.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_blas_tpsv: tpsv ==== Solves a system of linear equations whose coefficients are in a triangular packed matrix. .. _onemkl_blas_tpsv_description: .. rubric:: Description The ``tpsv`` routines solve a system of linear equations whose coefficients are in a triangular packed 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, supplied in packed form, ``b`` and ``x`` are vectors of length ``n``. ``tpsv`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` * - ``std::complex`` * - ``std::complex`` .. _onemkl_blas_tpsv_buffer: tpsv (Buffer Version) --------------------- .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { void tpsv(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, sycl::buffer &x, std::int64_t incx) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { void tpsv(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, 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 Numbers of rows and columns of ``A``. Must be at least zero. a Buffer holding input matrix ``A``. Must have size at least (``n``\ \*(``n``\ +1))/2. See :ref:`matrix-storage` for more details. x Buffer holding the ``n``-element right-hand side vector ``b``. 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``. .. container:: section .. rubric:: Throws This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here. :ref:`oneapi::mkl::invalid_argument` :ref:`oneapi::mkl::unsupported_device` :ref:`oneapi::mkl::host_bad_alloc` :ref:`oneapi::mkl::device_bad_alloc` :ref:`oneapi::mkl::unimplemented` .. _onemkl_blas_tpsv_usm: tpsv (USM Version) ------------------ .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::blas::column_major { sycl::event tpsv(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, T *x, std::int64_t incx, const std::vector &dependencies = {}) } .. code-block:: cpp namespace oneapi::mkl::blas::row_major { sycl::event tpsv(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, 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 Numbers of rows and columns of ``A``. Must be at least zero. 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. x Pointer to the ``n``-element right-hand side vector ``b``. The array holding the ``n``-element right-hand side vector ``b`` 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. .. container:: section .. rubric:: Throws This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here. :ref:`oneapi::mkl::invalid_argument` :ref:`oneapi::mkl::unsupported_device` :ref:`oneapi::mkl::host_bad_alloc` :ref:`oneapi::mkl::device_bad_alloc` :ref:`oneapi::mkl::unimplemented` **Parent topic:** :ref:`blas-level-2-routines`