.. _onemkl_blas_gemv:

gemv
====

Computes a matrix-vector product using a general matrix.

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

The ``gemv`` routines compute a scalar-matrix-vector product and add the result to a scalar-vector product, with a general matrix. 
The operation is defined as:

.. math::

      y  \leftarrow alpha*op(A)*x + beta*y

where:

- op(``A``) is one of op(``A``) = ``A``, or op(``A``) = ``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`

- ``alpha`` and ``beta`` are scalars

- ``A`` is ``m`` x ``n`` matrix

- ``x`` and ``y`` are vectors

``gemv`` supports the following precisions:

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

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


gemv (Buffer Version)
*********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       void gemv(sycl::queue &queue,
                 oneapi::mkl::transpose trans,
                 std::int64_t m,
                 std::int64_t n,
                 T alpha,
                 sycl::buffer<T,1> &a,
                 std::int64_t lda,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 T beta,
                 sycl::buffer<T,1> &y,
                 std::int64_t incy)
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       void gemv(sycl::queue &queue,
                 oneapi::mkl::transpose trans,
                 std::int64_t m,
                 std::int64_t n,
                 T alpha,
                 sycl::buffer<T,1> &a,
                 std::int64_t lda,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 T beta,
                 sycl::buffer<T,1> &y,
                 std::int64_t incy)
   }

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

queue
   The queue where the routine should be executed.

trans
   Specifies op(``A``), the transposition operation applied to matrix ``A``. See :ref:`data-types` for more details.

m
   Number of rows of matrix ``A``. Must be at least zero.

n
   Number of columns of matrix ``A``. Must be at least zero.

alpha
   Scaling factor for the matrix-vector product.

a
   Buffer holding input matrix ``A``. Size of the buffer must be 
   at least ``lda`` * ``n`` if column major layout is used, or 
   at least ``lda`` * ``m`` if row major layout is used. See :ref:`matrix-storage` for more details.

lda
   Leading dimension of matrix ``A``. Must be positive and at least ``m`` if column major layout is used or at least ``n`` if row major layout is used.

x
   Buffer holding input vector ``x``. The length ``len`` of vector ``x`` is ``n`` if ``A`` 
   is not transposed, and ``m`` if ``A`` is transposed. Size of the buffer must be 
   at least (1 + (``len`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

beta
   The scaling factor for vector ``y``.

y
   Buffer holding input/output vector ``y``. The length ``len`` of vector ``y`` 
   is ``m``, if ``A`` is not transposed, and ``n`` if ``A`` is transposed. 
   Size of the buffer must be at least (1 + (``len`` - 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 ``gemv`` can be found in the |O-MKL| installation directory, under:

.. code-block::

   examples/dpcpp/blas/source/gemv.cpp


gemv (USM Version)
******************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       sycl::event gemv(sycl::queue &queue,
                        oneapi::mkl::transpose trans,
                        std::int64_t m,
                        std::int64_t n,
                        T alpha,
                        const T *a,
                        std::int64_t lda,
                        const T *x,
                        std::int64_t incx,
                        T beta,
                        T *y,
                        std::int64_t incy,
                        const std::vector<sycl::event> &dependencies = {})
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       sycl::event gemv(sycl::queue &queue,
                        oneapi::mkl::transpose trans,
                        std::int64_t m,
                        std::int64_t n,
                        T alpha,
                        const T *a,
                        std::int64_t lda,
                        const T *x,
                        std::int64_t incx,
                        T beta,
                        T *y,
                        std::int64_t incy,
                        const std::vector<sycl::event> &dependencies = {})
   }

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

queue
   The queue where the routine should be executed.

trans
   Specifies op(``A``), the transposition operation applied to matrix ``A``. See :ref:`data-types` for more details.

m
   Number of rows of matrix ``A``. Must be at least zero.

n
   Number of columns of matrix ``A``. Must be at least zero.

alpha
   Scaling factor for the matrix-vector product.

a
   Pointer to input matrix ``A``. Size of the array must be at least ``lda`` * ``n`` if column major layout is used, or at least ``lda`` * ``m`` if row major layout is used.

lda
   Leading dimension of matrix ``A``. Must be positive and at least ``m`` if column major layout is used or at least ``n`` if row major layout is used.

x
   Pointer to the input vector ``x``. The length ``len`` of vector ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` is transposed. Size of the array holding vector ``x`` must be at least (1 + (``len`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

beta
   Scaling factor for vector ``y``.

y
   Pointer to input/output vector ``y``. The length ``len`` of vector ``y`` is ``m``, if ``A`` is not transposed, and ``n`` if ``A`` is transposed. Size of the array holding input/output vector ``y`` must be at least (1 + (``len`` - 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.