.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_getrs: getrs ===== Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides. .. container:: section .. rubric:: Description getrs supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double * - std::complex * - std::complex The routine solves for :math:X the following systems of linear equations: .. list-table:: :header-rows: 1 * - \ :math:AX = B\ - if trans\ =\ oneapi::mkl::transpose::nontrans\ * - \ :math:A^TX = B\ - if trans\ =\ oneapi::mkl::transpose::trans\ * - \ :math:A^HX = B\ - if trans\ =\ oneapi::mkl::transpose::conjtrans\ Before calling this routine, you must call :ref:onemkl_lapack_getrf to compute the LU factorization of :math:A. getrs (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void getrs(sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, sycl::buffer &a, std::int64_t lda, sycl::buffer &ipiv, sycl::buffer &b, std::int64_t ldb, sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. trans Indicates the form of the equations: If trans=oneapi::mkl::transpose::nontrans, then :math:AX = B is solved for :math:X. If trans=oneapi::mkl::transpose::trans, then :math:A^TX = B is solved for :math:X. If trans=oneapi::mkl::transpose::conjtrans, then :math:A^HX = B is solved for :math:X. n The order of the matrix :math:A and the number of rows in matrix :math:B(0 \le n). nrhs The number of right-hand sides (:math:0 \le \text{nrhs}). a Buffer containing the factorization of the matrix :math:A, as returned by :ref:onemkl_lapack_getrf. The second dimension of a must be at least :math:\max(1, n). lda The leading dimension of a. ipiv Array, size at least :math:\max(1, n). The ipiv array, as returned by :ref:onemkl_lapack_getrf. b The array b contains the matrix :math:B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least :math:\max(1,\text{nrhs}). ldb The leading dimension of b. scratchpad_size Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by :ref:onemkl_lapack_getrs_scratchpad_size function. .. container:: section .. rubric:: Output Parameters b The buffer b is overwritten by the solution matrix :math:X. scratchpad Buffer holding scratchpad memory to be used by routine for storing intermediate results. getrs (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { sycl::event getrs(sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t *ipiv, T *b, std::int64_t ldb, T *scratchpad, std::int64_t scratchpad_size, const std::vector &events = {}) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. trans Indicates the form of the equations: If trans=oneapi::mkl::transpose::nontrans, then :math:AX = B is solved for :math:X. If trans=oneapi::mkl::transpose::trans, then :math:A^TX = B is solved for :math:X. If trans=oneapi::mkl::transpose::conjtrans, then :math:A^HX = B is solved for :math:X. n The order of the matrix :math:A and the number of rows in matrix :math:B(0 \le n). nrhs The number of right-hand sides (:math:0 \le \text{nrhs}). a Pointer to array containing the factorization of the matrix :math:A, as returned by :ref:onemkl_lapack_getrf. The second dimension of a must be at least :math:\max(1, n). lda The leading dimension of a. ipiv Array, size at least :math:\max(1, n). The ipiv array, as returned by :ref:onemkl_lapack_getrf. b The array b contains the matrix :math:B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least :math:\max(1,\text{nrhs}). ldb The leading dimension of b. scratchpad_size Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by :ref:onemkl_lapack_getrs_scratchpad_size function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters b The array b is overwritten by the solution matrix :math:X. scratchpad Pointer to scratchpad memory to be used by routine for storing intermediate results. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:onemkl_lapack-linear-equation-routines