.. _onemkl_blas_geru:

geru
====

Computes a rank-1 update (unconjugated) of a general complex matrix.

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

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

.. math::

      A \leftarrow alpha*x*y^T + A

where:

- ``alpha`` is a scalar

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

- ``x`` is a vector of length ``m``

- ``y`` is a vector of length ``n``

``geru`` supports the following precisions:

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

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


geru (Buffer Version)
*********************

Syntax
------

.. code-block:: cpp

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

.. code-block:: cpp

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

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

queue
   The queue where the routine should be executed.

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.

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

incx
   Stride of vector ``x``.

y
   Buffer holding input/output 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``.

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.

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.

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

a
   Buffer holding updated matrix ``A``.


geru (USM Version)
******************

Syntax
------

.. code-block:: cpp

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

.. code-block:: cpp

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

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

queue
   The queue where the routine should be executed.

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.

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

incx
   Stride of vector ``x``.

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

incy
   Stride of vector ``y``.

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.

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

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

a
   Pointer to updated matrix ``A``.

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

Output event to wait on to ensure computation is complete.