kokkos::View`` with extent 1 (the coefficient will be applied to all columns)
  - a rank-1 device-accessible ``Kokkos::View`` with extent ``Y.extent(1)`` (one coefficient per column)

The function will throw a runtime exception if any of the following conditions are **not** met:
  - ``Y.extent(0) == X.extent(0) && Y.extent(1) == X.extent(1)``

If ``a`` is a rank-1 ``View``:
  - ``a.extent(0) != 1 && a.extent(0) != X.extent(1)``

Parameters
==========

:space: execution space instance

:a: scaling factor

:X, Y: vector(s) of input and output values respectively

Type Requirements
-----------------

- `execution_space` must be a Kokkos `execution space <https://kokkos.org/kokkos-core-wiki/API/core/execution_spaces.html>`_

- `XMV` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 1 or 2 that satisfies

  - ``Kokkos::SpaceAccessibility<execution_space, typename XMV::memory_space>::accessible == true``

- `YMV` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ that satisfies

  - ``YMV::rank == XMV::rank``
  - ``std::is_same_v<typename YMV::value_type, typename YMV::non_const_value_type> == true``
  - ``Kokkos::SpaceAccessibility<execution_space, typename YMV::memory_space>::accessible == true``

- `AV` must be a scalar or a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ that satisfies one of the following:

  - ``AV::rank == 0`` 
  - ``AV::rank == 1 && Kokkos::SpaceAccessibility<execution_space, typename YMV::memory_space>::accessible``

Example
=======

.. literalinclude:: ../../../../example/wiki/blas/KokkosBlas1_wiki_axpy.cpp
  :language: c++

output:

.. code::

  Sum: 65, Expected: 65, Diff: 0