.. _onemkl_blas_tbsv: tbsv ==== Solves a system of linear equations whose coefficients are in a triangular band matrix. .. _onemkl_blas_tbsv_description: .. rubric:: Description The ``tbsv`` routines solve a system of linear equations whose coefficients are in a triangular band matrix. The operation is defined as: .. math:: op(A)*x = b where: op(``A``) is one of op(``A``) = ``A``, or op(``A``) = ``A``\ :sup:`T`, or op(``A``) = ``A``\ :sup:`H`, ``A`` is an ``n``-by-``n`` unit or non-unit, upper or lower triangular band matrix, with (``k`` + 1) diagonals, ``b`` and ``x`` are vectors of length ``n``. ``tbsv`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` * - ``std::complex`` * - ``std::complex`` .. _onemkl_blas_tbsv_buffer: tbsv (Buffer Version) --------------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { void tbsv(sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose trans, onemkl::diag unit_nonunit, std::int64_t n, std::int64_t k, sycl::buffer &a, std::int64_t lda, sycl::buffer &x, std::int64_t incx) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { void tbsv(sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose trans, onemkl::diag unit_nonunit, std::int64_t n, std::int64_t k, sycl::buffer &a, std::int64_t lda, sycl::buffer &x, std::int64_t incx) } .. 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. trans Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. unit_nonunit Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. n Number of rows and columns of ``A``. Must be at least zero. k Number of sub/super-diagonals of the matrix ``A``. Must be at least zero. a Buffer holding input matrix ``A``. Must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for more details. lda Leading dimension of matrix ``A``. Must be at least (``k`` + 1), and positive. 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``. .. container:: section .. rubric:: Output Parameters x Buffer holding the solution vector ``x``. .. _onemkl_blas_tbsv_usm: tbsv (USM Version) ------------------ .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { sycl::event tbsv(sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose trans, onemkl::diag unit_nonunit, std::int64_t n, std::int64_t k, const T *a, std::int64_t lda, T *x, std::int64_t incx, const std::vector &dependencies = {}) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { sycl::event tbsv(sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose trans, onemkl::diag unit_nonunit, std::int64_t n, std::int64_t k, const T *a, std::int64_t lda, T *x, std::int64_t incx, 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. trans Specifies op(``A``), the transposition operation applied to ``A``. See :ref:`onemkl_datatypes` for more details. unit_nonunit Specifies whether the matrix ``A`` is unit triangular or not. See :ref:`onemkl_datatypes` for more details. n Number of rows and columns of ``A``. Must be at least zero. k Number of sub/super-diagonals of the matrix ``A``. Must be at least zero. a Pointer to input matrix ``A``. The array holding input matrix ``A`` must have size at least ``lda``\ \*\ ``n``. See :ref:`matrix-storage` for more details. lda Leading dimension of matrix ``A``. Must be at least (``k`` + 1), and positive. 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``. dependencies List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies. .. container:: section .. rubric:: Output Parameters x Pointer to the solution vector ``x``. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:`blas-level-2-routines`