.. _onemkl_blas_axpy:

axpy
====

Computes a vector-scalar product and adds the result to a vector.

Description
***********

The ``axpy`` routines compute a scalar-vector product and add the result
to a vector. The operation is defined as:

.. math::

      y \leftarrow alpha*x+y

where:

- ``x`` and ``y`` are vectors of ``n`` elements

- ``alpha`` is a scalar

``axpy`` supports the following precisions:

.. list-table::
   :header-rows: 1

   * -  T
   * -  ``float``
   * -  ``double``
   * -  ``std::complex<float>``
   * -  ``std::complex<double>``


axpy (Buffer Version)
*********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       void axpy(sycl::queue &queue,
                 std::int64_t n,
                 T alpha,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 sycl::buffer<T,1> &y,
                 std::int64_t incy)
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       void axpy(sycl::queue &queue,
                 std::int64_t n,
                 T alpha,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 sycl::buffer<T,1> &y,
                 std::int64_t incy)
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

alpha
   Specifies scalar ``alpha``.

x
   Buffer holding input vector ``x``. Size of the buffer must be at least  (1 + (``n`` – 1)*abs(``incx``)). See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

y
   Buffer holding input vector ``y``. Size of the buffer must be at least (1 + (``n`` – 1)*abs(``incy``)). See :ref:`matrix-storage` for more details.

incy
   Stride of vector ``y``.

Output Parameters
-----------------

y
   Buffer holding updated vector ``y``.

Examples
********

An example of how to use ``axpy`` can be found in the |O-MKL|
installation directory, under:

.. code-block::

   examples/dpcpp/blas/source/axpy.cpp

axpy (USM Version)
******************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       sycl::event axpy(sycl::queue &queue,
                        std::int64_t n,
                        T alpha,
                        const T *x,
                        std::int64_t incx,
                        T *y,
                        std::int64_t incy,
                        const std::vector<sycl::event> &dependencies = {})
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       sycl::event axpy(sycl::queue &queue,
                        std::int64_t n,
                        T alpha,
                        const T *x,
                        std::int64_t incx,
                        T *y,
                        std::int64_t incy,
                        const std::vector<sycl::event> &dependencies = {})
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

alpha
   Specifies scalar ``alpha``.

x
   Pointer to input vector ``x``. Size of the array holding vector ``x``
   must be at least (1 + (``n`` – 1)*abs(``incx``)). See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

y
   Pointer to input vector ``y``. Size of the array holding vector ``y``
   must be at least (1 + (``n`` – 1)*abs(``incy``)). See :ref:`matrix-storage` for more details.

incy
   Stride of vector ``y``.

dependencies
   List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters
-----------------

y
   Pointer to updated vector ``y``.

Return Values
-------------

Output event to wait on to ensure computation is complete.