.. _onemkl_blas_hpr2:

hpr2
====

Performs a rank-2 update of a hermitian packed matrix.

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

The ``hpr2`` routines compute two scalar-vector-vector products and add
them to a hermitian packed matrix. The operation is defined as:

.. math::

      A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A

where:

- ``alpha`` is a scalar

- ``A`` is ``n`` x ``n`` hermitian matrix, supplied in packed form

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

``hpr2`` supports the following precisions:

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

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


hpr2 (Buffer Version)
*********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       void hpr2(sycl::queue &queue,
                 oneapi::mkl::uplo upper_lower,
                 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)
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       void hpr2(sycl::queue &queue,
                 oneapi::mkl::uplo upper_lower,
                 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)
   }

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

queue
   The queue where the routine should be executed.

upper_lower
   Specifies whether matrix ``A`` is upper or lower triangular. See :ref:`data-types` for more details.

n
   Number of rows and 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 + (``n`` - 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
   (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for more details.

   The imaginary parts of the diagonal elements need not be set and
   are assumed to be zero.

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

a
   Buffer holding updated upper triangular part of the hermitian
   matrix ``A`` if ``upper_lower=upper``, or updated lower
   triangular part of the hermitian matrix ``A`` if
   ``upper_lower=lower``.

   The imaginary parts of the diagonal elements are set to zero.


hpr2 (USM Version)
******************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       sycl::event hpr2(sycl::queue &queue,
                        oneapi::mkl::uplo upper_lower,
                        std::int64_t n,
                        T alpha,
                        const T *x,
                        std::int64_t incx,
                        const T *y,
                        std::int64_t incy,
                        T *a,
                        const std::vector<sycl::event> &dependencies = {})
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       sycl::event hpr2(sycl::queue &queue,
                        oneapi::mkl::uplo upper_lower,
                        std::int64_t n,
                        T alpha,
                        const T *x,
                        std::int64_t incx,
                        const T *y,
                        std::int64_t incy,
                        T *a,
                        const std::vector<sycl::event> &dependencies = {})
   }

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

queue
   The queue where the routine should be executed.

upper_lower
   Specifies whether matrix ``A`` is upper or lower triangular. See :ref:`data-types` for more details.

n
   Number of rows and 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 + (``n`` - 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 holding input matrix
   ``A`` must be at least (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for more details.

   The imaginary parts of the diagonal elements need not be set and
   are assumed to be zero.

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

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

a
   Pointer to updated upper triangular part of the hermitian
   matrix ``A`` if ``upper_lower=upper``, or updated lower
   triangular part of the hermitian matrix ``A`` if
   ``upper_lower=lower``.

   The imaginary parts of the diagonal elements are set to zero.

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

Output event to wait on to ensure computation is complete.