.. 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(cl::sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &ipiv, cl::sycl::buffer &b, std::int64_t ldb, cl::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. .. 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::host_bad_alloc :ref:oneapi::mkl::device_bad_alloc :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument :ref:oneapi::mkl::lapack::computation_error Exception is thrown in case of problems during calculations. The info code of the problem can be obtained by info() method of exception object: If info=-i, the :math:i-th parameter had an illegal value. If info=i, the :math:i-th diagonal element of :math:U is zero, and the solve could not be completed. If info equals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object. getrs (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event getrs(cl::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:: 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::host_bad_alloc :ref:oneapi::mkl::device_bad_alloc :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument :ref:oneapi::mkl::lapack::computation_error Exception is thrown in case of problems during calculations. The info code of the problem can be obtained by info() method of exception object: If info=-i, the :math:i-th parameter had an illegal value. If info=i, the :math:i-th diagonal element of :math:U is zero, and the solve could not be completed. If info equals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:onemkl_lapack-linear-equation-routines