.. _onemkl_blas_gbmv: gbmv ==== Computes a matrix-vector product with a general band matrix. .. _onemkl_blas_gbmv_description: .. rubric:: Description The ``gbmv`` routines compute a scalar-matrix-vector product and add the result to a scalar-vector product, with a general band 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 an ``m``-by-``n`` matrix with ``kl`` sub-diagonals and ``ku`` super-diagonals, ``x`` and ``y`` are vectors. ``gbmv`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` * - ``std::complex`` * - ``std::complex`` .. _onemkl_blas_gbmv_buffer: gbmv (Buffer Version) --------------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { void gbmv(sycl::queue &queue, onemkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t kl, std::int64_t ku, T alpha, sycl::buffer &a, std::int64_t lda, sycl::buffer &x, std::int64_t incx, T beta, sycl::buffer &y, std::int64_t incy) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { void gbmv(sycl::queue &queue, onemkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t kl, std::int64_t ku, T alpha, sycl::buffer &a, std::int64_t lda, sycl::buffer &x, std::int64_t incx, T beta, sycl::buffer &y, std::int64_t incy) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. trans Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. m Number of rows of ``A``. Must be at least zero. n Number of columns of ``A``. Must be at least zero. kl Number of sub-diagonals of the matrix ``A``. Must be at least zero. ku Number of super-diagonals of the matrix ``A``. Must be at least zero. alpha Scaling factor for the matrix-vector product. a Buffer holding input matrix ``A``. Must have size 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 at least (``kl`` + ``ku`` + 1), and positive. 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. The buffer must be of size 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 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. The buffer must be of size at least (1 + (``len`` - 1)*abs(``incy``)) where ``len`` is this length. See :ref:`matrix-storage` for more details. incy Stride of vector ``y``. .. container:: section .. rubric:: Output Parameters y Buffer holding the updated vector ``y``. .. _onemkl_blas_gbmv_usm: gbmv (USM Version) ------------------ .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { sycl::event gbmv(sycl::queue &queue, onemkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t kl, std::int64_t ku, 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 &dependencies = {}) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { sycl::event gbmv(sycl::queue &queue, onemkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t kl, std::int64_t ku, 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 &dependencies = {}) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. trans Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. m Number of rows of ``A``. Must be at least zero. n Number of columns of ``A``. Must be at least zero. kl Number of sub-diagonals of the matrix ``A``. Must be at least zero. ku Number of super-diagonals of the matrix ``A``. Must be at least zero. alpha Scaling factor for the matrix-vector product. a Pointer to input matrix ``A``. The array holding input matrix ``A`` must have size 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 at least (``kl`` + ``ku`` + 1), and positive. x Pointer to input vector ``x``. The length ``len`` of vector ``x`` is ``n`` if ``A`` is not transposed, and ``m`` if ``A`` is transposed. The array holding input vector ``x`` must be of size 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. The array holding input/output vector ``y`` must be of size at least (1 + (``len`` - 1)*abs(``incy``)) where ``len`` is this length. 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. .. container:: section .. rubric:: Output Parameters y Pointer to the updated vector ``y``. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:`blas-level-2-routines`