.. _onemkl_blas_hpr: hpr === Computes a rank-1 update of a Hermitian packed matrix. .. _onemkl_blas_hpr_description: .. rubric:: Description The ``hpr`` routines compute a scalar-vector-vector product and add the result to a Hermitian packed matrix. The operation is defined as .. math:: A \leftarrow alpha*x*x^H + A where: ``alpha`` is scalar, ``A`` is an ``n``-by-``n`` Hermitian matrix, supplied in packed form, ``x`` is a vector of length ``n``. ``hpr`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``std::complex`` * - ``std::complex`` .. _onemkl_blas_hpr_buffer: hpr (Buffer Version) -------------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { void hpr(sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T alpha, sycl::buffer &x, std::int64_t incx, sycl::buffer &a) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { void hpr(sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T alpha, sycl::buffer &x, std::int64_t incx, sycl::buffer &a) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. upper_lower Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. n Number of rows and columns of ``A``. Must be at least zero. alpha Scaling factor for the matrix-vector product. x Buffer holding input vector ``x``. The buffer must be of size at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details. incx Stride of vector ``x``. a Buffer holding input matrix ``A``. Must have size at least (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for more details. The imaginary part of the diagonal elements need not be set and are assumed to be zero. .. container:: section .. rubric:: Output Parameters a Buffer holding the updated upper triangular part of the Hermitian matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower triangular part of the Hermitian matrix ``A`` if ``upper_lower``\ \=\ ``lower``. The imaginary parts of the diagonal elements are set to zero. .. _onemkl_blas_hpr_usm: hpr (USM Version) ----------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { sycl::event hpr(sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T alpha, const T *x, std::int64_t incx, T *a, const std::vector &dependencies = {}) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { sycl::event hpr(sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T alpha, const T *x, std::int64_t incx, T *a, const std::vector &dependencies = {}) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. upper_lower Specifies whether ``A`` is upper or lower triangular. See :ref:`onemkl_datatypes` for more details. n Number of rows and columns of ``A``. Must be at least zero. alpha Scaling factor for the matrix-vector product. x Pointer to input vector ``x``. The array holding input vector ``x`` must be of size at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details. incx Stride of vector ``x``. a Pointer to input matrix ``A``. The array holding input matrix ``A`` must have size at least (``n``\ \*(``n``-1))/2. See :ref:`matrix-storage` for more details. The imaginary part 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. .. container:: section .. rubric:: Output Parameters a Pointer to the updated upper triangular part of the Hermitian matrix ``A`` if ``upper_lower``\ \=\ ``upper``, or the updated lower triangular part of the Hermitian matrix ``A`` if ``upper_lower``\ \=\ ``lower``. The imaginary parts of the diagonal elements are set to zero. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:`blas-level-2-routines`